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PERFORMANCE EVALUATION OF TRANSIT
ROUTES
*****************************************************
Khac Duong Tran
Bachelor of Road and Highway Engineering
Master of Automobile and Urban Road Engineering
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
School of Civil Engineering and Built Environment
Science and Engineering Faculty
Queensland University of Technology
2019
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Keywords
Transit System Performance/ Operation
Transit Route Performance/ Operation
Transit Performance Indicators
Technical Efficiency
Service Effectiveness
Operational Effectiveness
Efficiency Evaluation/ Measurement
Data Envelopment Analysis
Bootstrap Technique
Smartcard Data
Automatic Fare Collection
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Abstract
Transit agencies aim to allocate limited resources properly and maximise ridership.
Measuring the performance of individual transit routes within a transit system plays a critical
role in identifying operational issues and increasing transit ridership. However, evaluating the
performance of a transit route is a complex procedure because multiple objectives and
multiple input and output variables exist. Transit agencies thus need an appropriate method
to evaluate the efficiency of the transit routes’ performance and identify the key factors
influencing overall efficiency. The Data Envelopment Analysis (DEA) approach has been
utilised widely for comparing the performance of different transit systems or different transit
routes as production units. However, due to the simple transit data collected through manual
survey, the application of DEA models for measuring the performance of transit routes is fairly
limited. Addressing the aforementioned needs, this study aims to develop a scientific and
practical framework to evaluate the spatial and temporal performance of individual transit
routes that compose a transit network, and investigate sources of inefficiency.
To achieve this research aim, four major objectives are raised including to (1) develop
a conceptual framework to measure the operational effectiveness of individual bus routes
within a bus network, (2) measure the temporal and spatial performance of several key bus
routes within a bus network using the proposed framework, (3) investigate the external
sources of inefficiency by using the truncated regression model, and (4) provide general
recommendations to transit agencies based on the research findings for performance
improvement of bus routes of the case study. A network DEA model is adopted for efficiency
analysis, and the double bootstrap model is selected for sensitivity analysis of DEA efficiency
scores obtained to external factors (demographic and socio-economic characteristics).
Smart-card data from Brisbane, Australia is used to extract relevant inputs and outputs for
DEA models, and the ArcGIS spatial information tool is employed to collect external factors
within the service areas of individual bus routes. Those sources of data provide the spatial
and temporal performance of individual transit routes in detail. Therefore, this research helps
to fill the gaps of preceding studies, which use monthly or annual data to evaluate the average
efficiency and effectiveness of transit routes.
Using detailed data to evaluate the spatial and temporal performance of transit routes
enables the transit agency to rank performance, and then identify both internal and external
sources of inefficiency (bus schedule, vehicle type, socioeconomic and demographic
characteristics etc.). Furthermore, the proposed approach will assist decision makers to
optimally allocate limited resources across their transit system. At the route level, this
approach allows the transit agencies to reallocate the resources across different components
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of a transit route appropriately (vehicle capacity, stops facility, bus lanes, bus frequency,
information systems etc.).
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Table of Contents
Keywords .................................................................................................................. ii
Abstract ................................................................................................................... iii
Table of Contents ..................................................................................................... v
List of Figures .......................................................................................................... ix
List of Tables .......................................................................................................... xii
List of Abbreviations................................................................................................ xv
Statement of Original Authorship .......................................................................... xvii
Acknowledgements .............................................................................................. xviii
1 Introduction ........................................................................................................ 1
Research Background ................................................................................ 1
Research Problem and Purpose ................................................................. 5
Research Aim ............................................................................................. 6
Research Hypothesis .................................................................................. 6
Research Questions ................................................................................... 7
Research Objectives ................................................................................... 7
Research Scope ......................................................................................... 7
Scientific and Practical Significance ............................................................ 8
Study Outline .............................................................................................. 8
Publications ........................................................................................... 10
2 Literature Review ............................................................................................. 11
Transit policy making ................................................................................ 11
The Performance Measurement of Bus System ........................................ 13
Application of DEA for Bus Performance Evaluation ................................. 15
2.3.1 Transit Performance Concepts ............................................................ 15
2.3.2 Technical Efficiency Assessment for Transit System Performance ...... 16
2.3.3 Two Dimensions Assessment for Transit System Performance ........... 17
2.3.4 Assessment for Transit Route Performance ........................................ 19
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2.3.5 Summary of findings ............................................................................. 20
Research Gaps ......................................................................................... 28
3 Methodology .................................................................................................... 29
Introduction ................................................................................................ 29
Efficiency Measurement Concepts ............................................................ 31
3.2.1 Production function............................................................................... 31
3.2.2 Input-Oriented Measure ....................................................................... 31
3.2.3 Output-Oriented Measure ..................................................................... 33
Data Envelopment Analysis (DEA) ............................................................ 33
3.3.1 CCR- DEA Model ................................................................................. 34
3.3.2 BCC-DEA model .................................................................................. 37
3.3.3 Network DEA model ............................................................................. 38
3.3.4 The need of using DEA model .............................................................. 42
Sensitivity analysis in DEA ........................................................................ 43
3.4.1 Sensitivity analysis of DEA efficiency scores ........................................ 43
3.4.2 The bootstrap approach ....................................................................... 44
Transit Productiveness Indexes ................................................................. 45
Discussion ................................................................................................. 46
4 Framework for Bus Route Performance Measurement ..................................... 48
Introduction ................................................................................................ 48
The Study Goals Needed To Be Achieved................................................. 48
Develop the Framework for Bus Route Performance Measurement .......... 49
Inputs and Outputs Selection for Bus Routes ............................................ 50
4.4.1 Some crucial recommendations for input and output variables selection,
and the combination of inputs and outputs in DEA ...................................................... 50
4.4.2 Selection of inputs and outputs ............................................................ 52
External Variables (EVs) Selection ............................................................ 56
Discussion ................................................................................................. 57
5 Data Collection ................................................................................................. 58
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Introduction ............................................................................................... 58
Internal Variables ...................................................................................... 58
External Variables..................................................................................... 62
Summary .................................................................................................. 66
6 Data Analysis for Individual Bus Route of the Case Study ............................... 68
Introduction ............................................................................................... 68
Data Analysis for Bus Route 111 .............................................................. 68
6.2.1 DEA-based performance evaluation of route 111 ................................ 69
6.2.2 Comparison between DEA efficiency score and basic transit
productiveness indexes .............................................................................................. 75
DEA-based Performance Analysis of Individual Routes ............................ 78
6.3.1 High frequency bus routes ................................................................... 79
6.3.2 Low frequency bus routes for long service period ................................ 82
6.3.3 Low frequency bus routes for short service period ............................... 86
Summary of Findings ................................................................................ 89
7 Empirical Analysis for Bus System in the Case Study ...................................... 91
Introduction ............................................................................................... 91
Efficiency Analysis of Key Bus Routes for Separate Node ........................ 91
Efficiency Analysis of Key Bus Routes Using Network model ................... 99
Ranking the Performance of 52 Bus Routes ........................................... 105
7.4.1 Technical efficiency measure for bus routes (Model 1) ...................... 106
7.4.2 Service effectiveness measure (Model 2) .......................................... 113
7.4.3 Network performance measurement .................................................. 119
Identification of External Sources of Inefficiency and Recommendations 126
Summary of Findings .............................................................................. 133
8 Conclusion and Recommendations................................................................ 135
Summary of Research Findings .............................................................. 135
Research Contributions .......................................................................... 139
Practical Implications .............................................................................. 141
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Limitations ............................................................................................... 143
Recommendation for Future Research .................................................... 144
References .......................................................................................................... 146
SPATIAL EFFICIENCY SCORES OF INDIVIDUAL BUS ROUTES
151
DISCUSSION ON SLACKS ........................................................ 158
EXAMPLES FOR DETAILED SAMPLE CALCULATION USING THE
DEA MODELS 159
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List of Figures
Figure 1-1: Multiple objectives related to transit stakeholders of a transit route
(Source: Sheth et al. (2007)) ............................................................................................... 2
Figure 1-2: Framework for a transit network performance concept model (adapted
from Fielding et al. (1985)) .................................................................................................. 3
Figure 1-3: Research outline .................................................................................... 9
Figure 3-1: The outlines of research methodology ................................................. 30
Figure 3-2: Input-oriented technical and allocative efficiencies (Source: Coelli,
Prasada Rao et al. (1998)) ................................................................................................ 32
Figure 3-3: Output-oriented technical and allocative efficiencies (Source: Coelli,
Prasada Rao et al. (1998) ................................................................................................. 33
Figure 3-4: Production frontier of (a) CCR and (b) BCC models ............................. 37
Figure 3-5: The aggregated technology (Source: Färe et al. (2000)) ...................... 39
Figure 3-6: The network technology (Source: Färe et al. (2000)) ........................... 40
Figure 4-1: Framework for a transit route performance evaluation ......................... 50
Figure 4-2: The operational framework for a bus route performance evaluation ..... 54
Figure 5-1: Brisbane, Australia high frequency bus network map (Source:
http://translink.com.au) ...................................................................................................... 59
Figure 5-2: Flowchart for extracting transit route performance indicators ............... 61
Figure 5-3: An example of a bus route service area ............................................... 63
Figure 5-4: An example of pieces of land (POL) within the service corridor of bus route
.......................................................................................................................................... 64
Figure 6-1: Bus route 111 map (Source: Google map) ........................................... 70
Figure 6-2: The DEA efficiency score of the case 1, 2, and 3 for inbound direction 72
Figure 6-3: The DEA efficiency score of the case 1, 2, and 3 for outbound direction
.......................................................................................................................................... 73
Figure 6-4: The CRS-DEA efficiency score of the inbound, outbound, and combined
directions ........................................................................................................................... 74
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Figure 6-5: The VRS-DEA efficiency score of the inbound, outbound, and combined
directions ............................................................................................................................ 74
Figure 6-6: Transit work load factor and Passenger transmission efficiency of 111. 77
Figure 6-7: Correlation of Transit work load factor and DEA efficiency scores in case
1 ......................................................................................................................................... 77
Figure 6-8: Correlation of Transit passenger transmission efficiency and DEA
efficiency scores in case 2.................................................................................................. 77
Figure 6-9: Correlation of Transit passenger transmission efficiency and DEA
efficiency scores in case 3.................................................................................................. 78
Figure 6-10: Correlation of Transit passenger transmission efficiency and DEA
efficiency scores in case 4.................................................................................................. 78
Figure 6-11: CRS-DEA efficiency score of route 100 (follows pattern 1) ................. 80
Figure 6-12: CRS-DEA efficiency score of route 333 (follows pattern 1) ................. 81
Figure 6-13: CRS-DEA efficiency score of route 140 (follows pattern 2) ................. 81
Figure 6-14: CRS-DEA efficiency score of route 444 (follows pattern 3) ................. 82
Figure 6-15: CRS-DEA efficiency score of route 200 (follows pattern 4) ................. 82
Figure 6-16: CRS-DEA efficiency score of route 124 .............................................. 83
Figure 6-17: CRS-DEA efficiency score of route 125 .............................................. 83
Figure 6-18: CRS-DEA efficiency score of route 185 (follows pattern 1) ................. 84
Figure 6-19: CRS-DEA efficiency score of route 230 (follows pattern 2) ................. 84
Figure 6-20: CRS-DEA efficiency score of route 170 (follows pattern 3) ................. 85
Figure 6-21: CRS-DEA efficiency score of route 220 (follows pattern 3) ................. 85
Figure 6-22: CRS-DEA efficiency score of route 335 (follows pattern 4) ................. 86
Figure 6-23: CRS-DEA efficiency score of route 135 (follows pattern 5) ................. 86
Figure 6-24: CRS-DEA efficiency score of route 113 .............................................. 87
Figure 6-25: CRS-DEA efficiency score of route 115 (follows pattern 6) ................. 87
Figure 6-26: CRS-DEA efficiency score of route 192 (follows pattern 3) ................. 88
Figure 6-27: CRS-DEA efficiency score of route 155 (follows pattern 5) ................. 88
Figure 7-1: The VRS-DEA efficiency score of bus routes in model 1 ...................... 93
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Figure 7-2: The VRS-DEA efficiency score of bus routes in model 2 ...................... 94
Figure 7-3: The network technology of bus route performance ............................ 100
Figure 7-4: DEA efficiency scores of network and separate nodes (the morning peak
hour) ................................................................................................................................ 101
Figure 7-5: Efficiency score of the network and aggregate model (the morning peak
hour) ................................................................................................................................ 105
Figure 7-6: Efficiency score variations of bus routes in model 1 for different periods of
time, following the gradual decrease of a day’s efficiency scores .................................... 112
Figure 7-7: Efficiency score variations of bus routes in model 2 for different periods of
time, following the gradual decrease of a day’s efficiency scores .................................... 118
Figure 7-8: Efficiency score variations of bus routes in network model for different
periods of time, following the gradual decrease of a day’s efficiency scores .................... 124
Figure 7-9: Efficiency score variations of bus routes in models 1 and 2 for a day
following the gradual decrease of model 2 efficiency scores............................................ 125
Figure 8-1: Policy implications of transit routes performance analysis .................. 142
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List of Tables
Table 2-1: Quality of service measures for fixed-route transit ................................. 14
Table 2-2: An overview of the application of DEA in measuring the transit performance
........................................................................................................................................... 24
Table 4-1: An overview of inputs and outputs selection for bus route performance
evaluation ........................................................................................................................... 51
Table 4-2: Selection of inputs and outputs for bus route performance measurement
........................................................................................................................................... 55
Table 5-1: Statistical description of the inputs and outputs of the 52 bus routes for a
morning and an afternoon peak hour, and an off-peak hour of 21 August 2013 .................. 62
Table 5-2: a) Statistical description; and b) Correlation analysis results of EVs of 52
bus routes of the case study in Brisbane, Australia ............................................................ 66
Table 6-1: Statistical description of the inputs and outputs of route 111 for inbound
direction ............................................................................................................................. 70
Table 6-2: Statistical description of the inputs and outputs of route 111 for outbound
direction ............................................................................................................................. 71
Table 6-3: Inputs and outputs using for DEA models in cases 1, 2, 3, and 4 ........... 71
Table 6-4: Efficiency scores and scale efficiency of route 111 (combined directions)
........................................................................................................................................... 75
Table 6-5: Typical patterns describing the changes of efficiency scores of bus routes
during a day ....................................................................................................................... 89
Table 7-1: The summary statistics of efficiency scores obtained through DEA for
models 1 and 2 ................................................................................................................... 92
Table 7-2: Inputs and outputs of a) route 175 and its benchmarks in model 1; and b)
route 220 and its benchmarks in model 2 during the morning peak hour ............................ 95
Table 7-3: Slacks for inefficient routes in model 1 during the morning peak hour .... 96
Table 7-4: Slacks for some inefficient routes in model 2 during the morning peak hour
........................................................................................................................................... 98
Table 7-5: Input slacks for the most inefficient routes in the NDEA model during the
morning peak hour ........................................................................................................... 102
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Table 7-6: Output slacks for the most inefficient routes in the NDEA model during the
morning peak hour .......................................................................................................... 102
Table 7-7: Efficiency analysis of routes 100 and 353 for the morning peak hour using
the NDEA model .............................................................................................................. 104
Table 7-8: Efficiency scores of 52 bus routes in model 1 from hour 7 to hour 13 .. 107
Table 7-9: Efficiency scores of 52 bus routes in model 1 from hour 14 to hour 19 108
Table 7-10: Efficiency scores of 52 bus routes in model 1 for different periods of time
and a day ........................................................................................................................ 109
Table 7-11: Ranking of 52 bus routes in model 1 for a day (21 Aug 2013) ........... 110
Table 7-12: Correlation analysis results of efficiency scores of different periods of time
........................................................................................................................................ 111
Table 7-13: Efficiency scores of 52 bus routes in model 2 from hour 7 to hour 13 114
Table 7-14: Efficiency scores of 52 bus routes in model 2 from hour 14 to hour 19
........................................................................................................................................ 115
Table 7-15: Efficiency scores of 52 bus routes in model 2 for different periods of time
and a day ........................................................................................................................ 116
Table 7-16: Ranking of 52 bus routes in model 2 for a working day (21 Aug 2013)
........................................................................................................................................ 117
Table 7-17: Correlation analysis results of efficiency scores of different periods of time
........................................................................................................................................ 118
Table 7-18: Network efficiency scores of 52 bus routes from hour 7 to hour 13 ... 120
Table 7-19: Network efficiency scores of 52 bus routes from hour 14 to hour 19 . 121
Table 7-20: Network efficiency scores of 52 bus routes for different periods of time
and a day ........................................................................................................................ 122
Table 7-21: Ranking of 52 bus routes in network model for a working day (21 Aug
2013) ............................................................................................................................... 123
Table 7-22: Correlation analysis results of efficiency scores of different periods of time
........................................................................................................................................ 123
Table 7-23: Efficiency scores statistics of some routes for models 1 and 2 .......... 126
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Table 7-24: a) Original and bias-corrected efficiency scores; and b) Truncated
Regression ....................................................................................................................... 129
Table 7-25: Recommendations for performance improvement of inefficient bus routes
......................................................................................................................................... 131
Table 7-26: Reduction of service duration for inefficient bus routes in model 1 (the
morning peak hour) .......................................................................................................... 132
Table 7-27: Reduction of space-km for inefficient bus routes in model 2 (the morning
peak hour) ........................................................................................................................ 133
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List of Abbreviations
ABS: Australian Bureau of Statistics
AFC: Automated Fare Collection
BCC: Banker, Charnes, Cooper
CCR: Charnes, Cooper, Rhodes
CA: Comparative Analysis
CO: Car Ownership
CRS: Constant Returns to Scale
DEA: Data Envelopment Analysis
DMUs: Decision Making Units
EVs: External Variables
FDH: Free Disposal Hull
GIS: Geographic Information System
ID: Identification
MSL: Maximum Schedule Load
NDEA: Network Data Envelopment Analysis
OLS: Ordinary Least Square
OTP: On-Time Performance
PT: Public Transit
PR: Transit Provider
PA: Passenger
POP: Population
POD: Population Density
POL: Piece of Land
QOS: Quality of Service
SFA: Stochastic Frontier Analysis
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SEQ: South East Queensland
SK: Seat Kilometres
SH: Seat Hours
SA1: Statistical Areas Level 1
TE: Technical Efficiency
VRS: Variable Returns to Scale
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Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any higher education institution. To the best of my
knowledge and belief, the thesis contains no material previously published or written by
another person except where due reference is made.
Signature: Khac Duong Tran
Date: January 2019
QUT Verified Signature
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Acknowledgements
I would like to acknowledge my principle supervisor, Dr Ahish Bhaskar, and my
associate supervisors, Associate Professor Jonathan Bunker and Dr Boon Lee, for their kind
support and guidance throughout my PhD project. I greatly appreciate their inspiring
supervision, constructive criticism, and encouragement during my PhD journey.
I wish to thank TransLink Division of the Queensland Department of Transport and
Main Roads, which has supplied the smart-card data of the transit system in South East
Queensland (SEQ), Australia. I would also like to express my gratitude to Prof. Edward Chung
and the Smart Transport Research Centre (STRC) staff, especially Dr Le Minh Kieu, for their
useful comments and friendly feedback on this research in the STRC seminars. Furthermore,
I would like to thank my friends at QUT for their support and friendly advice. They have made
my life at QUT meaningful and enjoyable.
Professional editor, Diane Kolomeitz, provided copyediting and proofreading services,
according to the guidelines laid out in the university-endorsed national ‘Guidelines for editing
research theses’.
I would especially like to acknowledge Vietnam International Education Development
(VIED) and Queensland University of Technology (QUT) for providing me with a PhD
scholarship, which has definitely motivated me a lot throughout my study time at QUT. This
research would not be possible without their finance support. I would also like to take this
opportunity to acknowledge the University of Transport and Communications (UTC),
Vietnam, my employer, for their support during the time in which I have performed my PhD
project abroad.
Finally, I would like to express my deepest gratitude to my family for their
unconditional love, emotional support, and encouragement. I am especially grateful to my
wife, Mrs Thanh Van Pham, and my children, who have always given me emotional
encouragement during difficult times. Without their love and trust, I would have not been able
to complete this dissertation.
Introduction
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1 Introduction
Research Background
The rapid growth of population and the high level of dependence on private motor
vehicles are challenges that many urban areas worldwide are facing. This leads to the rapid
growth of private car use in urban areas and puts higher pressure on the urban transport
system. The increasing use of private motor vehicles has adverse impacts on the quality of
life of residents, such as excessive congestion, traffic noise and air pollution (Greene and
Wegener 1997). It is, thus, important to seek out effective solutions to reduce the use of
private cars and minimise their adverse effects on the urban environment. These solutions
include the improvement of city planning and infrastructure to reduce congestion; the
development of a new generation of private motor vehicles with less detrimental emissions;
establishment of travel behaviour change programs intended for active transport; and
provision of alternatives to private car use (Loukopoulos 2007). Public transport is considered
as a sustainable transport mode in urban areas and could be a viable alternative to private
motor vehicles (Holmgren 2007).
South East Queensland (SEQ), Australia, has experienced a rapid growth of
population. Between 2006 and 2016, SEQ witnessed a population increase of 24% (ABS
2016), which is forecasted to reach 4.2 million in 2031. This leads to increasing travel demand
within this region from just over 9 million daily trips in 2006 to an estimated 15 million daily
trips by 2031 (Government 2011). This region also witnesses a high level of dependence on
private motor vehicles, with the mode share of private cars being 83% compared to only 7%
mode share of public transport in 2006. Thus, Connecting SEQ 2031 (Government 2011),
the Queensland Government’s long-term transport plan to develop a sustainable transport
system in SEQ, has established a target to increase the mode share of transit in SEQ to 14%
in 2031, with a major shift from private car use.
To increase transit ridership effectively, transit agencies need to continuously
optimise their performance and improve the quality of service (QOS). Measuring the
performance of individual routes within a transit system plays a critical role in identifying
improvement needs in system design, operation and control; and in seeking means to
increase ridership.
However, evaluating the performance of individual transit lines/routes is complex
because multiple objectives, and multiple input and output variables, exist (Benn 1995, Sheth,
Triantis et al. 2007, Barnum, Tandon et al. 2008). As shown in Figure 1-1, there are multiple
Introduction
Khac Duong Tran Page 2
transit stakeholders relevant to bus operations including provider, user, and community.
Multiple quality (e.g., comfort) and quantity (e.g., revenue) objectives also apply to bus
operations on a given route. For example, bus operators strive to minimise the operational
cost (fuel, maintenance, staffs, vehicles), the negative impacts on environment and
community (emission, accidents), and maximise ridership. Subsequently, bus users strive to
maximise the span of service, the on-time performance, and service frequency (Benn 1995,
Barnum, Tandon et al. 2008). Each objective relates to some performance indicators and
relevant variables. For instance, ridership depends on population density, average residents’
income, parking space near bus stops, private car ownership, travel time, stop arrival
reliability, total kilometres traversed and service duration over a day. Furthermore, some
objectives are in conflict with others, such as the operational cost borne by the
provider versus service frequency and span of service offered to the user. Figure 1-1
presents the typical relationship between the ridership, the operational costs and key transit
performance indicators as well as relevant variables.
Figure 1-1: Multiple objectives related to transit stakeholders of a transit route (Source: Sheth et al.
(2007))
The complexity of transit performance led to the development of a framework by
Fielding et al. (1985) for transit system performance measurement. This framework, made
PT stakeholders Objectives
Minimise the operational costs
PT Provider
PT User
Community
Maximise the ridership
Maximise the revenue
Minimise the travel time
Maximise the on-time performance
Maximise the duration of service
Maximise the service frequency
Maximise the comfort
Minimise the emission
Minimise the number of accidents
Minimise the congestion
Minimise the resource degradation
Maximise the service coverage
PT Performance indicators
and relevant variables
Length of PT route
Number of stops
Number of intersections
Number of priority lanes
Service duration a day
Service frequency (headway)
Travel time
Dwell time at stops
Stop arrival reliability
Vehicle-km
Seat-km
Vehicle passenger loading
Stop Accessibility
Stop parking space availability
Linked stops
Population density
Private car ownership
Corridor congestions
PT vehicle size
Average corridor speed
Average resident's income
Introduction
Khac Duong Tran Page 3
up of three dimensions, comprises technical efficiency, operational effectiveness (also
termed cost effectiveness), and service effectiveness. Figure 1-2 illustrates the relationship
between the three performance measures and presents a sample list of variables related to
various inputs and outputs.
• Technical efficiency represents the process through which service inputs are
transformed into outputs. This means that a transit agency invests capital in
vehicles, fuel, information systems, employees, maintenance, and other costs
(inputs). This investment produces a certain service for a community such as
vehicle-km, seat-km, and seat-hours (outputs). An agency is considered efficient
if it can reduce the inputs to produce a fixed amount of outputs, or increase the
outputs while using similar or fewer inputs.
• Operational effectiveness indicates the relationship between service inputs and
consumed service. A transit agency spends money to offer its service, and a
number of passengers (per day or week) consume its service. The transit agency
will achieve higher cost effectiveness, if it increases ridership without increasing
the total cost of producing the service.
• Service effectiveness examines the relationship between produced outputs and
consumed service or how well a service offered by operators is consumed by a
community (Georgiadis, Politis et al. 2014). This means that not all of the services
offered (measured by vehicle-km, seat-km, and/or seat-hours) would be used by
a community. If it attracts more passengers without increasing service, or reduces
service but still serves a similar number of passengers, it will be more effective.
Figure 1-2: Framework for a transit network performance concept model (adapted from Fielding et al.
(1985))
Introduction
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The framework of Fielding et al. (1985) allows one to compare the performance of
different transit systems for a particular performance concept (such as vehicle efficiency, fuel
efficiency, and operating safety) by using single ratios of service output and service input.
This approach cannot provide a single overall measure for transit performance evaluation.
This issue is addressed by using Data Envelopment Analysis (DEA), which is a non-
parametric approach to evaluate the efficiency of different production units or decision making
units (DMUs) accounting for multiple inputs and outputs (Sheth, Triantis et al. 2007, Barnum,
Tandon et al. 2008, Lao and Liu 2009, Georgiadis, Politis et al. 2014). However, different
transit performance concepts (technical efficiency, service effectiveness, and operational
effectiveness) are treated separately in those studies, leading to different efficiency
measures. Furthermore, these studies failed to adequately measure the temporal and spatial
performance of transit routes due to their limited data, collected from manual survey. For
instance, travel time is estimated on the basis of the standard of bus operating speed, which
depends upon the distribution of transit routes in the urban or suburban area, or schedule
reliability is estimated on the basis of traffic congestion (Sheth, Triantis et al. 2007).
Additionally, the influence of external factors (such as private car ownership, population
density, individual income, and employment distribution) on bus routes’ operation was not
examined sufficiently because of the lack of detailed data within the service areas of a single
bus route. Hence, it is worth developing a comprehensive approach for evaluating the
performance of transit routes within a network using a rich data source, considering the
influence of external factors.
Recently, the availability of smartcard-based automated fare collection systems (AFC)
in the transit sector has provided a valuable opportunity for better understanding the transit
operation in detail (Trépanier, Morency et al. 2009). This research, therefore, focuses on the
performance measurement of individual transit routes within a network, using AFC data. The
City of Brisbane, Australia, is opted as the case study, where the transit services are provided
by the Translink Division of the Queensland Department of Transport and Main Roads. As
bus transport has the most significant transit mode share in Brisbane (TransLink 2017), this
study selects the bus network in this region for empirical analysis.
The study findings provide transit agencies with a comprehensive approach for transit
route performance analysis. The knowledge gained helps to identify the most efficient routes
(the benchmarks), the most inefficient routes, and sources of inefficiency; and then effectively
assists policy makers in developing more practical and appropriate policies. The performance
improvement of inefficient routes will lead to the performance improvement of the whole
transit system (Barnum, Tandon et al. 2008).
Introduction
Khac Duong Tran Page 5
This chapter is organised as follows: Section 1.2 introduces the research problem and
purpose. The research aims and hypotheses are presented in section 1.3 and 1.4
respectively. Thereafter, the research questions are stated in section 1.5. Section 1.6
introduces the research objectives. The research scope is mentioned in section 1.7, which is
followed by the research significance in section 1.8. Section 1.9 represents the study outline.
Finally, the list of publications from this thesis is provided in section 1.10.
Research Problem and Purpose
If a given transit agency, such as Translink in Queensland, Australia, aims to improve
its transit system performance (for example a bus system) as efficiently and economically as
possible, it needs to investigate the performance of individual routes (the basic unit for
delivering services) within this network and identify the sources of inefficiencies that should
support the policy makers and network planners. However, as shown in Figure 1-1, evaluating
bus route performance is complex, as multiple bus indicators and variables exist.
This problem has raised questions:
• How can multiple objectives and performance indicators of bus routes be taken
into consideration when comparing the operation of different bus routes?
• Can a single composite score be generated that fairly and objectively aggregates
the various objectives of a bus route, to compare the operation of different bus
routes?
• How can the influences of external factors on bus routes’ performance be
investigated?
Answers to such questions would definitely be useful to transit agencies and policy
makers, to optimise current transit system performance.
Researchers have used both parametric (ordinary least squares (OLS) and stochastic
frontier analysis (SFA)) and non-parametric (free disposal hull (FDH) (Tulkens 1993), Data
Envelopment Analysis (DEA) (Ray 2004, Cooper, Seiford et al. 2007)) approaches for transit
performance evaluation. DEA is a non-parametric method based on linear programming and
optimisation. It measures the relative efficiencies of DMUs using multi-inputs and multi-
outputs. Most studies, thus, have developed DEA-based approaches to measure the
performance of transit agencies, as well as individual transit lines/routes within a transit
system (Chu, Fielding et al. 1992, Viton 1997, Viton 1998, Sheth, Triantis et al. 2007,
Georgiadis, Politis et al. 2014). However, most studies have treated transit agencies as DMUs
(macro level), while a limited number of studies have treated transit routes as DMUs (micro
Introduction
Khac Duong Tran Page 6
level) although this work, as above indicated, is of importance for short-term planning such
as network redesign (Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao and Liu
2009, Georgiadis, Politis et al. 2014, Rohácová 2015).
Regarding transit routes’ performance evaluation, particular performance concepts
such as technical efficiency, service effectiveness, and operational effectiveness are
measured separately. Thus, they cannot provide an overall and single measure for the whole
production process of transit routes. Furthermore, population information (regarded as an
external factor) is used as an input for efficiency analysis in those studies. For instance, Lao
and Liu (2009) use number of retirees within the service areas of a bus route as an input to
measure spatial effectiveness of bus routes; and Sheth et al. (2007) use population density
factor as an input of user node for estimating the efficiency scores of bus routes. Therefore,
the impact of a wide range of external factors (socioeconomic and demographic
characteristics) on transit route performance was not examined adequately.
With the availability of AFC data in the case study of Brisbane, and the socio-
economic and demographic data drawn from Australia Bureau of Statistics (ABS), this
research will develop a network DEA-based approach to compare and rank the performance
of several key bus routes within the Brisbane bus network. The approach developed helps to
provide insights into the performance of transit routes and identify internal factors related to
the inefficiency. Furthermore, the influence of a wide range of external factors (such as private
car ownership, population density, individual income, and route characteristics) on bus route
operation is examined in the second stage, using a truncated regression model. This provides
insights into the external reasons behind the poor performance of some routes.
Research Aim
This research aims to develop a scientific and practical framework to evaluate the
spatial and temporal performance of individual transit routes composing a transit network,
and investigate the sources of operational inefficiency of transit routes.
Research Hypothesis
The performance efficiency of transit routes within a network can be estimated using
a non-parametric approach, which accounts for the influences of external factors within the
service areas.
Introduction
Khac Duong Tran Page 7
Research Questions
Based on the aforementioned research aim and hypothesis, the following research
questions are identified:
1. Which models can be the best tools to measure the efficiency of bus routes?
2. Which inputs and outputs are used for the selected model to estimate the
efficiency scores of bus routes?
3. Which external factors potentially have most impact on the performance of bus
routes?
4. How can the sensitivity of external variables to efficiency scores of bus routes be
tested?
5. How can the robustness of the results be tested?
Research Objectives
The following research objectives have been set to achieve the research aim:
1. Build up a framework to measure the operational effectiveness of key bus routes
within a bus network.
2. Measure the temporal and spatial performance of key bus routes within the
Brisbane bus network using the proposed framework in objective 1.
3. Examine the influence of external variables on the efficiency scores estimated in
objective 2.
4. Provide recommendations to transit agencies and policy makers to improve bus
route performance considering the knowledge generated through the case study
conducted.
Research Scope
In an urban area, the transit system includes various modes such as bus, ferry, and
rail. An operator may employ one or more modes. While this study examines the performance
of individual urban bus routes within a transit agency, the framework developed in this
research is applicable to other modes (rail and ferry).
The case study performed in the research focuses on the weekdays and normal
running conditions only. Consideration of non-recurrent congestion due to incidents and
unplanned events are beyond the scope of the research.
Introduction
Khac Duong Tran Page 8
As abovementioned, the aim of this study is to provide insights into bus routes’
operation by using AFC data. Hence, the proposed approach is worth applying for AFC-based
transit networks.
Scientific and Practical Significance
▪ This research develops a comprehensive framework for performance evaluation
of bus routes, and investigates sources of inefficiencies using the AFC data.
▪ Transit agencies can apply the approach presented in this research to identify bus
routes that have the best performance (regarded as benchmark), fairly good
performance, and the worst performance. Sources of inefficiency related to
internal factors can also be identified.
▪ Findings from the current research will identify sources of inefficiency related to
external factors (socioeconomic and demographic characteristics of bus service
areas). This assists regulators in developing appropriate policies to enhance the
transit mode share.
▪ The application of the proposed approach assists transit agencies to optimally
allocate limited resources across their bus network. They can retain efficient bus
routes while reducing the operation of some inefficient bus routes to the extent
possible. At the route level, this approach allows transit agencies to reallocate the
resources across different components of bus route appropriately (vehicle
capacity, stops facility, bus lanes, bus frequency, information systems).
Study Outline
The remainder of this thesis is organised as follows:
Chapter 2 reviews key approaches for the performance measurement of bus systems
and transit policy making for the performance improvement of bus systems, and the
application of a non-parametric approach (DEA) for bus performance measurement.
Chapter 3 presents the basic DEA models and network DEA model, sensitivity
analysis in DEA, and several transit productiveness indexes.
Chapter 4 discusses and develops the framework for the performance measurement
of bus routes using network DEA models, with the selection of appropriate variables.
Chapter 5 introduces the case study site and the relevant data used for developing
and testing the proposed approach.
Introduction
Khac Duong Tran Page 9
Chapter 6 investigates the temporal performance of several bus routes of the case
study using DEA models. It enhances substantial understandings of each bus route
performance.
Chapter 7 compares the temporal and spatial performance of sample bus routes
using network DEA models. Sensitivity analysis is conducted for DEA-based efficiency scores
to investigate the influences of external factors on the efficiency level of bus routes.
Chapter 8 discusses the research findings, contributions, practical implications, and
limitations. Finally, future research directions are provided.
An outline of the present research is expressed in Figure 1-3, which consists of five
research questions (Q1, Q2, Q3, Q4, and Q5) and four research objectives (Obj 1, Obj 2, Obj
3, and Obj 4).
Figure 1-3: Research outline
Chapter 1: Introduction
Chapter 2: Literature Review
Chapter 3: Methodology
CCR-DEA and
BCC-DEA models
Network DEA models Sensitivity analysis in
DEA models
Chapter 4: Framework for bus route performance
evaluation and relevant variables
Chapter 5: Data collection
Internal variables External variables
Chapter 6: Data analysis for
individual bus routes of the case study
Chapter 7: Data analysis for
bus system of the case study
Chapter 8: Conclusions and recommendations
and future research directions
Obj 1
Obj 2 Obj 3
Obj 4
Q1
Q2, Q3
Q4
Q5
Introduction
Khac Duong Tran Page 10
Publications
Conference papers
1. Tran, Khac-Duong, Bhaskar, Ashish, Bunker, Jonathan M., & Lee, Boon
L. (2016) Data envelopment analysis (DEA) based transit route temporal
performance assessment: A pilot study. In 38th Australasian Transport Research
Forum (ATRF 2016), 16-18 November 2016, Melbourne, Vic.
2. Tran, Khac-Duong, Bhaskar, Ashish, Bunker, Jonathan M., & Lee, Boon
L. (2017) Data Envelopment Analysis (DEA) based transit routes performance
evaluation. In Transportation Research Board 96th Annual Meeting (TRB 2017),
8-12 January 2017, Washington D.C.
Literature Review
Khac Duong Tran Page 11
2 Literature Review
This chapter begins with a review of transit policy making for the performance
improvement of bus systems (in section 2.1) and a description of the main approaches used
for bus performance measurement (in section 2.2). Thereafter, the literature on DEA-based
transit performance evaluation and ranking for bus systems and routes are reviewed in
section 2.3. Finally, research gaps are outlined in section 2.4. Readers who are not familiar
with the DEA models may read Chapter 3 for further details about this approach.
Transit policy making
This section provides an overview of transit policy making to improve the performance
of bus routes and systems in literature. As the previous discussion in Chapter 1, there are
three main stakeholders who are interested in the transit performance, including:
• Transit users, who make choices of which travel mode to use when they have
more than an option to choose, or which travel route to use (based on the quality
of service) when they do not have a mode choice;
• Transit operators (agencies), who have to make decisions on how to effectively
allocate a finite amount of resources to best meet their goals and objectives, and
who also have to report on transit operation to funding supporters; and
• Community, who may indirectly benefit from the operation of transit (such as
congestion relief, air quality, mobility, source of employment) and may directly
contribute to transit service through taxes.
Each of these major transit stakeholders has its own objectives (points of view). Some
of these points of view may be the first priorities of each stakeholder and others may be
overlapped by those of other transit stakeholders. Therefore, the policy-making process aims
to address the points of view of each stakeholder and/or address the points of view of multiple
transit stakeholders (Ryus, Danaher et al. 2013).
Regarding the users’ perception or satisfaction, there are several studies appearing
in the literature that help identify key quality of service (QoS) factors important to passengers
(Eboli and Mazzulla 2007, Nathanail 2008, Tyrinopoulos and Antoniou 2008, Eboli and
Mazzulla 2009, Eboli and Mazzulla 2011, Ryus, Danaher et al. 2013, de Oña and de Oña
2014). The most common aspects of transit service are the reliability, hours of service,
frequency, convenience of route, capacity, fare, cleanliness, comfort, security, staff,
information, and the ticketing system. Particularly, Transit Capacity and Quality of Service
Literature Review
Khac Duong Tran Page 12
Manual (TCQSM) (2013) provided the quality of service framework for fixed-route transit
which consists of six quality of service factors (frequency, service span, access, passenger
load, reliability, and travel time) that are important to passengers (refer to Table 2-1). In this
framework, six factors are categorized into (1) transit availability (including frequency, service
span, and access) and (2) transit comfort and convenience (including passenger load,
reliability, and travel time). This framework significantly provides transit decision makers with
detailed and comprehensive criteria to measure the performance of transit routes and
propose appropriate recommendations for transit performance improvement.
In terms of transit operators’ perception, researchers used “efficiency” indicators to
quantify the productivity of the system components (vehicle, routes, stops, and operation),
cost, environment, and safety. The calculation of efficiency indicators is based on the different
input and output variables relevant to transit demand and operation such as ridership/loading,
travel time, route length, frequency, service duration, size of vehicle, operation and
maintenance costs, labors, fuel consumption, accident, and emission (Ceder and Wilson
1986, Viton 1997, Vuchic 2005, Vuchic 2007, Barnum, Tandon et al. 2008, Lao and Liu 2009,
Bunker 2013, Georgiadis, Politis et al. 2014, Rohácová 2015). The empirical analysis in these
studies helps to identify the internal issues of the system operation and components, and
then effectively support the decision-making processes of transit operators. It is notable that
The TCQSM (2013) also provided several bus preferential treatments (infrastructure
improvement) that have been developed in urban areas throughout the world to make bus
transit more competitive with the private cars and to provide a higher quality of service for
passengers. These bus preferential treatments mainly driven by capacity, travel speed, and
travel time reliability include:
• Reducing delay associated with bus stops (deceleration, bus stop failure, boarding
lost time, dwell time, traffic signal delay, reentry delay, and acceleration);
• Reducing delay associated with bus facilities (stop spacing, exposure to general
traffic, facility design, and bus operations);
• Factors determining bus capacity (loading capacity, bus stop capacity, and bus
facility capacity)
• Provision of Busway and freeway managed lanes;
• Provision of urban street bus lanes on arterial urban road;
• Using Transit Signal Priority (TSP) on the bus routes;
Literature Review
Khac Duong Tran Page 13
• Site-Specific priority treatments (queue jumps, boarding islands, and curb
extensions); and
• Bus stop placement (bus stop relocation and bus stop consolidation).
For community perception, transit performance is measured based on the impact of
transit service on different aspects of a community such as employment and economic
growth. This point of view also includes the contributions of transit to community mobility,
safety, congestion relief, and environment protection (Hassan, Hawas et al. 2013, Alam,
Nixon et al. 2015). Some researchers in the literature address the issues of transit
performance based on multiple points of views (Sheth, Triantis et al. 2007, Yu, Chen et al.
2015).
Due to the unavailability of user’s perception-based dataset of the case study in
Brisbane, this research aims to evaluate the performance of bus routes within a system based
on the perception of transit operators. Therefore, next section reviews the main approaches
for the performance measurement of bus routes/ system using different input and output
variables relevant to system design and transit demand and operation.
The Performance Measurement of Bus System
There are three main approaches to measure the performance of the bus system:
• Comparative Analysis (CA);
• Stochastic Frontier Analysis (SFA); and
• Data Envelopment Analysis (DEA)
The early approach applied for bus performance measurement is known as
comparative analysis. This approach normally uses different key performance indicators
(KPIs) to compare the performance of different bus systems with regard to different
performance concepts, such as labour efficiency, vehicle efficiency, fuel efficiency, operating
safety, and service consumption per expense. KPIs are defined as ratios of bus service
outputs to service inputs (revenue vehicle hours per operating expense or passenger trips
per revenue vehicle hour). Fielding et al. (1985) defined a wide range of KPIs for comparing
the performance of bus systems. Vuchic (2007) provided efficiency ratios (output quantity
produced per resource quantity expended) and utilisation (a ratio of demand to supply) to
measure the performance of a transit system. The Transit Cooperative Research Program
Report 88 (2003) provided a process for developing a performance-measurement program,
including both traditional and non-traditional performance indicators.
Literature Review
Khac Duong Tran Page 14
The Transit Capacity and Quality of Service Manual (TCQSM) (2013) presented the
quality of service framework for fixed-route quality of service (QOS) measures. In this
framework (refer to Table 2-1) QOS measures are clustered into two groups: (1) availability;
and (2) comfort and convenience. The core availability QOS measures describe how often
(frequency), how long (service span), and where (access) transit service is available, while
the core measures of comfort and convenience reflect passenger load, reliability, and travel
time. Furthermore, each QOS measure at the route level is described by a spectrum of
grades, according to the separate perspectives of passenger and operator. Therefore, transit
professionals are able to employ TCQSM’s framework to evaluate the temporal performance
of a single transit route, or compare the performance of several transit routes for those six
QOS measures. This work contributes to insights into the performance of transit routes for
different core QOS aspects.
Table 2-1: Quality of service measures for fixed-route transit
Availability Comfort and Convenience
Frequency
Service Span
Access
Passenger Load
Reliability
Travel Time
The CA approach is easy to apply for comparing the performance of bus at the route
and system levels, but for a particular performance concept/indicator. The comparison,
implemented for each KPI separately, leads to different levels of efficiency of one bus system
for different KPIs. This approach, therefore, cannot provide a single overall measure of bus
performance (Chu, Fielding et al. 1992).
The latter two approaches, SFA and DEA, are frontier methods, which build up the
frontier production function for evaluating the efficiency level of a set of production units. SFA
(a parametric approach introduced independently by Aigner et al. (1977) and Meeusen and
van Den Broeck (1977)) uses econometric techniques, while DEA (a non-parametric
approach) employs mathematical programming techniques for the frontier production function
estimation. The advantage of the DEA approach is that it does not require a functional form
to estimate the frontier production function. However, if the data are contaminated by
statistical noise, the frontier estimation may be inaccurate. SFA, on the other hand, imposes
an explicit functional form for technology. This can handle statistical noise, but possibly
makes functional form overly restrictive (Bauer 1990). Those two frontier methods provide
a single and comprehensive measure for evaluating the efficiency levels of a set of
production units with multiple input and output variables. Therefore, they were broadly
Literature Review
Khac Duong Tran Page 15
used for evaluating the performance of bus systems. De Borger et al. (2002) provided a
comprehensive review of the application of both DEA and SFA for performance measurement
of bus systems worldwide.
SFA and DEA each have their own advantages and disadvantages, which raises the
question of which method is superior in measuring bus performance? Michaelides et al.
(2010) employed both SFA and DEA (under constant returns to scale assumption) for
examining the technical efficiency of trolley buses in Athens, Greece. The efficiency scores
obtained from SFA are compared with those from DEA, providing consistent results in general
terms. This indicates that one can use SFA or DEA for efficiency estimation of bus
performance.
The current research employs the DEA method for bus route performance analysis of
the case study in Brisbane for two reasons. The first reason is that DEA requires no specific
functional form for the production function (Fried, Schmidt et al. 1993), and the second reason
is that the drawback of DEA related to data statistical noise can be addressed by using AFC
data, being a fairly accurate data source. Therefore, in the next section, DEA-based
performance evaluation of bus systems and routes in literature are investigated.
Application of DEA for Bus Performance Evaluation
To date, DEA models have been developing for over thirty years and have been
applied widely in many fields, namely banking, hospitals, schools, electricity, farming and
transportation. This section reviews the application of DEA models in transit performance
evaluation, including measuring the technical efficiency of different transit systems (in section
2.3.1 and 2.3.2), both the technical efficiency and cost effectiveness of different transit
systems (in section 2.3.3), and finally transit route performance (in section 2.2.4)
2.3.1 Transit Performance Concepts
As mentioned above, measuring the performance of urban transit systems with regard
to efficiency and effectiveness is greatly challenging to transit agencies, as multiple factors
simultaneously influence the operation of any public transport system. Fielding et al. (1985)
thus used cluster analysis to construct 12 peer groups of fixed-route urban transit systems
based on size, average speed and peak-to-base ratios of urban. Peak-to-base ratio was
computed by the ratio of vehicles in service in the largest peak over the midday base vehicle
requirement. The authors then analysed the variance and discriminant among the peer
groups in terms of operating characteristics to build up a decision tree typology, which is an
intellectual device for clarifying the performance similarities as well as differences among
transit agencies. This approach provided the basics for developing the Irvine Performance
Literature Review
Khac Duong Tran Page 16
Evaluation methodology (IPEM), which subsequently was used by some researchers to study
the performance of transit agencies like Perry et al. (1986), Yu (1988) and Fielding et al.
(1988). However, the IPEM statistics is a cumbersome method for evaluating transit
performance. It does not provide a single overall measure of transit performance (Chu,
Fielding et al. 1992).
To address this issue, Chu and Fielding et al. (1992) were pioneers in applying DEA
models to measure the efficiency and effectiveness of public transit agencies in the United
States (USA). The output data for efficiency and effectiveness assessment were annual
revenue vehicle hours (RVH) and annual unlinked passenger trips (TPAS) respectively.
Based on the results of analysis, the authors reinforced the notion of Hatry (1980) that in
public agencies, efficiency should be evaluated separately from effectiveness.
The three categories of performance concepts: technical efficiency, operational
effectiveness, and service effectiveness are expressed in Figure 1-2, which is adapted from
the ‘Framework for a transit performance concept model’ of Fielding et al. (1985). This figure
illustrates that there are a number of environmental factors (population density, accessibility,
parking space availability, car ownership) influencing the actual service consumption of a
community with regard to the effectiveness perspective. Furthermore, concerning the
efficiency component, external factors (traffic conditions, location of transit stops) significantly
affect the service outputs. Thus, it is not comprehensive and accurate if one evaluates the
performance of an urban transit system without considering the impacts of these external
(uncontrollable) variables.
2.3.2 Technical Efficiency Assessment for Transit System Performance
Using DEA models to evaluate the performance of transit agencies with regard to
technical efficiency perspective, we can look at some typical research hereafter. Obeng
(1994) utilised the DEA method to examine the influence of subsidies on the efficiency of 73
transit systems in the USA. After employing DEA to estimate the production frontier using
traditional variables (labour, fuel, fleet size, vehicle miles), this study re-estimated the
production frontier with subsidies being considered as one of the independent variables. It
found that subsidies improve technical efficiency in approximately 75% of the transit systems
investigated.
Nolan (1996) also applied the DEA model to evaluate technical efficiency of 25 mid-
sized bus transit agencies in the United States using data from the 1989-1993 Section 15
reports (USDOT). It is notable that this study exploited a two-stage data envelopment analysis
method developed by Oum and Yu (1994) to measure the performance of those transit
Literature Review
Khac Duong Tran Page 17
agencies. In the first stage, the DEA model was used to compute the average output oriented
technical efficiency scores of the sample for each year. Then in the second stage, the Tobit
model was used to take into account transit characteristics believed to indirectly affect the
technical efficiency scores. These characteristics are not a direct part of the production
process examined in the previous stage.
Kerstens (1996) provided an empirical analysis of 114 French urban transit
companies. Radial efficiency measures in the outputs were calculated for the variable returns
to scale DEA model with strong and weak disposability in both inputs and outputs. At the
same time, the Free Disposal Hull (FDH) model was used to evaluate corresponding
efficiencies. Based on the efficiency distributions coincided with the three different frontier
methods, the study confirmed the important role of the alternatives among deterministic
nonparametric reference technologies for technical efficiency assessment.
Viton (1997) analysed the technical efficiency of 217 multi-mode United States motor-
bus transit systems in 1990 using DEA models with variable returns to scale and weak
disposal. The data sample covered a wide range of system sizes and included both private
and public providers. The results indicated no systematic efficiency differences between
public and private systems with a high proportion of technically efficient systems, accounting
for around 80% compared to only 5.5% of the systems having Russell inefficiency measures
less than 0.8. Furthermore, to answer the question of whether the USA bus transit productivity
had declined recently, Viton (1998) used the Russell and Malmquist DEA models to measure
the productivity changes of multi-mode USA bus transit between 1988 and 1992. All data was
from the Section-15 data-set (USDOT) including a total of 183 systems in 1988, and 169 in
1992. Looking only at the averages, those two approaches demonstrated that bus transit
efficiency has improved slightly throughout the period.
2.3.3 Two Dimensions Assessment for Transit System Performance
Some researchers have examined both technical efficiency and effectiveness of
transit systems. Boilé (2001) proposed a DEA-based method to determine the efficiencies
and scale inefficiencies of 23 transit systems in the United States. In the first case, the inputs
are operating costs and output is vehicle revenue hours. In the second case, inputs are similar
to case 1, but outputs include both vehicle revenue hours and annual unlinked passenger
trips. Data of two cases were analysed under CCR and BCC-DEA models, respectively, to
determine the technical efficiency of DMUs. Inefficient units were then examined for
sensitivity to determine sources of inefficiency and ways to improve the performance of those
units.
Literature Review
Khac Duong Tran Page 18
Karlaftis (2004) utilised a large data set consisting of 256 US transit systems over a
five-year time period (1990-1994) to measure transit system efficiency and effectiveness as
well as the relationship between these two dimensions of transit performance. Additionally,
economies of scale in transit systems were evaluated based on their performance
assessment. The output oriented-DEA model was applied three times for three different sets
of data. Each of them utilised the same inputs (total vehicles, fuel, total employees) but
different outputs with total annual vehicle-miles as output for efficiency measurement, total
annual ridership for effectiveness, and both those outputs for the combined performance. The
finding results indicated that efficiency and effectiveness are positively related.
Tsamboulas (2006) applied a similar approach to Karlaftis (Karlaftis 2004) to analyse
15 European transit systems. Their data set refers to a ten-year period of time (1990-2000)
and covers a variety of situations concerning regulatory and organisational forms in European
cities. Using a CRS-DEA model to analyse data sets at yearly levels in the first stage, the
results obtained indicated that private systems tended to be more efficient, while public
systems achieved higher effectiveness scores. Furthermore, in the second stage, the Tobit
regression model was employed to identify which factors are the ones causing the inefficiency
and to what extent. The results of a Tobit regression analysis presented that the transit
systems appear to have experienced a certain growth during the examined time period with
respect to their efficiency and effectiveness as well as their overall performance.
Ayadi (2013) measured and compared the levels of efficiency and of pure technical
effectiveness in the twelve urban transit systems in Tunisia during the period 2000-2010 using
the DEA method. After determining technical efficiency according to input orientation and
pure technical efficiency with regard to output orientation, this study applied linear regression
to estimate the link between pure technical efficiency and the explanatory variables (the living
standard of residents, the capital per labour unit, the network length, and the technical
progress). The results indicated that the input-oriented DEA model was the best explaining
this linkage.
Regarding the crucial role of societal and environmental factors in assessing transit
performance, Yu et al. (2006) added accident cost as undesirable output and network length
as environmental input to the data set to measure the cost effectiveness of 24 bus companies
in Taiwan. This study, based on the directional graph distance function and the multi-activity
DEA approach, illustrated that the overall cost effectiveness rankings seem to be fairly
sensitive to whether or not the graph multi-activity DEA approach is adopted. This confirmed
the important role of the conventional DEA model in measuring the cost effectiveness of firms
that carry out various activities while sharing common resources.
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Khac Duong Tran Page 19
2.3.4 Assessment for Transit Route Performance
The focus on the technical efficiency and effectiveness of transit agencies at system
level contributed by providing a general analysis of the actual performance of transit
organisations and problems related to such operations. However, there is a limited number
of studies focusing on the performance evaluation of transit at the transportation process
level (Triantis 2004), although this work is significantly essential to provide insight into the
performance of individual transit routes within a system. Several studies thus have examined
the performance of transit routes/lines within a transit agency.
Lao et al. (2009) combined the BCC-DEA model and geographic information system
(GIS) to measure the performance of bus lines in a transit system. In this study, GIS was
used to generate the input data for the spatial effectiveness DEA model and visualise the
distribution of bus stops and routes. The input data for operational efficiency measurement
includes operation time, round-trip distance, number of bus stops, while those for spatial
effectiveness assessment are bus users, population with disabilities, population 65 and older.
The output variable for the two models is total passengers. On the basis of operational
efficiency and spatial effectiveness scores of 24 fixed bus routes, this research ranked the
performance of individual bus routes and demonstrated that GIS can help to analyse the
spatial variation of efficiency and effectiveness against demographic settings.
Barnum et al. (2008) employed a CRS-DEA model to analyse 46 bus routes of a US
transit agency using weekday data. In the first stage, raw efficiency scores of individual bus
routes were computed by a DEA model without considering the environmental variables.
Then in the second stage, two environmental variables (population density, population), that
are beyond the control of the transit agency, were used to adjust the DEA outputs (Riders
and OTP). Then the adjusted DEA efficiency scores of DMUs are calculated. These external
variables are collected within a 0.805-km-width corridor along an entire bus route. The results
indicated that after adjusting the raw DEA scores, 20 bus routes became more efficient, 12
did not change, and 14 became less efficient.
Sheth et al. (2007) expanded the network DEA model of Färe and Grosskopf (2000)
to assess the performance of 60 different bus routes within a transit network in Virginia, USA.
In this study, all variables related to the service provider, the users, and the societal
perspectives were taken into consideration to compute the DEA efficiency scores with regard
to both CRS and VRS. Making comparison among these efficiency scores helped to rank the
performance of these 60 bus routes and capture the relationship among the supplier, the
customer of the public transportation service as well as the external and environmental
variables related to the urban transit performance. However, the data used in this research
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Khac Duong Tran Page 20
is average weekday data with some qualitative variables like average travel time and
schedule reliability being estimated through the route length, standard for average speed in
urban or suburban areas, traffic congestion, and number of stops. The results achieved thus
could not reflect accurately the actual performance of the given bus routes over the time
period of a weekday. Furthermore, external factors in transit, such as population density and
parking space availability, are used as inputs for a user node in the DEA model. Thus,
external factors are not examined appropriately in this study.
More recently, 60 individual bus lines within a public transport network in Thessaloniki,
Greece were examined by a DEA model (Georgiadis, Politis et al. 2014). For model 1 and 2,
input variables included trip length, span of service, and vehicles, while output variables were
revenue seat-km for efficiency measure (model 1) and passengers for operational
effectiveness assessment (model 2). Model 3 aimed at measuring combined effectiveness,
including revenue vehicle-km and vehicles for input variables, as well as passengers
regarded as an output variable. Along with calculating the efficiency and effectiveness scores
for the three above models, this study also employed bootstrapping techniques to check
robustness of DEA results for model 1 and model 2. This sensitivity analysis explained that it
is more reliable when correcting obtained scores for bias. The results also indicated that there
is not a clear positive or negative relationship between technical efficiency and operational
effectiveness. The results achieved from model 3 were utilised to classify DMUs into different
clusters using a clustering algorithm of Po et al. (2009). Then, variables of the piecewise
production function were defined to ensure that their modification would not influence one
another. Therefore, public agencies can possibly use such functions as a tool for tracking
performance improvement, which is achieved when they gradually modify the individual
design elements of their service. Applying this approach for the situation of Thessaloniki, it is
found that scheduling of buses with fewer seats would be a better solution than reducing their
span of services.
2.3.5 Summary of findings
Table 2-2 provides an overview of the application of DEA models in measuring the
transit performance at both system and route levels. Here, the review is separated into two
groups: the former focuses on the performance of transit systems and the latter focuses on
the performance of individual transit routes/lines. The columns represent the DEA models
used, number of Decision Making Units (DMUs), inputs and outputs selected for DEA models,
time frame of data, and finally the findings.
From the summary of Table 2-2, most of the research focuses on evaluating the
performance of different transit systems on yearly data (first group). Recently, some
Literature Review
Khac Duong Tran Page 21
researchers have focused on evaluating the performance of individual transit routes within a
system (Triantis 2004). Comparing the performance of different transit systems plays a key
role in determining the average operational efficiency of a transit system and problems related
to the operation of the whole system, but cannot explore the problems related to the internal
activities of each transit route. On the other hand, the performance evaluation of individual
transit routes within a transit system substantially provides the transit agency with opportunity
to understand its internal activities (Benn 1995, Barnum, Tandon et al. 2008), and then
investigate the source of inefficiency. Possible actions then can be taken by transit agencies
to optimise the operational efficiency of inefficient transit routes, and thus leads to
performance improvement for the whole transit system. Evaluating the performance of
individual transit routes therefore is of importance for optimising the operation of transit at the
route and system level.
Most of the studies have focused on technical efficiency and cost effectiveness.
Researchers have evaluated the relationship between the technical efficiency and cost
effectiveness, while the literature has had contrary findings. Chu et al. (1992) supposed that
these two dimensions of transit performance should be evaluated separately, while Karlaftis
(2004) claimed that efficiency and effectiveness seem to be positively related. Hence, the
correlation between technical efficiency and cost effectiveness should be further studied with
a larger sized dataset.
A few studies (Barnum, Tandon et al. 2008, Lao and Liu 2009) have been conducted
on service effectiveness. This is because of the complexity in modelling the service
effectiveness, which is often based on the uncontrolled factors (such as living standards of
the residents, quality of service with respect to passenger perception, parking space, and
private vehicle ownership). Moreover, the availability of the integrated data needed for the
modelling is also hard to obtain.
The DEA model only provides a mean of estimation of DMUs’ technical efficiency. To
evaluate the influence of external factors (socio-economic and demographic variables) on the
efficiency level of DMUs, a two-stage process was adopted (Nolan (1996), Georgiadis et al.
(2014)). Here, at the first stage, the DEA model is applied to estimate the efficiency scores of
DMUs, and thereafter a truncated regression model is applied at the second stage to analyse
the sensitivity of efficiency scores obtained in the first stage to those factors. However, the
limitation of these studies is that they lack information on some potentially uncontrollable
variables such as structure of population, private vehicle ownership, and average income of
residents. The influence of external factors on transit performance thus was not studied
Literature Review
Khac Duong Tran Page 22
sufficiently. This study attempts to overcome this issue by using external variables at the most
detailed level (the Statistical Areas Level 1 (SA1)) of the case study in Brisbane, Australia.
The performance evaluation of individual routes within a transit system has drawn the
attention of a few researchers (Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao
and Liu 2009, Georgiadis, Politis et al. 2014, Rohácová 2015). However, due to the simplistic
transit data collected through manual survey, temporal and spatial performance of routes in
those studies was not examined sufficiently. For instance, actual travel time was not used in
those studies (Lao and Liu 2009). Travel time, in reality, was estimated from operating speed,
which depends upon the distribution of transit routes in the urban or suburban area (Sheth,
Triantis et al. 2007). Most studies used “passenger-km” as an output to represent the service
consumption of a route, while the corresponding input is “seat-km” representing vehicle
passenger carrying capacity. However, due to the data limitation, “passenger-km” was
defined as the total number of passengers transported by a route multiplied by the total
number of kilometres travelled by all vehicles operating on that route during a weekday. This
definition does not reflect the service consumption accurately, because it considers the total
route length travelled by all vehicles instead of the average route length travelled by
passengers. This data limitation is addressed in the current study by using AFC data for the
case study in Brisbane.
Regarding the above relationship between the vehicle passenger carrying capacity
and the service consumption, Vuchic (2007) defined “transportation work” (𝑤) as the number
of transported objectives (𝑢) multiplied by the distance (𝑠) over which they are carried: 𝑤 =
𝑢. 𝑠.
Based on the work of Vuchic, Bunker (2013) introduced “transit work” and “transit
service work efficiency” of an individual transit service h along its route L with n segments
constituting route L. “Transit work” was the sum of the transit work performed along all
consecutive segments along the transit route.
Transit work performed by service h along its route L, given by (passenger-km):
𝑾𝒉,𝑳 = ∑ 𝑷𝑶𝑩,𝒉,𝒊𝒔𝒊𝒏𝒊=𝟏 (Equation 2-1)
Where: 𝑠𝑖 = length of segment 𝑖
𝑃𝑂𝐵,ℎ,𝑖 = Passengers on board for service h along segment 𝑖
𝑛 = Number of consecutive segments constituting line L traversed by h
Compared to “passenger-km”, “transit work” reflects the service consumption more
accurately, because it takes the actual route length traversed by passengers into account
Literature Review
Khac Duong Tran Page 23
and reflects the vehicle’s loading level along the transit route. This research will provide a
comprehensive framework for DEA application for transit route performance evaluation with
the use of “transit work” as an output to present the service consumption of the community.
Literature Review
Khac Duong Tran Page 24
Table 2-2: An overview of the application of DEA in measuring the transit performance
Referen-
ces
DEA model DMUs Inputs Outputs Time
frame
conside-
red
The findings
Obeng
(1994)
DEA model 73 bus
agencies in
USA
Labour; Fuel; Fleet size
Vehicle- Miles
Annual
data
Subsidies improve technical efficiency
(TE) in approximately 75% of the
transit systems studied
Nolan
(1996)
DEA model
(BCC-DEA) and
Tobit model
25 mid-sized
bus agencies
in USA
Vehicle operated; Fuel; Labour. Vehicle- Miles
Annual
data
Average fleet age is significantly and
negatively correlated with the TE
measure.
Operating subsidies can create
significant and negative impacts on
TE.
Kerstens
(1996)
DEA model and
Free Disposal
Hull (FDH) DEA
model
114 French
urban transit
companies
Vehicles; Employees; Fuel.
Explanatory variables: Owner; Group;
Linelength; Stoplength; Popdens;
Vehage; Ctype; Cterm; Ssub; Tax.
Vehicle-Km;
Seat-Km.
Annual
data
It confirms the important role of the
alternatives among deterministic
nonparametric approaches for TE
assessment, and the relevance of
ownership and the harmful impact of
subsidies.
Viton
(1997)
Russel DEA
model, with
VRS + Weak
Disposal
217 multi-
mode motor-
bus transit
systems in
USA
Average speed; Average Fleet age;
Number of directional miles; The fleet
sizes; Fuel; Labour hours for
transportation, maintenance, admin,
Vehicle-miles;
Passenger-
trips.
Annual
data
Public and private systems do not
have an observed systematic
efficiency difference.
Literature Review
Khac Duong Tran Page 25
capital; Tyres and material cost; Service
cost; Utilities cost; Insurance cost.
Around 80% of the sample is
technically efficient. The extent of
inefficiency in the industry is slight.
Viton
(1998)
The Russell and
Malmquist DEA
models
183 US bus
systems in
1988, and
169 systems
in 1992.
Average speed; Average fleet age;
Number of directional miles; The fleet
sizes; Fuel; Labour hours for
transportation, maintenance, admin,
capital; Tyres and material cost; Service
cost; Utilities cost; Insurance cost.
Vehicle-miles;
Passenger-
trips;
Vehicle-hours.
Annual
data
Bus transit efficiency has improved
slightly over the period. The
proportion of technically efficient
systems rose from 74% in 1988 to
82% in 1992. In most inefficiency
categories, there were proportionately
fewer systems in 1992 than in1988.
Chu et al.
(1992)
DEA model 86 bus
agencies in
USA
Vehicle operating cost; Maintenance
cost; General cost; Other expenses;
Revenue vehicle hours; Population
density; % of household with car;
Subsidy passenger
Revenue
vehicle hours
Unlinked
passenger-
trips
Annual
data
Average input-oriented TE: 85%
Average input-oriented cost
effectiveness: 65%
Boilé
(2001)
DEA model 23 bus
agencies in
USA
The operating costs;
Vehicle revenue hours
Vehicle
revenue hours;
Unlinked
passenger-
trips
Annual
data
Systems that operate locally
inefficiently may improve their service
by using operation strategies.
Systems that exhibit scale
inefficiencies may be improved upon
by identifying and dealing with
external factors.
Karlaftis
(2004)
DEA model and
the Return to
scale analysis.
256 US
transit
systems
Total vehicles;
Fuel;
Total employees
Total annual
vehicle-miles;
Annual
data
Efficiency and effectiveness are
positively related.
Literature Review
Khac Duong Tran Page 26
Total annual
ridership
(1990-
1994)
Optimal scale of operation varies
significantly and depends on the
output specification selected and the
performance dimension.
Tsambo-
ulas
(2006)
DEA model and
Tobit regression
model
15 European
transit
systems
Total vehicles;
Total employees;
Transit system characteristics:
Population; Area.
Vehicle-Km;
Passengers.
Annual
data
(1990-
2000)
Private systems are more efficient,
while public systems are more
effective. The transit systems appear
to have experienced a certain growth
during the examined time period.
Ayadi
(2013)
DEA model and
an econometric
regression
model.
12 urban
transit
systems in
Tunisia
Total number of bus park;
Number of staff;
Annual amount of fuel consumed
Travelled Km Annual
data
(2000-
2010)
The annual technical efficiency (input
orientation) is 92.44%. The average
technical efficiency (output
orientation) is 90.13%
Lao et al.
(2009)
DEA model and
geographic
information
system (GIS)
24 fixed bus
routes in
Monterey
County,
California,
USA.
Operation time;
Round trip distance;
Number of bus stops;
Commuters who use buses; Population
65 and older;
Persons with disabilities
Total number
of passenger.
Total number
of passenger.
Annual
data
For TE: 6 bus lines are technically
efficient, 6 bus lines are fairly efficient
(scores ≥ 0.6), and 12 bus lines are
inefficient.
For spatial effectiveness: 11 of them
are technically efficient (scores ≥ 0.8)
and 13 bus lines are inefficient
Barnum et
al. (2008)
DEA model 46 bus
routes of a
US transit
agency
Seat kilometre (SK);
Seat hours (SH);
Population density;
Population.
Ridership;
Span of
service;
Average
frequency;
The
average
weekday
trips
Comparing the performance of
multiple bus routes of one transit
agency.
Literature Review
Khac Duong Tran Page 27
Maximum
frequency; On-
time
performance.
20 bus routes became more efficient,
12 did not change, and 14 became
less efficient.
Sheth et
al. (2007)
Network DEA
model
60 bus
routes in
Virginia,
USA.
The provider node: Headway; Service
duration; Costs; Number of
intersections; Priority lanes.
The societal variable: Number of
accidents; Emissions; Noise pollution;
Resources degraded.
The environmental variables:
Accessibility; Parking space availability;
Population density; Connectivity;
Comfort standards factor.
The provider
node and
inputs for the
passenger
node: Vehicle-
mile; Schedule
reliability;
Average travel
time.
The passenger
node:
Passenger-
mile
The
average
weekday
trips
Capture the relationship among the
supplier, the customer of the
transportation service as well as the
external and environmental variables
related to the urban transit
performance.
Georgia-
dis et al.
(2014)
DEA model and
Bootstrap-ping
techniques
60 bus
routes in
Greece.
Model 1: Length; Span of service;
Vehicles.
Model 2: Length; Span of service;
Vehicles.
Model 3: Revenue vehicle-km; Vehicles.
Revenue seat-
km;
Passenger
Passenger
Annual
data
(2009-
2011)
There is not clear relationship
between efficiency and operational
effectiveness.
Evaluating the transit route
performance is more reliable when
correcting for bias.
Literature Review
Khac Duong Tran Page 28
Research Gaps
The findings in the literature review indicate that a limited number of studies have
examined the performance of individual bus routes composing a transit system, using a DEA
model. For performance evaluation of bus routes, different performance concepts defined in
the framework of Fielding, Babitsky et al. (1985) (technical efficiency, service effectiveness,
and operational effectiveness) were separately examined in preceding studies using a DEA
model. This method thus cannot provide an overall measure for bus route performance.
Additionally, the above-mentioned limitation of an annual dataset only enables one to
measure the average efficiency of bus routes for a given month or year (at a macro level). It
is essential to characterise the detailed operation (at a micro level) of such bus routes during
a shorter period of time (such as every hour or key periods of time within a weekday), and
changes of the efficiency level of bus routes over a time series (different hours or weekdays
for instance) because this offers the chance to identify the operational issues of bus routes
across the daytime. AFC data reveals information on how the transit network is rendered and
used on a continuous basis, promisingly providing practitioners with a rich dataset for practice
and understanding the spatial and temporal performance of bus routes (Trépanier, Morency
et al. 2009). Hence, there is a great need to develop a network DEA-based approach using
AFC data for bus route performance evaluation. This helps to bridge the above research gaps
in literature.
Taylor, Miller et al. (2009) indicated that external factors (population, population
density, personal/household income, employment, auto/highway system characteristics, and
car ownership) substantially affect the variation in transit ridership among urbanised areas.
However, perhaps partially due to the lack of those data, external factors were not studied
sufficiently for route-based transit performance analysis. Previous work has focused only on
the influences of population on transit patronage (Barnum, Tandon et al. 2008, Lao and Liu
2009). Barnum et al. account for the total population of the entire buffer zone (with 0.4025 km
width for each side) along the whole route, and Lao et al. employ the population of pensioners
and persons with a disability within bus route service areas (0.4 km radius around bus stops)
as inputs for bus routes spatial effectiveness analysis. From those limitations, there is a great
need for examination of the influences of external factors (within service areas) on bus routes’
operation. This research addresses this issue by using a wide range of external variables
within the bus stop-based service areas to test the sensitivity of the DEA efficiency scores to
these external variables, and then identifying the factors influencing the efficiency levels of
bus routes.
Methodology
Khac Duong Tran Page 29
3 Methodology
Introduction
To achieve objectives two and three stated in Chapter 1, this research first employs
the DEA models to compare and rank the performance of some key bus routes of the case
study. The reason is that the DEA model was proved to be an appropriate tool to evaluate
the technical efficiency level of individual DMUs with multiple inputs and outputs by
generating a single efficiency score (Charnes, Cooper et al. 1978, Seiford and Thrall 1990,
Coelli, Prasada Rao et al. 1998, Tone, Cooper et al. 1999, De Borger, Kerstens et al. 2002).
Then, a double bootstrap model (truncated regression model) of Simar and Wilson (2007) is
employed in the second stage of analysis to examine the impact of external factors on
efficiency scores of bus routes obtained in the first stage of analysis (details are shown in
Figure 3-1). To investigate the impact of external factors on the efficiency level of bus routes
in the second stage, one can employ a censored (Tobit) model (Nolan 1996, Tsamboulas
2006) or a linear model by ordinary least squares (OLS) (Thomas, Sally et al. 1994).
However, McDonald (2009) indicated that in case the efficiency scores are not generated by
a censoring process but are fractional data, Tobit estimation is inappropriate. Simar and
Wilson (2007) demonstrated that OLS is inconsistent in the second-stage regression, and
proposed single and double bootstrap procedures to overcome this issue. The double
bootstrap procedure can produce consistent inference and statistical properties and improve
statistical efficiency in the second-stage regression. In the double bootstrap model, the DEA
efficiency scores are dependent variables, while external variables within the stop-based
service areas of individual bus routes are independent variables.
This research uses both static DEA models (CCR and BCC model) and a network
DEA model for empirical analysis. The operational effectiveness of a bus route includes two
sub-processes: (1) the technical efficiency and (2) the service effectiveness. Thus, the
network DEA helps to evaluate the overall performance of bus routes by a single efficiency
score, accounting for the linkage between sub-processes. The DEA model was first
developed by Charnes, Cooper, and Rhodes (CCR) in 1978 and later modified by Banker,
Charnes and Cooper (BCC) in 1984. It builds upon the frontier efficiency concept first
elucidated in Farrell (1957). To better support the readers who have limited background on
the efficiency measurement concepts and the DEA models, this chapter briefly provides basic
information about the modelling processes of the DEA models. Therefore, this chapter first
introduces the efficiency measurement concepts of Farrell (1957), then presents details about
Methodology
Khac Duong Tran Page 30
CCR and BCC models, and the network DEA model. Furthermore, the sensitivity analysis of
DEA efficiency scores using a double bootstrap model is presented.
To clarify the work and usefulness of DEA in dealing with DMUs with multiple inputs
and outputs, this research compares the two transit productiveness indexes (transit work load
factor and transit service passenger transmission efficiency) with temporal efficiency scores
of a bus route (route 111) for a direction (inbound direction). The results of this comparison
are presented in Section 6.2.2. Thus, these two transit productiveness indexes are introduced
in this chapter.
Figure 3-1: The outlines of research methodology
This chapter is organised as follows: section 3.2 presents the efficiency measurement
concepts of Farrell, followed by the DEA models in section 3.3. Section 3.4 introduces
sensitivity analysis of DEA efficiency scores. Section 3.5 provides two basic transit
productiveness indexes. Finally, the chapter is concluded in section 3.6 where discussion is
provided.
Objectives
Objective 2:Evaluate and rank theperformance of bus routesof the case study
Objective 3:Examine the impact ofexternal factors on theefficiency scores of givenbus routes
Chapter 4: Methodology
CCR-DEA andBCC-DEA model
Transit productivenessindexes
Compare results
Network DEA model
Truncated regressionmodel: Double Bootstrapmodel
BC
C-D
EA
eff
icie
ncy
sco
res
of
node
2 (
dep
enden
t var
iable
s)
External variables withinthe stop-based serviceareas of bus routes
Indep
enden
t var
iable
s
ABS 2011 Census at theSA1 and Arc GIS
Methodology
Khac Duong Tran Page 31
Efficiency Measurement Concepts
The efficiency of an industry consists of two components: technical efficiency and
allocative efficiency (Farrell 1957). Technical efficiency is defined as the ability of an industry
to achieve maximal output using a given set of inputs. Allocative efficiency is defined as the
ability of an industry to use the inputs in optimal proportion, given certain constraints on prices
and the production technology. The combination of technical and allocative efficiency
provides a measure of total economic efficiency (Coelli, Prasada Rao et al. 1998).
Technical efficiency of an industry can be viewed from two perspectives: input-
oriented; and output-oriented measures. This section would provide the definition of
production function, input-oriented and output-oriented measures of an industry.
3.2.1 Production function
Consider an industry in which each DMU produces a vector of M outputs using a
vector of N inputs. The kth DMU produces outputs 𝑦𝑘 = (𝑦𝑘1, 𝑦𝑘2, … , 𝑦𝑘𝑀) from inputs 𝑥𝑘 =
(𝑥𝑘1, 𝑥𝑘2, … , 𝑥𝑘𝑁). The production function (technology) is described by the production
possibility set 𝑇 of feasible output vectors 𝑦 producible from input vectors 𝑥 (Viton 1997):
𝑇 = {(𝑥, 𝑦): 𝑦 𝑖𝑠 𝑓𝑒𝑎𝑠𝑖𝑏𝑙𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑓𝑟𝑜𝑚 𝑥}
The production technology also can be described using output and input sets:
• The input set, 𝐿(𝑦), consists of all input vectors, 𝑥, which can produce a given
output vector, 𝑦. The input set 𝐿(𝑦) is defined as:
𝐿(𝑦) = {𝑥: (𝑥, 𝑦) ∈ 𝑇}
• The output set, 𝑃(𝑥), includes all output vectors, 𝑦, which can be produced
using a given input vector, 𝑥. The output set 𝑃(𝑥) is defined as:
𝑃(𝑥) = {𝑦: (𝑥, 𝑦) ∈ 𝑇}
3.2.2 Input-Oriented Measure
The purpose of an input-oriented technical efficiency measure is to answer the
question: by how much can input quantities be proportionally reduced to produce the given
quantities of output?
From the original idea of Farrell, consider DMUs that use two inputs (𝑥1 and 𝑥2) to
produce an output (𝑦), under the assumption of CRS. Figure 3-2 graphically presents a given
DMU, defined by point P, and the corresponding production frontier (or isoquant), presented
Methodology
Khac Duong Tran Page 32
by SS’. The production possibility set, including P, will distribute from SS’ to the upper part.
All DMUs lying on SS’ (such as Q and Q’) use the minimal amount of inputs to produce output.
The line OP intersects SS’ at point Q. Therefore, the distance QP presents the amount of
inputs that could be reduced to produce a given output.
Figure 3-2: Input-oriented technical and allocative efficiencies (Source: Coelli, Prasada Rao et al. (1998))
The Farrell input-oriented technical efficiency of the DMU at point P is measured by
the ratio: TEi = OQ/OP. Its value varies from 0 to 1, presenting the level of inefficiency of this
DMU. If TEi equals to one, this DMU lies on the Isoquant (at point Q) and is efficient.
In addition, if the input prices are available, 𝑤1 and 𝑤2, for 𝑥1 and 𝑥2 respectively, it is
possible to estimate allocative efficiency (AEi) of this DMU: AEi = OR/OQ. The isocost line,
AA’, presents the minimal price of inputs to produce output of this production possibility set.
The ratio, AEi, indicates that although the DMU at point Q is technically efficient, it is inefficient
in terms of allocation. The distance, RQ, presents the reduction of cost that Q can be made
to get the highest value of AEi (equals to 1).
The total economic efficiency (EEi) of DMU operating at point P is calculated by the
ratio: EEi=OR/OP. Here, the distance, RP, represents the cost reduction of this DMU. EEi is
the combination of the technical and allocative efficiency: (OQ/OP) x (OR/OQ) = OR/OP =
EEi. The optimal production option of this production possibility set is point Q’, where all
technical, allocative, and economic efficiencies obtain the value of unity.
X1/Y
X2/Y
o
Production Frontier
or Isoquant- SS'
R
Q
P
Q'S'
S
A
A'
Methodology
Khac Duong Tran Page 33
3.2.3 Output-Oriented Measure
The output-oriented technical efficiency measure, in contrast to the above input-
oriented measures, will answer the question: by how much can the output quantities be
proportionally increased without increasing the quantities of input used?
Figure 3-3 graphically illustrates the case of the output-oriented measures of a DMU
(at point A) within a production possibility set distributing from the isoquant line, ZZ’, to the
lower part. It means that ZZ’ presents the upper boundary of this production possibility set.
Here, DMUs produce two outputs (𝑦1 and 𝑦2) using an input (𝑥), under the assumption
of CRS. DD’ presents the isorevenue line, if the price of outputs is available.
The Farrell output-oriented efficiency measures are calculated as follows:
The technical efficiency is the ratio: TEo = OA/OB
The allocative efficiency is the ratio: AE0 = OB/OC
The economic efficiency is presented as: EE0 = TE0 x AE0 = OA/OC
The optimal production option of this production possibility set is point B’, where all
technical, allocative, and economic efficiencies obtain the value of unity.
Figure 3-3: Output-oriented technical and allocative efficiencies (Source: Coelli, Prasada Rao et al.
(1998)
Data Envelopment Analysis (DEA)
DEA is a non-parametric method based on linear programming and optimisation. It
measures the relative efficiencies of production units or decision making units (DMUs) using
multi-inputs and multi-outputs. This is the important advantage of DEA over traditional
Y1/X
Y2/X
o
Production Frontier
or Isoquant- ZZ'
A
B
C
B'
D'
D
Z
Z'
Methodology
Khac Duong Tran Page 34
methods, which have limitations to evaluate efficiency of DMUs when multiple inputs and
outputs need to be considered. This is the reason why literature is abundant with its
application in banking (Mohamed Shahwan and Mohammed Hassan 2013, Depren and
Depren 2016), hospitals (Jat, Sebastian et al. 2013, Torabipour, Najarzadeh et al. 2014),
schools (Agasisti 2013, Rosenmayer 2014), electricity (Andrade, Alves et al. 2014, Azadeh,
Motevali Haghighi et al. 2015), and transportation (Lao and Liu 2009, Zhao, Triantis et al.
2011, Fancello, Uccheddu et al. 2014, Georgiadis, Politis et al. 2014).
The modelling process of DEA includes: a) identification of the production frontier (or
isoquant) of a set of comparable DMUs. Within a set of comparable DMUs, those exhibiting
the best use of inputs to produce outputs are identified, and would form an efficient frontier;
b) measures the efficiency level of each DMU by comparing its production function with the
production frontier (Cook and Seiford 2009).
Measuring the efficiency level of DMUs using DEA models, one may consider
technology under constant returns to scale (CRS) assumption (i.e. CCR model) or under
variable returns to scale (VRS) assumption (i.e. BCC model). Over the three decades since
the appearance of the first work of Charnes et al. in 1978, DEA has been developed by
researchers to substantially meet the actual demands. Therefore, there are different types of
the DEA model, such as the Additive model, Slacks-based measures, Russell measure, other
Non-radial models, upper-efficiency DEA, FDH model, Network model, etc. This research
employs basic DEA models (CCR and BCC model) because they were employed widely in
literature for empirical analysis of transit (refer to Table 2-2).
3.3.1 CCR- DEA Model
Charnes et al. (1978, 1981) introduced the CCR-DEA model to evaluate the efficiency
of each DMUj in a reference set of n DMUs. This model was built on the assumption of
constant returns to scale (CRS) of activities (see Figure 3-4a) and was divided into two
versions, input-oriented model and output-oriented model. While input-oriented model
examines the possibility of reducing inputs to produce a given output, output-oriented model
investigates the possibility of increasing outputs from the DMUs observed input bundle (Viton
1997).
Suppose that each DMUj (j=1, …, n) uses m inputs xij (i=1, …, m) to generate s outputs
yrj (r=1, …, s), and the vi and ur are the variable weights of inputs and outputs, respectively.
This method uses the known inputs and outputs of all DMUs in the given set of data
to determine the efficiency of one member, DMUj (j=1, …, n), which is assigned as DMU0.
Methodology
Khac Duong Tran Page 35
The efficiency of DMU0 is obtained by solving the following fractional programming problem
n times, each DMU once.
𝐦𝐚𝐱 𝒉𝟎 =∑ 𝒖𝒓 𝒚𝒓𝟎
𝒔𝒓=𝟏
∑ 𝒗𝒊𝒙𝒊𝟎𝒎𝒊=𝟏
Equation 3-1
Subject to:
∑ 𝑢𝑟 𝑦𝑟𝑗𝑠𝑟=1
∑ 𝑣𝑖𝑥𝑖𝑗𝑚𝑖=1
≤ 1; 𝑗 = 1, … , 𝑛
𝑢𝑟, 𝑣𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚.
Where ε is a “non-Archimedian infinitesimal”, which is smaller than any positive real
number. This means that all variables are constrained to positive values.
The objective is to obtain the input and output weights, vi and ur, as variables that
maximise the ratio of the DMU0, the DMU being evaluated. The value of h0 obtained from this
formulation represents the efficiency score of the DMU0. The constraints mean that h0*, the
optimal value of h0, should not exceed 1 for every DMU. In case h0*=1, this DMU places on
the efficiency frontier (Tone, Cooper et al. 1999).
To solve this problem, the theory of Charnes et al. (1962) is applied to convert this
fractional programming problem to the linear programming (LP) model with the changes of
variables 𝑡(∑ 𝑣𝑖 𝑥𝑖0) = 1𝑚
𝑖=1; 𝜇𝑟 = 𝑡𝑢𝑟 and 𝜗𝑖 = 𝑡𝑣𝑖. The above problem is replaced by the
following equivalent:
𝐦𝐚𝐱 𝒉𝟎 = ∑ 𝝁𝒓 𝒚𝒓𝟎𝒔𝒓=𝟏 Equation 3-2
Subject to
∑ 𝜗𝑖 𝑥𝑖0 = 1
𝑚
𝑖=1
∑ 𝜇𝑟 𝑦𝑟𝑗
𝑠
𝑟=1
− ∑ 𝜗𝑖 𝑥𝑖𝑗 ≤ 0 𝑗 = 1, … , 𝑛
𝑚
𝑖=1
𝜇𝑟, 𝜗𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚.
The dual problem of the linear programming (DLP) reproduced here for the input-
oriented model is as follows:
𝐦𝐢𝐧 𝜽 Equation 3-3
Subject to
Methodology
Khac Duong Tran Page 36
𝜃𝑥𝑖0 − ∑ 𝜆𝑗 𝑥𝑖𝑗 ≥ 0
𝑛
𝑗=1
𝑖 = 1, … , 𝑚
∑ 𝜆𝑗 𝑦𝑟𝑗 ≥ 𝑦𝑟0 𝑛
𝑗=1 𝑟 = 1, … , 𝑠
𝜆𝑗 ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗; 𝜃 𝑓𝑟𝑒𝑒
Here, the constraints of DLP require the activity (𝜽𝒙𝟎, 𝒚𝟎) to belong to the production
possibility set T, while the objective seeks the minimum 𝜃 that reduces the input vector 𝑥0
radially to 𝜃𝑥0 while remaining in T. In DLP, the aim is to look for an activity in T that
guarantees at least the output level 𝑦0 of DMU0 in all components while reducing the input
vector 𝑥0 radially to the smallest value. Therefore, it can be said that (𝑿𝝀, 𝒀𝝀) outperforms
(𝜽𝒙𝟎, 𝒚𝟎) when 𝜃∗ < 1. Regarding this property, the input excesses (𝒔𝒊− ∈ 𝑅) and the output
shortfalls (𝒔𝒊+ ∈ 𝑅) are defined as slack variables. The input and output slack vectors are
identified as follows:
𝒔𝒊− = 𝜽𝒙𝟎 − 𝑿𝝀, 𝒔𝒊
+ = 𝒀𝝀 − 𝒚𝟎 Equation 3-4
Therefore, the dual problem (DLP) for the input-oriented model can be expressed as
follows:
𝐦𝐢𝐧 𝜽 − 𝜺(∑ 𝒔𝒓+𝒔
𝒓=𝟏 + ∑ 𝒔𝒊−𝒎
𝒊=𝟏) Equation 3-5
Subject to
∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝜃𝑥𝑖0
𝑛
𝑗=1
𝑖 = 1, … , 𝑚
∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝑦𝑟0
𝑛
𝑗=1 𝑟 = 1, … , 𝑠
𝜆𝑗 , 𝑠𝑖+, 𝑠𝑖
− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗; 𝜃 𝑓𝑟𝑒𝑒
Where: (𝑠𝑖+, 𝑠𝑖
−) are output and input slack variables, respectively.
In the case of the output-oriented model, the dual problem can be expressed as
follows:
𝐦𝐚𝐱 𝝋 − 𝜺(∑ 𝒔𝒓+𝒔
𝒓=𝟏 + ∑ 𝒔𝒊−𝒎
𝒊=𝟏) Equation 3-6
Subject to
Methodology
Khac Duong Tran Page 37
∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝑥𝑖0
𝑛
𝑗=1
𝑖 = 1, … , 𝑚
∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝜑𝑦𝑟0
𝑛
𝑗=1 𝑟 = 1, … , 𝑠 𝜆𝑗 , 𝑠𝑖
+, 𝑠𝑖− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗 𝜑 𝑓𝑟𝑒𝑒
Where: (𝑠𝑖+, 𝑠𝑖
−) are output and input slack variables, respectively.
3.3.2 BCC-DEA model
Banker et al. (1984) introduced the BCC-DEA model, which exhibits various returns
to scale on the production frontier as shown in Figure 3-4b.
(a) Production frontier of CCR model (b) Production frontier of BCC model
Figure 3-4: Production frontier of (a) CCR and (b) BCC models
According to the BCC model, the production frontiers have piece-wise linear and
concave characteristics, which represent increasing, constant, and decreasing return-to-
scale.
𝐦𝐚𝐱 𝒉𝟎∗ =
∑ 𝒖𝒓 𝒚𝒓𝟎−𝒖𝟎𝒔𝒓=𝟏
∑ 𝒗𝒊𝒙𝒊𝟎𝒎𝒊=𝟏
Equation 3-7
Subject to:
∑ 𝑢𝑟 𝑦𝑟𝑗𝑠𝑟=1 − 𝑢0
∑ 𝑣𝑖𝑥𝑖𝑗𝑚𝑖=1
≤ 1; 𝑗 = 1, … , 𝑛
𝑢𝑟, 𝑣𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚. 𝑢0 𝑓𝑟𝑒𝑒 𝑖𝑛 𝑠𝑖𝑔𝑛
The linear programming equivalent of equation 3-7 is
𝐦𝐚𝐱 𝒉𝟎∗ = ∑ 𝝁𝒓 𝒚𝒓𝟎
𝒔𝒓=𝟏 − 𝝁𝟎 Equation 3-8
Subject to
Input
Ou
tpu
t
o
Production
Possibility
Set
Production Frontier
Input
Ou
tpu
t
o
Production
Possibility
Set
Production Frontier
Methodology
Khac Duong Tran Page 38
∑ 𝜗𝑖 𝑥𝑖0 = 1
𝑚
𝑖=1
∑ 𝜇𝑟 𝑦𝑟𝑗
𝑠
𝑟=1
− 𝜇0 − ∑ 𝜗𝑖 𝑥𝑖𝑗 ≤ 0 𝑗 = 1, … , 𝑛
𝑚
𝑖=1
𝜇𝑟, 𝜗𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚 𝜇0 𝑓𝑟𝑒𝑒
By duality, the input-oriented BCC model evaluates the efficiency of DMU0 (0=1, …,
n) by solving the linear program (Equation 3-9). In terms of evaluating the output-oriented
efficiency, this problem can be converted to maximising ratio 𝜑 like CCR model.
𝐦𝐢𝐧 𝜽𝟎 − 𝜺(∑ 𝒔𝒓+𝒔
𝒓=𝟏 + ∑ 𝒔𝒊−𝒎
𝒊=𝟏) Equation 3-9
Subject to
∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝜃0𝑥𝑖0
𝑛
𝑗=1
𝑖 = 1, … , 𝑚
∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝑦𝑟0
𝑛
𝑗=1
𝑟 = 1, … , 𝑠
∑ 𝜆𝑗 = 1 𝑛
𝑗=1 𝜆𝑗 , 𝑠𝑖
+, 𝑠𝑖− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗 𝜃 𝑓𝑟𝑒𝑒
Where: (𝑠𝑖+, 𝑠𝑖
−) are output and input slack variables, respectively. Input slack (𝑠𝑖−) is
the amount of input that a DMU could reduce to produce the same output, while output slack
(𝑠𝑖+) is the amount of output that a DMU could increase using unchangeable input. Therefore,
looking at the values of slack variables obtained from DEA-based empirical analysis, transit
practitioners may identify key factors (with slack variables > 0) greatly influencing the
performance of DMUs, and may quantitively indicate the input reduction and output increase
to improve the performance of inefficient DMUs.
3.3.3 Network DEA model
The traditional DEA models (CCR and BCC models) treat their reference technologies
as black boxes. Inputs are transformed in this box into outputs without modelling the actual
process explicitly (see Figure 3-5). One simply specifies what enters and what exits the box
(Färe and Grosskopf 2000).
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Khac Duong Tran Page 39
Figure 3-5: The aggregated technology (Source: Färe et al. (2000))
However, some production processes include several divisions that are linked to each
other like hospitals and electric power companies. Traditional DEA models neglect the
intermediate products and the linkage among those divisions. Thus, traditional DEA models
cannot interpret the performance of sub-technologies or components in the box as well as
evaluate the impact of division-specific inefficiencies on the overall efficiency of the
production process (Tone and Tsutsui 2009).
The network DEA model was first developed by Färe et al. (1996) to allow one to look
into the internal structure of a production process and evaluate the performance of the whole
technology as well as its component performance. The network DEA model then was
employed by researchers, such as Löthgren et al. (1999), who utilised this model to assess
the efficiency and productivity as well as customer satisfaction in Swedish pharmacies, Lewis
et al. (2004) focussed on the organisations with complex internal structure, and Tone et al.
(2009) proposed a slack-based network DEA model to evaluate divisional efficiencies along
with the overall efficiency of DMUs.
The network DEA model of Färe and Grosskopf (2000) is expressed as follows:
Assume that there are 𝑘 = 1, … , 𝐾 DMUs or observations of 𝑁 inputs and 𝑀 outputs,
(𝑥𝑘 , 𝑦𝑘) = (𝑥𝑘1, … , 𝑥𝑘𝑁, 𝑦𝑘1, … , 𝑦𝑘𝑀). The coefficients (𝑥𝑘𝑛, 𝑦𝑘𝑚) (𝑛 = 1, … , 𝑁; 𝑚 = 1, … , 𝑀; 𝑘 =
1, … , 𝐾) are required to satisfy certain conditions. These are:
(i) 𝑥𝑘𝑛 ≥ 0, 𝑦𝑘𝑚 ≥ 0, 𝑛 = 1, … , 𝑁; 𝑚 = 1, … , 𝑀; 𝑘 = 1, … , 𝐾
(ii) ∑ 𝑥𝑘𝑛 > 0, 𝑛 = 1, … , 𝑁.𝐾𝑘=1
(iii) ∑ 𝑥𝑘𝑛 > 0, 𝑘 = 1, … , 𝐾.𝑁𝑛=1
(iv) ∑ 𝑦𝑘𝑚 > 0, 𝑚 = 1, … , 𝑀.𝐾𝑘=1
(v) ∑ 𝑦𝑘𝑚 > 0, 𝑘 = 1, … , 𝐾.𝑀𝑚=1
The first conditions in (i) merely state that inputs and outputs are non-negative
numbers. The second requirement (ii) means that each input is used in at least one activity.
The third condition (iii) illustrates that each activity uses at least one input. The condition (iv)
x yThe production process
P
"Black box"
Methodology
Khac Duong Tran Page 40
requires that each output is produced by some activity, while (v) says that each activity
produces some output.
Assume that there is a production process involving three sub-processes or sub-
technologies (1, 2, and 3), a source (0), and an outlet (4) as illustrated in Figure 3-6. This full
network model includes a total of five nodes (0, …, 4), intermediate products, and allocative
inputs. A product is intermediate to the production system if it is both an input and an output
within the network. For instance, 𝑦13 is both an output of node 1 and an input of node 3. Not
all of the intermediate goods are necessarily consumed or used up within the network. They
may be the final output as well, such as 𝑦14 is the final output of node 1.
Figure 3-6: The network technology (Source: Färe et al. (2000))
Let the vector of (exogenous) inputs be denoted by 𝑥 and let 𝑥0𝑖 , 𝑖 = 1,2,3 denote the
amount of the vector of exogenous inputs that is allocated to node 𝑖.
The constraints for the allocation of the exogenous inputs:
𝒙 ≥ ∑ 𝒙𝟎𝒊
𝟑
𝒊=𝟏 Equation 3-10
Or
𝒙𝒏 ≥ 𝒙𝟎𝟏 + 𝒙𝟎
𝟐 + 𝒙𝟎𝟑 , 𝒏 = 𝟏, … , 𝑵. Equation 3-11
Let the vector of outputs produced by sub-process 𝑖 and delivered to node 𝑗 be
denoted by 𝑦𝑖𝑗
. In Figure 3-6, it can be seen that the total production of node 1 is ( 𝑦13 + 𝑦1
4 ),
where 𝑦13 is its output of intermediate products and 𝑦1
4 is its final output. Note 1 does not use
any intermediate products as inputs. However, sub-process or node 3 uses intermediate
products from node 1 and node 2 as inputs ( 𝑦13 , 𝑦2
3 respectively) as well as exogenous inputs,
𝑥03 . This node produces only final outputs, 𝑦3
4 . Given that each sub-process produces distinct
output vectors, 𝑦𝑗4 ∈ 𝑅+
𝑀𝑗, 𝑗 = 1,2,3, where 𝑀 = 𝑀1 + 𝑀2 + 𝑀3, the outlet or collection node 4
can be written as:
30 4x y
1
2
x0
1
x0
2
x0
3y
1
3
y2
3
y3
4
y1
4
y2
4
Methodology
Khac Duong Tran Page 41
𝒚 = ( 𝒚𝟏𝟒 , 𝒚𝟐
𝟒 , 𝒚)𝟑𝟒 Equation 3-12
If each node does not produce distinct outputs, total production can be written as the
sum ∑ 𝑦𝑗4
3
𝑗=1 of the individual nodes’ outputs. The appropriate number of zeros must be
added.
The piecewise linear or network DEA technology associated with 𝑘 = 1, … , 𝐾
observations may be written in terms of the output set as:
ᴃ(𝑥) = {𝑦 =( 𝑦14 , 𝑦2
4 , 𝑦)34 :
Node 3 (a) 𝑦𝑚 ≤34 ∑ 𝑧𝑘
3 𝑦𝑘𝑚, 𝑚 =34 1, … , 𝑀3,
𝐾
𝑘=1
(b) ∑ 𝑧𝑘3 𝑥𝑘𝑛 ≤ 𝑥𝑛0
3 , 𝑛 =03 1, … , 𝑁,
𝐾
𝑘=1
(c) ∑ 𝑧𝑘3 𝑦𝑘𝑚 ≤ 𝑦𝑚1
3 , 𝑚 =13 1, … , 𝑀1,
𝐾
𝑘=1
(d) ∑ 𝑧𝑘3 𝑦𝑘𝑚 ≤ 𝑦𝑚2
3 , 𝑚 =23 1, … , 𝑀2,
𝐾
𝑘=1
(e) 𝑧𝑘3 ≥ 0, 𝑘 = 1, … , 𝐾
Node 1 (f) ( 𝑦𝑚13 + 𝑦𝑚) ≤1
4 ∑ 𝑧𝑘1( 𝑦𝑘𝑚1
3 + 𝑦𝑘𝑚), 𝑚 =14 1, … , 𝑀1,
𝐾
𝑘=1
(g) ∑ 𝑧𝑘1 𝑥𝑘𝑛 ≤ 𝑥𝑛0
1 , 𝑛 =01 1, … , 𝑁,
𝐾
𝑘=1
(h) 𝑧𝑘1 ≥ 0, 𝑘 = 1, … , 𝐾
Node 2 (i) ( 𝑦𝑚23 + 𝑦𝑚) ≤2
4 ∑ 𝑧𝑘2( 𝑦𝑘𝑚2
3 + 𝑦𝑘𝑚), 𝑚 =24 1, … , 𝑀2,
𝐾
𝑘=1
(j) ∑ 𝑧𝑘2 𝑥𝑘𝑛 ≤ 𝑥𝑛0
2 , 𝑛 =02 1, … , 𝑁,
𝐾
𝑘=1
(k) 𝑧𝑘2 ≥ 0, 𝑘 = 1, … , 𝐾
Distribution of exogenous
inputs
(l) 𝑥𝑛01 + 𝑥𝑛0
1 + 𝑥𝑛01 ≤ 𝑥𝑛, 𝑛 = 1, … , 𝑁} Equation 3-13
In the network model (Equation 3-13), the three sub-processes can be identified. The
third, ᴃ3( 𝑥03 , 𝑦1
3 , 𝑦)23 , consists of expressions (a)-(e). The first, ᴃ1( 𝑥0
1 ), is given by (f)-(h), and
the last, ᴃ2( 𝑥02 ), by (i)-(k). Here 𝑧𝑘
𝑖 is the weight of input and output variables. It means that
the network model has three sets of intensity variables, compared to one set of such variables
in the standard DEA model. The network model has a distribution node that allows one to
study optimal distribution of the exogenous inputs among sub-processes, whereas the
standard model does not. Furthermore, the network model can model intermediate inputs
explicitly, so it allows practitioners to interpret the sources of inefficiency in the whole system.
Methodology
Khac Duong Tran Page 42
The framework for evaluating the performance or the operational effectiveness of a
transit system as shown in Figure 1-2 includes two sub-processes, the technical efficiency
and the service effectiveness. Bus routes composing a transit system are regarded as sub-
units in the production process of such a transit system. Therefore, measuring the
performance of bus routes needs to go the two such sub-processes. In which, the technical
efficiency represents the service production process, while the service effectiveness
represents the service consumption process of bus routes. The outputs in the first sub-
process will become the inputs in the second sub-process. From these analyses, the network
DEA (NDEA) model should be used for examining the performance of bus routes.
3.3.4 The need of using DEA model
The advantages and disadvantages of using the DEA approach for efficiency analysis
of a set of peer DMUs are excessive in the literature (Charnes, Cooper et al. 1978, Seiford
and Thrall 1990, Coelli, Prasada Rao et al. 1998, Tone, Cooper et al. 1999, De Borger,
Kerstens et al. 2002). Coelli et al. (1998) provided a comprehensive comparison between
four methods, including: (1) least-squares (LS) econometric production models; (2) total
factor productivity (TFP) indices; (3) DEA; and (4) SFA. Here, the advantage of DEA and SFA
(frontier methods) over traditional methods (LS and the engineering ratio approach) is clearly
indicated that it allows one to evaluate the technical efficiency level of individual DMUs with
multiple inputs and outputs by generating a single efficiency score. The main characteristics
of DEA are summarised as follows:
Advantages of DEA approach
• Compared with traditional econometric methods, DEA using standard
techniques of linear programming allows one to distinguish between efficient
and inefficient production, estimate the degree of inefficiency of each DMU
(efficiency scores), and identify sources of inefficiency. The computation, dual
variables, and clear interpretations are available in DEA (Seiford and Thrall
1990).
• Compared with the usual index number approaches, DEA does not require
one to prescribe weights for each input and output. Compared with the
parametric approach (SFA), DEA does not require the functional form for
production frontier estimation (Tone, Cooper et al. 1999).
• DEA is useful to evaluate the efficiency of non-profit entities operating in public
programs where the apparent market for outputs is unavailable, such as
schools and hospitals (Charnes, Cooper et al. 1978). This is because a
Methodology
Khac Duong Tran Page 43
variable that is neither an economic resource nor a product but is an attribute
of the production process can be used in the DEA model (Charnes, Cooper et
al. 1985, Seiford and Thrall 1990).
Limitations of DEA approach
• DEA could be sensitive to data errors. The production frontier function is built
up directly from the dataset, so any noise in data may influence the placement
of the DEA frontier.
• DEA could also be sensitive to variable selection. The exclusion of an
important input or output can lead to biased results.
• The DEA efficiency scores of DMUs are only relative to the best DMUs in a
given sample. The changes of sample size may reduce efficiency scores of
DMUs.
Based on the characteristics of DEA compared with other approaches, Coelli et al.
(1998) concluded that the SFA approach is only well-developed for single-output
technologies, and that in the non-profit service area where multiple-output production is
important and prices are difficult to define, the DEA approach should be applicable. This
research aims to evaluate the operational efficiency of bus routes with multiple outputs.
Therefore, DEA is selected for empirical analysis.
Sensitivity analysis in DEA
3.4.1 Sensitivity analysis of DEA efficiency scores
The DEA model only provides a mean of estimation of DMUs’ efficiency scores. Many
researchers thus employed truncated regression models in the second stage to analyse the
sensitivity of efficiency scores obtained in the first stage to factors possibly affecting the
efficiency level of DUMs. Factors used to test the sensitivity of efficiency scores are usually
socio-economic factors, regarded as environmental/external variables.
Some studies used the censored (Tobit) model in the second stage to evaluate the
performance of transit systems (Nolan 1996, Tsamboulas 2006), while others employed the
bootstrapping technique (Georgiadis, Politis et al. 2014). However, McDonald (2009)
indicated that in case the efficiency scores are not generated by a censoring process but are
fractional data, Tobit estimation is inappropriate, while ordinary least square (OLS) is a
consistent estimator. Interestingly, Simar and Wilson (2007) proposed single and double
bootstrap procedures, and demonstrated that both procedures can produce consistent
inference and statistical properties, and the double bootstrap procedure improves statistical
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Khac Duong Tran Page 44
efficiency in the second-stage regression. The bootstrapping technique thus will be applied
to the present study, in which DEA efficiency scores are dependent variables and
environmental factors are independent variables.
3.4.2 The bootstrap approach
Simar and Wilson (1998) were the first to introduce the bootstrap approach in DEA to
obtain statistical properties of the efficiency scores. Then they extended their approach to
consider the impact of environmental variables on efficiency (Simar and Wilson 2007). The
importance of the procedure introduced by Simar and Wilson (2007) is that it estimates the
bias-corrected efficiency scores of all DMUs, valid estimates for the parameters in the
regression model (Barros and Assaf 2009). Based on the work of Simar and Wilson (2007),
Barros and Assaf (2009) describe the bootstrap algorithm as follows:
i. Calculate the DEA output-orientated efficiency score ��𝒊 for each DMU, using
the linear programming technique.
ii. Estimate the truncated regression of 𝛿𝑖 on the environmental variable 𝑧𝑖, using
the maximum likelihood estimation method to provide (𝛽, ��𝜀) of (𝛽, 𝜎𝜀). Here,
the efficiency model is described as 𝛿𝑖 = 𝛽𝑧𝑖 + 휀𝑖 in which 𝛽 refers to a vector
of parameters with some statistical noise 휀𝑖, and 𝜎𝜀 is standard deviation of 휀𝑖.
iii. For each DMUi (𝑖 = 1, … , 𝑛), the following four steps (1-4) are repeated B1
times to produce a set of bootstrap estimates, {��𝑖,𝑏∗ , 𝑏 = 1, … , 𝐵1}.
1. Draw 휀𝑖 from the 𝑁(0, 휀��) distribution with left truncation at (1 − ��𝑧𝑖).
2. Compute 𝛿𝑖∗ = ��𝑧𝑖 + 휀𝑖.
3. Construct a pseudo data set (𝑥𝑖∗, 𝑦𝑖
∗) based on 𝛿𝑖∗, 𝛿𝑖
∗ and the actual data set,
where 𝑥𝑖∗ = 𝑥𝑖 and 𝑦𝑖
∗ = 𝛿𝑖𝑦𝑖/𝛿𝑖∗.
4. Compute a new DEA score, 𝛿𝑖∗, based on the pseudo data set.
iv. For each DMU, compute the bias-corrected efficiency score 𝛿𝑖 = 𝛿𝑖 − 𝑏𝑖��𝑠𝑖,
where 𝑏𝑖��𝑠𝑖 is the bootstrap estimator of bias obtained as: 𝑏𝑖��𝑠𝑖 =
1/𝐵1 ∑ 𝛿𝑖,𝑏∗ − ��𝑖
𝐵1𝑏=1 .
v. Use the maximum likelihood method to estimate the truncated regression of
𝛿𝑖 on 𝑧𝑖 providing estimates (𝛿, ��𝜀) of (𝛽, 𝜎𝜀).
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Khac Duong Tran Page 45
vi. Repeat the following three steps (1-3) B2 times to obtain a set of estimates
{��𝑏∗, ��∗, 𝑏 = 1, … , 𝐵2}.
1. For 𝑖 = 1, … , 𝑛, 휀𝑖 is drawn from 𝑁(0, ��) with left truncation at (1 − ��𝑧𝑖)
2. For 𝑖 = 1, … , 𝑛, compute 𝛿𝑖∗∗ = ��𝑧𝑖 + 휀𝑖
3. Use the maximum likelihood method to estimate the truncated regression of
𝛿𝑖∗∗ on 𝑧𝑖, providing estimates (𝛿∗, ��∗
𝜀)
vii. Use the bootstrap results to construct the confidence interval for the efficiency
scores.
Transit Productiveness Indexes
This section provides the two basic transit productiveness indexes: Transit work load
factor; and Transit service passenger transmission efficiency of Bunker (2013, 2015). The
DEA efficiency scores of a bus route will be compared with these two indexes in section 6.2.2
of chapter 6. Such comparison helps to elaborate the difference between the DEA efficiency
scores and transit productiveness indexes, validate the obtained results of the DEA model,
and demonstrate the significance of a DEA approach in dealing with multiple input and output
DMUs.
Bunker (2015) defined transit work load factor (passenger-km/space-km), of transit
route R within time window Z by:
𝑳𝑭𝑹,𝒁𝒘𝒐𝒓𝒌 =
∑ (𝒔𝒊 ∑ 𝑷𝑶𝑩,𝒌,𝒊)𝒎𝒌=𝟏
𝒏𝒊=𝟏
∑ (𝒔𝒊 ∑ 𝑷𝑴𝑺𝑳,𝒌)𝒎𝒌=𝟏
𝒏𝒊=𝟏
Equation 3-14
Where:
𝑠𝑖 = length of segment 𝑖 (km)
𝑃𝑂𝐵,𝑘,𝑖 = passenger on board kth service on segment 𝑖 (passenger)
𝑃𝑀𝑆𝐿,𝑘 = maximum scheduled load of kth service (passenger)
Bunker (2013) defined transit service passenger transmission efficiency of service 𝑘
in completing transit route R as:
𝜼𝑹,𝒌 =𝑻𝑺,𝒌,𝑹(∑ 𝑷𝑶𝑩,𝒌,𝒊𝒔𝒊)𝒏
𝒊=𝟏
𝑻𝒌,𝒏(∑ 𝑷𝑴𝑺𝑳,𝒌𝒔𝒊)𝒏𝒊=𝟏
Equation 3-15
Where:
𝑇𝑆,𝑘,𝑅 = scheduled time for kth service to complete route R (min)
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𝑇𝑘,𝑛 = actual time for kth service to complete route R (min)
It is clear that 𝐿𝐹𝑅,𝑍𝑤𝑜𝑟𝑘
describes how productive a service or line is over a time period
of interest with regard to vehicle loading, while 𝜂𝑅,𝑘 reflects the productiveness of a service or
line in terms of both loading and travel time used.
Discussion
Regarding transit, due to the constraint of capacity (for instance bus station capacity)
and operating vehicle speed (because of schedule travel time), the output (OTP, transit work,
average vehicle speed) might not have a constant increase when increasing the inputs (bus
size, service frequency etc.). Therefore, the constant return to scale is not always existent
and it needs to consider VRS so as to reflect this constraint.
In terms of the model orientation, as mentioned in the section 3.2 the technical
efficiency of an industry can be viewed from two perspectives: input-oriented; and output-
oriented measures. For CCR model, input-oriented and output-oriented models will yield the
same results regarding technical inefficiency. However, the input-oriented and output-
oriented BCC models may give different estimates when inefficiencies are present (Tone,
Cooper et al. 1999). The appropriate selection of input or output orientation in the DEA
analysis should be based on what is to be achieved from that analysis (Cook, Tone et al.
2014). If the objective is the identification of DMUs that are over-utilising resources, then the
input reduction should be the central focus. In this situation, the input-oriented DEA model
would be more appropriate than output-oriented model. On the other hand, if the output
enhancement is desirable objectives in an application, then the output-oriented DEA model
may be more appropriate to evaluate the performance of DMUs. The overall objective of this
study is to evaluate the performance of bus routes based on the operator’s perception
(maximising ridership and quality of service). Thus, the output-oriented measure is adopted
for empirical analysis.
This study aims to develop a framework for transit routes’ performance evaluation on
the basis of maximising the outputs. DMU is, thus, defined as the performance of each bus
route during a given hour (all bus services of the corresponding route in an hour for both
inbound and outbound directions). However, because one bus service may operate across
two different hours, bus services in a given hour are selected based on the schedule start
time.
Applying the proposed approach for data analysis of the case study in Brisbane,
Australia, this research first evaluates the temporal performance of each selected bus route
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Khac Duong Tran Page 47
across the working days of a week (which excludes public holidays). This work helps to gain
more understanding of the performance of individual bus routes without the impact of external
factors on the results obtained. In the second stage, NDEA models are employed for
comparing the performance of several bus routes within the bus network of the case study.
This helps to provide insights into the spatial and temporal performance and investigate the
internal reasons for inefficiency of given bus routes.
This study compares the two basic transit productiveness indexes developed by
Bunker (2013, 2015) with DEA efficiency scores obtained from temporal performance
analysis of a typical route for one direction (inbound direction). Results obtained from those
two approaches, using the similar variables for analysis, can be useful to indicate the
significance of the DEA approach for bus route performance analysis.
The double bootstrap approach of Simar and Wilson (2007), proven to be a reliable
tool for investigating the influences of external variables on DMUs’ efficiency scores, will be
used in the second-stage analysis. This helps to identify the external sources of inefficiency
of bus routes’ performance.
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4 Framework for Bus Route Performance Measurement
Introduction
The literature review section has shown that the performance of bus routes is
examined by a limited number of studies. In those studies, bus routes’ performance
measurement is conducted explicitly for particular performance concepts such as technical
efficiency, service effectiveness or operational effectiveness (Lao and Liu 2009, Georgiadis,
Politis et al. 2014). It thus cannot provide an overall and single measure for the production
process of bus routes. To provide an overall performance evaluation of bus routes, this
chapter aims to develop a network framework, which consists of two linked divisions (nodes):
technical efficiency (node 1); and service effectiveness (node 2).
Additionally, data used to examine the bus routes’ performance are broadly clustered
into two groups: (1) internal variables; and (2) external variables (Taylor and Fink 2003, Alam,
Nixon et al. 2015). The first group consists of bus performance indicators and relevant
variables within the control of a transit agency (such as route length, schedule, headway,
quality of service), while the latter refers to socio-economic and demographic factors beyond
the control of the transit agency (such as private car ownership, parking facility, transit
accessibility, road system, traffic condition, and employment distribution). In this research,
internal factors are employed in DEA-based data analysis to produce DMUs’ efficiency
scores, and external factors then are used in a truncated regression model. Thus, there is a
need to discuss and select appropriate internal and external variables for bus route
performance measurement.
Section 4.2 identifies the study goals needing to be achieved. Thereafter, section 4.3
presents the proposed framework for bus route performance measurement, which is followed
by the selection of corresponding inputs and outputs in section 4.4, and the selection of
external variables in section 4.5. Finally, the chapter concludes in section 4.6 where
discussion is given.
The Study Goals Needed To Be Achieved
To develop an appropriate DEA-based framework for efficiency analysis of a set of
DMUs, identifying the study’s goals is of importance, because these goals substantially
influence the model choice (input or output orientation) and input and output variable
selection. For example, Lao et al. (2009) selected the total number of passengers as output,
because their study goal was to measure the productivity of supply. Barnum et al. (2008)
Framework for Bus Routes Performance Measurement
Khac Duong Tran Page 49
aimed to identify the variations of bus route performance regarding operational effectiveness,
so ridership, span of service, average frequency, maximum frequency, and on-time
performance were selected as outputs in their DEA model (refer to Table 4-1)
In this research, the aim is to compare the operational effectiveness of several bus
routes within the case study in Brisbane on the basis of transit operators’ perception. This
means that the aim is to optimize the service outputs and assist transit agencies in identifying
the underlying reasons for inefficient performance of some bus routes. Therefore, the output-
oriented NDEA model is adopted.
Develop the Framework for Bus Route Performance Measurement
As an individual route is a subunit within a system, its performance evaluation should
follow the framework of transit system performance evaluation (see Figure 1-2), which
consists of three separate dimensions: technical efficiency; service effectiveness; and
operational effectiveness. To evaluate the overall performance of bus routes, this research
develops a network framework which consists of two linked divisions: (1) Technical efficiency;
and (2) Service effectiveness. Service outputs are intermediate variables in this framework
(which are output variables of technical efficiency measure and input variables of service
effectiveness measure). By this network framework, the operational effectiveness measure
accounting for both divisions (1 and 2) generates the overall efficiency scores of bus routes.
At the same time, divisions 1 and 2 can be evaluated separately to provide insights into the
performance of the bus route production process.
Considering the performance of a route, it can be seen clearly that service outputs
include two major groups of performance elements: quantity of service (such as vehicle-km,
seat-km, and space-km); and level of service (such as operating speed, schedule reliability,
and safety) (Vuchic 2007). In these, performance elements regarding level of service greatly
affect transit users’ travel decisions. Therefore, the proposed framework for transit route
performance evaluation considers both quantity of service and level of service (see Figure
4-1).
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Figure 4-1: Framework for a transit route performance evaluation
Inputs and Outputs Selection for Bus Routes
After building up the appropriate framework for bus route performance evaluation, the
selection of input and output variables and the combination of those inputs and outputs play
a crucial role in achieving the accurate results. Hence, this section discusses and selects the
appropriate variables for bus route performance measurement.
4.4.1 Some crucial recommendations for input and output variables selection, and
the combination of inputs and outputs in DEA
Rohácová et al. (2015) noted some qualifications in selecting inputs and outputs, and
the combination among those variables as follows:
• All input and output variables should characterise the operation of DMUs.
• The availability of the data required.
• The combination of inputs and outputs ensures the suitability of variables with
respect to the economic purpose of technical efficiency (the production process).
• The number of DMUs needs to be at least three times greater than the total
number of inputs and outputs (Cooper, Seiford et al. 2007).
• Uniqueness of information contained in inputs and outputs, and high information
value of the relationship among them.
The last point means that all individual inputs and outputs should not duplicate
information, and there should be strong relationship between inputs and outputs. The outputs
should be generated directly by the respective inputs. Thus, the number of inputs or outputs
should be reduced based on the correlation analysis before using in DEA model. Table 4-1
presents several typical studies for bus route performance evaluation using DEA models in
Service
Inputs
Service
Consumption
Service
Outputs Service effectivenessTechnical efficiency
Operational effectiveness
Quantity of Service
Level of Service
(for consumption process)(for production process)
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literature. In these, the selection of input and output variables is based on the aforementioned
recommendations and the study goals.
Table 4-1: An overview of inputs and outputs selection for bus route performance evaluation
Studies Models
used
Input variable Output variable Purpose of In-Output selection
Lao et al.
(2009)
1,2Output
orientation
BCC-DEA
model.
1Operation time;
Round trip distance;
Number of bus stops.
2Commuters who use
buses;
Population 65 and
older;
Persons with
disabilities.
1Total number of
passengers.
2Total number of
passengers.
1Operational efficiency measures the
productivity of supply. In the absence
of actual costs (labour, fuel, others),
this study used those inputs as
operational costs. The total number
of passengers represents the total
revenue.
2Spacial effectiveness measures the
benefit of demand (service
consumption).
Barnum
et al.
(2008)
1Output
orientation
CCR- DEA
model.
1Seat kilometres (SK);
Seat hours (SH);
2Population density;
Population; Title 6
Routes (at least 1/3
route length in zones
with high percentage
of minority
population); Key
Routes (the most
productive routes).
1Ridership;
Span of service;
Average frequency;
Maximum frequency;
On-time performance
(OTP).
1Assist the agency management in
identifying differences in route
performance. Inputs are the
resources that supply the transit
service. Outputs are the use and the
quality of service.
2Adjusting the raw DEA scores to
account for the environmental
influences on riders and OTP.
Sheth et
al.
(2007)
Network
DEA model.
1The inputs for the
provider node:
Headway; Service
duration; Costs;
Number of
intersections; Number
of priority lanes.
The environmental
variables:
Accessibility factor;
Parking space
availability factor;
Population density
1,2The outputs for
the provider node
and inputs for the
passenger node:
Vehicle-miles;
Schedule reliability;
Average travel time.
2The outputs for the
passenger node:
Passengers-miles
The externalities:
Number of accidents;
Emissions; Noise
Taking into consideration the service
providers, the users, and the societal
perspectives.
1Inputs are scarce resources used
and outputs are service provided for
society (the quantity and quality of
service)
2Output relates to service
consumption and the societal
influences.
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factor; Connectivity
factor; Comfort
standards factor.
pollution; Resources
degraded.
Georgia-
dis et al.
(2014)
DEA model
and
Bootstrap
model.
1Model 1: Length;
Span of service;
Vehicles. (output
orientation)
2Model 2: Length;
Span of service;
Vehicles. (output
orientation)
3Model 3: vehicle-km;
Vehicles. (input
orientation)
1Revenue seat-km;
2Passengers
3Passengers
1Model 1 explores the productivity of
the available resources allocated to
each bus line (cost efficiency).
2Model 2 investigate the relationship
between available supply and
observed demand.
3Model 3 explores the possibilities of
balancing supply with observed
demand.
1, 2, 3: models used for data analysis
4.4.2 Selection of inputs and outputs
There are two divisions in the whole production process of a bus route (see Figure
4-1), the service production and the service consumption. In the first process, service inputs
are defined as all resources needed to produce service outputs (quantity of service and level
of service) for a community. Then, in the next process, service outputs (regarded as
intermediate products) are used as inputs, while observed demand is considered as the final
output.
Service inputs include labour, vehicle, operational cost, and bus route infrastructure
such as the length of route, bus stops, bus lane priority, and signalised intersections along
the bus routes. Service outputs that a bus route offers to a community include service
availability (such as vehicle-km, seat-km, and space-km) and performance elements related
to the level of service (such as on-time performance (OTP) and average operating speed)
(Vuchic 2007). Finally, the service consumption is observed demand, such as the total
number of passengers, passenger-km or passenger-mile. However, some service inputs
such as fuel consumption, operating cost, and maintenance cost are unavailable at the route
level of the case study. Therefore, this research uses proxies to refer to those service inputs.
Based on the proposed framework in Figure 4-1 and relevant arguments in the
literature review section of Chapter 2, the corresponding inputs and outputs are adopted and
shown in Table 4-2. The rationale behind this selection of inputs and outputs is as follows:
Technical efficiency: the output variables should present service outputs offered by
the operator, which include variables regarding quantity of service and level of service.
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However, to ensure the close relationship between inputs and outputs, this research employs
quantity of service only for a technical efficiency measure (division 1). Here, space-km is
selected as an output because space-km provided in a given period of time (an hour, peak
period, a day) represents the offered quantity of service outputs, accounting for the vehicle
capacity. Space-km is estimated by equation 4-1:
𝑺𝒑𝒂𝒄𝒆 − 𝒌𝒎 = ∑ 𝑪𝒌𝒍𝒌𝒏𝒌=𝟏 Equation 4-1
Where: 𝐶𝑘 is the number of spaces (seat and stand) of a bus vehicle used for service
𝑘; 𝑙𝑘 is the route length travelled by service 𝑘; 𝑛 is the number of services performed within a
given period of time.
The relevant inputs to the technical efficiency should correspond to the resources
used by the operator to produce the quantity of service (space-km). Here, route length,
Busway length, service duration, and number of services are considered as inputs to the
technical efficiency measure. Route length and Busway length is a proxy for the operation
and maintenance resources (Sheth, Triantis et al. 2007, Lao and Liu 2009, Georgiadis, Politis
et al. 2014). Number of services is a proxy for the number of vehicles and drivers used (Lao
and Liu 2009, Georgiadis, Politis et al. 2014). Service duration is a proxy for the fuel
consumption and operating expenses (information system and working hours etc.) (Lao and
Liu 2009, Georgiadis, Politis et al. 2014).
Service effectiveness: the outputs should represent the service consumption. Here,
we select Transit work and OTP as outputs. Transit work by definition represents the service
consumption of the community. Regarding schedule reliability, OTP is one of the most widely
used reliability measures in transit sector (Kittelson, Associates et al. 2003, Chen, Yu et al.
2009, Ryus, Danaher et al. 2013, Qu, Oh et al. 2014). The TCQSM (2003, 2013) defined
OTP as the percentage of trips arriving at the stops on time (less than five minutes later and
less than one minute earlier than scheduled arrival). However, Camus, Longo et al. (2005)
indicated that the TCQSM method for estimation of transit schedule reliability (OTP) was not
be able to consider the amount of delay, and proposed a new performance measure called
weighted delay index to address this issue using the automated vehicle location (AVL) data
collected in Trieste, Italy. This method allows one to both estimate the OTP and the amount
of delay of transit trips. This study uses the OTP defined by TCQSM (2013) as an output in
the DEA models because it was widely used in the preceding studies (Sheth, Triantis et al.
2007, Barnum, Tandon et al. 2008).
Note: OTP is generally used as a variable of service output (Sheth, Triantis et al.
2007). We argue that transit operators, in principle, desire to maximise the OTP to increase
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the transit quality of service. Therefore, we consider OTP as the service consumption output
variable. Space-km and average vehicle speed are corresponding inputs for this dimension.
For the service effectiveness measure, this research uses average vehicle speed as
the second variable of service outputs along with space-km. The rationale behind this
selection is that average vehicle speed represents the time efficiency of offered services
along the corresponding bus route, and is one of the most important performance elements
determining bus level of service (Vuchic 2007). The higher average vehicle speed is, the
more attractive to users the bus route is. In literature, Sheth et al. (2007) also used average
travel time (with unit: hour-1) as a variable of service outputs, and Zhao et al. (2011) built up
a network framework to evaluate the performance of a transportation network, which uses
average speed as one of the inputs of user node. Thus, average speed in both theory and
practice was widely used to present service outputs regarding level of service.
The operational framework for a bus route is depicted in Figure 4-2. There are two
nodes (1 and 2) in the overall production process of a bus route, including production process
(node 1) and consumption process (node 2). The production process is to produce the
availability of bus service, while the consumption process transfers space-km, average
vehicle speed to final outputs (transit work, OTP). Here, space-km is used as an
intermediate/linked variable of those two nodes (which is an output of node 1 and then
becomes an input of node 2). The detailed definition of all variables is given in the notes
below Table 4-2.
Figure 4-2: The operational framework for a bus route performance evaluation
Ave. vehicle speed
Space-Km
OTP
Transit work
Pro
du
ctio
n p
roce
ss
Co
nsu
mp
tio
n p
roce
ss
Route length
Number of service
Service duration
Service Inputs
(resources)
Service
Consumption
Service
OutputsService effectivenessTechnical efficiency
Operational effectiveness
Busway length
Node 1
Node 2
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Table 4-2: Selection of inputs and outputs for bus route performance measurement
Model Performance
dimension
Orientation Returns
to scale
Input variables Output
variables
Node 1
(model 1)
Technical efficiency Output VRS Route length;
Service duration;
Number of services;
Busway length
Space-km
Node 2
(model 2)
Service
effectiveness
Output VRS Space-km;
Average vehicle speed
Transit work;
OTP
Notes:
1- Space-km (p-km): bus vehicle capacity multiplied by total kilometres traversed by
vehicle on the corresponding route and summed for all services that start within a
given hour (see equation 4-1).
2- Service duration (hour): total actual travel time taken by all services on the route
during a given hour.
3- Number of services: total number of services operated on the route in a given hour
for both inbound and outbound directions.
4- Busway length (km): length of Busway (roadways that are accessible by buses
only) used by bus vehicles on the route.
5- Average vehicle speed (km/h): length of route divided by the average travel time
taken by all completed services on the route during a given hour.
6- Priority lane (%): percentage of Busway length to total route length.
7- Stop spacing (km/stop): length of bus route divided by total number of stops on
the route.
8- Signalised intersection spacing (km/intersection): the length of bus route divided
by total number of signalised intersections on the route.
9- Vehicle-km (km): the total number of kilometres travelled by all the vehicles
operating on that route.
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10- OTP/ Schedule reliability (%): the proportion of observed services that arrive at
the destination on time, where “on time” is less than 1 min early or less than 5 min
later than the scheduled arrival (Ryus, Danaher et al. 2013).
External Variables (EVs) Selection
External variables (EVs) should be the potential factors that greatly affect the final
outputs (Transit work, OTP), because this model aims to maximise outputs. Miller et al. (2009)
categorised external factors, which can influence the transit ridership among urbanised areas
in the United States (USA), into four divisions: (1) regional geography (area of urbanisation,
population, population density, and regional location); (2) metropolitan economy
(personal/household income, income distribution, and unemployment level); (3) population
characteristics (age distribution, percent of population in college, and percent of population
in poverty); and (4) auto/highway system (congestion level, fuel prices, the precent carless
households, vehicle per capita, and parking availability). For DEA-based transit performance
evaluation, only a few studies used population within the service area of bus systems or
routes to explain the variation of transit ridership (Chu, Fielding et al. 1992, Kerstens 1996,
Tsamboulas 2006, Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao and Liu
2009). Therefore, the influences of external factors on the efficiency level of bus routes were
not studied sufficiently.
In this research, EVs are selected, broadly based on the relevant literature and data
availability, comprising of population for ages, car ownership, and individual income. These
EVs are relevant to ridership of bus routes, which is of primary focus. The presented approach
can be repeated with additional EVs related to OTP, if available.
Population (Pop) is clustered into the following four typical groups, which generally
have different patterns of travelling, so the clustering helps to identify the impact of each age
group on transit demand:
• POPC: Pop under 18, which includes children and school students;
• POPYA: Pop from 18 to 35, which includes senior students and young adults)
• POPOA: Pop from 36 to 64, which includes older adults; and
• POPP: Pop 65 and older, which includes pensioners.
The corresponding population density of the above age groups is labelled as follows:
• PODC: average Pop density of age group under 18;
• PODYA: average Pop density of age group from 18 to 35;
• PODOA: average Pop density of age group from 36 to 64; and
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• PODP: average Pop density of age group 65 and older.
Regarding the individual income (Pop 15 and older only), this research clusters it into
three major groups, based on the taxable incomes applied to Australian residents for tax
purposes (ATO 2017) and Australia community profile (Profile.id 2017):
• LI: Low income with income under 400 AUD per week;
• MI: Medium income with income between 400 to 1500 AUD per week; and
• HI: High income with income over 1500 AUD per week.
Car ownership (CO) is given by cars per capita, in which Pop 18 and older is taken
into account only because those in that category are eligible to drive a car.
Discussion
AFC data is a rich source of data offering opportunities for insights into the bus route
performance. However, there are still some limitations for mining this data. One of the
drawbacks of AFC data is that if there is no passenger boarding or alighting at a given bus
stop, the boarding or alighting time cannot be recorded leading to the missing information of
bus arrival time at this stop. Therefore, using AFC data to calculate the OTP at intermediate
stops along a bus route may result in different values for different services, although those
services have similar operation in reality. Furthermore, OTP at the destination is of
importance because it can positively impact on the arrival time of a bus at previous stops.
Thus, this research estimates the OTP at the destination (final stop) of bus routes only. In
other words, the value of OTP at the final stop represents the OTP of the whole service.
According to TCQSM (2013), on-time at the intermediate stops means that the arrival
time of a bus is less than 1 minute early and 5 minutes late compared to the scheduled time,
and at the destination on time is less than 5 minutes late only. In other words, the on-time at
the destination accounts for all early services. This research estimates the OTP at the
destination of a bus route only, so it should apply the standard of less than 5 minutes late for
OTP estimation. However, the actual situation in Brisbane is that limited parking space is
available in bus stations for early arrival of buses. This research, thus, adopts less than 1
minute early and 5 minutes late at the destination as on-time.
The framework for bus route performance evaluation was proposed in this chapter
with appropriate inputs and outputs. To run this framework, it needs a process for extracting
bus performance indicators from AFC data, and a suitable method to obtain accurate EVs’
data for a single bus route of the case study in Brisbane. Therefore, Chapter 5 presents the
data collection process, for empirical analysis in Chapters 6 and 7.
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5 Data Collection
Introduction
Brisbane, the case study area in this research, is the capital of Queensland, Australia.
The Brisbane Statistical Division has a population of 2.4 million people (around 49% of
Queensland’s population is in Brisbane) (ABS 2016). The transit network in Brisbane
comprises more than 380 km of heavy rail and numerous bus lines, including three
segregated busway lines: South East Busway; Northern Busway; and Eastern Busway (a
total of 25 km of busway was built up to 2011) (Yang and Pojani 2017). Figure 5-1 illustrates
the high frequency bus routes along major corridors in Brisbane. Here, the backbone of the
bus system is composed of two continuous Bus Rapid Transit corridors; the South East
Busway (see spine route 111 for example) and the Inner Northern Busway (see spine route
333 for example). The AFC smart card was used on 86.6 percent of all trips taken across the
TransLink Division transit network during the second quarter (Q2) of the financial year
2016/2017 (TransLink 2017). The case study sample comprises 52 key bus routes in the
South East Queensland (SEQ) bus network, which connect suburban areas with the Brisbane
central business district (CBD).
Regarding internal variables, bus performance indicators are drawn from AFC data
supplied by the TransLink Division of the Queensland Department of Transport and Main
Roads, Australia. AFC data of one week (working days only), from 19th to 23nd August 2013,
is employed for the empirical data analysis in this research. Other relevant data such as route
length, section length between stops, and timetable, were obtained from the TransLink
website (http://translink.com.au). On the other hand, external variables are collected in the
service corridor of each bus route using Geographic Information System (GIS) and database
of the Australia Bureau of Statistics (ABS). Therefore, this chapter introduces the process for
extracting key bus performance indicators from AFC data, and external variables of bus
routes from ABS using GIS.
Section 5.2 presents the process for internal variable collection. The collection of
external variables is represented in section 5.3. Finally, the chapter is concluded in section
5.4, where discussion is presented.
Internal Variables
AFC data from TransLink provides details of individual passenger journeys. This
includes the following fields:
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• Operator, operation date (date corresponding to the bus operation);
• Smart card ID (encrypted at the passenger level);
• Route (bus route used by the passenger);
• Direction (inbound or outbound);
• Schedule start (the schedule start time of corresponding trip);
• Actual start (actual timestamp of bus departing from origin stop);
• Actual end (actual timestamp of bus arriving at terminus stop);
• Boarding and alighting stop (by passenger, IDs of stops used to board and alight);
• Boarding and alighting times (timestamps when passengers touched on when
boarding and touched off when alighting);
• Vehicle ID (encrypted ID of bus vehicle);
• Journey ID (encrypted ID of bus trip); and
• Ticket type (type of smart card used by passengers such as adult, student or
child).
Figure 5-1: Brisbane, Australia high frequency bus network map (Source: http://translink.com.au)
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The smart-card data provides information that can be used to reconstruct a vehicle’s
service performed along all consecutive segments composing a transit route during a given
time window (a day or an hour).
Steps implemented to extract needed inputs and outputs are shown in Figure 5-2,
where inputs and outputs are extracted utilising the smart-card data fields:
1. Based on the raw smart-card data, data for a given route and direction (inbound
and outbound) is separated.
2. Based on the working day calendar and month index, data for a given month and
working days only are extracted. Here, working days exclude school holidays.
3. Based on the day index, data for a given working day are extracted. Data for a
given vehicle will then be extracted on the basis of vehicle index.
4. Based on the schedule starting time index, data for each service (revenue trip) of
a given vehicle are extracted.
5. Service data for a given segment of bus route are extracted on the basis of
alighting stop index and boarding stop index. Transit work can then be calculated
for each service based on segment data (see Equation 2-1).
6. Based on the actual starting time (𝑡0 ) and actual ending time (𝑡1 ) index of each
service, the actual travel time (∆𝑡 ) of a given service is calculated: ∆𝑡 = 𝑡1 − 𝑡0 .
Comparing the arrival time of a vehicle at bus stops and destination with
scheduled time yields the OTP indicator.
7. The total number of passengers equals the total number of boarding passengers
or alighting passengers. At each bus stop, smart-card data can provide the first
and last alighting time as well as the first and last boarding time, if there are
passengers boarding and alighting. This is used to determine a proxy dwell time
(Widana Pathiranage, Bunker et al. 2013), and the time that a service arrives at a
given stop.
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Figure 5-2: Flowchart for extracting transit route performance indicators
Based on the steps in Figure 5-2, performance indicators of the 52 case study bus
routes with both inbound and outbound directions have been extracted from the raw smart-
card data during a period of one working week, from Monday 19th to Friday 23rd August 2013.
Table 5-1 summarises the statistical description of the inputs and outputs of 52 bus routes
for a morning peak hour (7:00 to 8:00), an afternoon peak hour (16:00 to 17:00), and an off-
peak hour (10:00 to 11:00) for Wednesday 21st August 2013.
Raw Smart-card data
Data for route and
direction
Data for a month and
working days only
Data for a given
working day
Data for a given
vehicle
Data for a given
service of vehicle
Data for a given
segment of route
Transit work of
service
Total passenger
Average dwell
time
On time
performance
Route
Direction
Month
Working calendar
Working calendar
Vehicle Index
Schedule starting time Index
Smart-card ID IndexActual starting time
Actual ending time
Travel time
Alighting stop Index
Boarding stop Index
Alighting time
Boarding time
First and last alighting time
First and last boarding time
Inputs and
outputs extracted
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Table 5-1: Statistical description of the inputs and outputs of the 52 bus routes for a morning and an
afternoon peak hour, and an off-peak hour of 21 August 2013
Variables Mean Minimum Maximum Standard deviation
Route length (km) 20.22 9.30 29.46 5.37
Busway length (km) 4.7 0.81 17 3.87
Signalised intersection spacing
(km/intersection)
0.88 0.27 5.67 0.96
Stop spacing (km/stop) 0.64 0.29 1.55 0.33
Lane priority (%) 24.18 4.74 100 21.3
Morning peak hour (7:00 to 8:00)
Service duration (hour) 5.2 1.05 13.43 3.33
Number of services 5.87 1 18 4.08
Space-km 8177.39 1891.12 28383.81 6449.16
Average vehicle speed (km/h) 21.69 14.69 36.09 5.06
OTP (%) 44.42 0 100 31.96
Transit work (p-km) 1808.29 113.49 9668.89 1984.26
Afternoon peak hour (16:00 to 17:00)
Service duration (hour) 5.12 0.3 15.50 3.55
Number of services 5.62 1 15 3.86
Space-km 7982.8 1303.61 31916.36 6556.13
Average vehicle speed (km/h) 22.35 14.26 62.08 7.51
OTP (%) 42.48 0 100 26.99
Transit work (p-km) 1569.59 10.26 8285.18 1956.81
Morning off-peak hour (10:00 to 11:00)
Service duration (hour) 3.38 0.72 9.1 2.15
Number of services 4.35 1 10 2.83
Space-km 6064.07 1170.89 20980.54 4618.95
Average vehicle speed (km/h) 25.86 17.42 53.6 7.78
OTP (%) 40.7 0 100 33.54
Transit work (p-km) 801.18 61.7 4901.13 958.8
External Variables
EVs are collected in the service corridor of a single bus route using GIS and ABS
2011 Census. There are two ways to generate this service corridor:
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• Stop buffering (Murray, Davis et al. 1998); and
• Route buffering (Peng and Dueker 1993, Peng and Dueker 1995).
The first one generates the buffer zones around bus stops, while the later creates the
buffer zone along the entire route with a certain access distance. The access distance of 400
metres is normally used because it is widely regarded as the most appropriate walking
distance for bus riders (Horner and Murray 2004, Burke and Brown 2007, Ryus, Danaher et
al. 2013). It is clear that the stop-level buffer is the more appropriate basis for estimating the
service corridor of a given transit route, because stops are the actual points where
passengers access this route (Horner and Murray 2004). Thus, stop buffering will be applied
in this research to generate service corridor of each bus route.
Using GIS tool, the buffer zones around all bus stops of a given route are first
generated by 400 metre radius circles with centres being bus stops. The service corridor of
this bus route then is formed by merging overlapping buffer zones into a single polygon.
Figure 5-3: An example of a bus route service area
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Figure 5-3 presents the service corridor of a typical bus route (route 111) of the case
study. Here, the buffer zones of some close stops on the upper part of the map are merged
into a single polygon, so this helps to avoid the double counting of service areas around the
bus stops. The service corridor of a bus route is then overlaid with the census block group
map to determine the intersection between them. In this research, the ABS 2011 Census map
at the Statistical Areas Level 1 (SA1) is used to collect EVs within the service corridor of given
bus routes. The SA1s have generally been designed as the smallest unit for the release of
census data. Each SA1 region has a unique identification (ID).
Based on the boundaries of SA1 regions, the bus service corridor is divided into
several pieces of land (POL) (see Figure 5-4). Each POL belongs to a certain SA1 region
which stores the database of population for ages, individual income for ages, car ownership,
land area, education and employment, etc. Using GIS, a POL inherits the ID and features of
a SA1 region that covers it. Thus, the SA1 data of a given POL can be estimated based on
its area (which is obtained by GIS) and the available data of SA1 region. This is the basis for
the estimation of EVs for the whole service corridor of a bus route. For example, Figure 5-4
shows that POLs 5 and 6 inherit the ID and SA1 data of region 6.
Figure 5-4: An example of pieces of land (POL) within the service corridor of bus route
The population (Pop) variables a of a given route are calculated within its service
corridor using the ABS 2011 (SA1) Census data as follows:
Boundaries of SA1Regions
POL 1
POL 3
POL 2
POL 4 POL 5POL 6
POL 7
POL 8
Region 1
Region 4
Region 2
Region 5
Region 6
Region 3
Region 7
Service corridor
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• Identify the area and the SA1 population density for different ages of each POL
within the service corridor of a bus route;
• Estimate the Pop of different age groups (under 18, age 18-35, age 36-64, and
age 65 and over) of each piece within the service corridor based on its area and
corresponding population density; and
• Calculate Pop of different age groups (under 18, age 18-35, age 36-64, and age
65 and over) of a single route by summing Pop values of all POLs within its service
corridor.
From the Pop obtained for each age group, the average Pop density of each age
group can be calculated by the ratio of Pop to the area of service corridor of a bus route (the
sum of areas of all POLs within the service corridor).
For income variables, based on the individual income data in ABS 2011 Census (for
age 15 and over), Pop density for different income levels are identified for each SA1 census
region. This SA1 Pop density then is used to calculate income variables of each bus route as
follows:
• Estimate the Pop of different income levels (low income, medium income, and
high income) of each POL within the service corridor based on its area and
corresponding SA1 Pop density;
• Calculate Pop of different income levels (low income, medium income, and high
income) of a single route by summing Pop values of all POLs within its service
corridor; and
• Calculate the percentage of each income group by the ratio of its Pop to the total
Pop of all income groups.
Finally, car ownership is determined by the ratio of the total number of cars to the Pop
with ages 18 and over in the service corridor of a given route. In this case, the Pop (age 18
and over) is estimated in similar way with the afore-mentioned Pop variable. The total number
of cars is determined as follows:
• Identify the car density of each SA1 census region. Car density of a given SA1
region is calculated based on its area and SA1 car ownership available in the ABS
2011 Census.
• Identify the number of cars within each POL based on its area and the SA1 car
density.
• Calculate the total number of cars of a route by summing the number of cars of all
POLs within the service corridor.
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Table 5-2a and Table 5-2b show the statistical description and correlation analysis
results of EVs used for the second stage regression analysis. It is notable that HI and CO
have a negative correlation (the correlation coefficient is -0.25), whilst correlation between MI
and CO is notably strong (which is 0.58). This indicates that within the bus service areas, the
private car seems to be unfavourable to the high-income group, who tend to live near transit
stations and use transit for travelling conveniently.
Table 5-2: a) Statistical description; and b) Correlation analysis results of EVs of 52 bus routes of the case
study in Brisbane, Australia
a) Statistical description of EVs
Variable Mean Minimum Maximum Standard deviation
PODC (person/km2) 389 241 507 55
PODYA (person/km2) 1014 665 1697 243
PODOA (person/km2) 817 553 1214 137
PODP (person/km2) 253 174 330 43
LI (%) 31 25 41 4
MI (%) 42 37 46 2
HI (%) 17 10 24 3
CO (car/capita) 0.59 0.48 0.71 0.05
b) Correlation analysis results of EVs
Variable PODC PODYA PODOA PODP LI MI HI CO
PODC 1.00 PODYA 0.17 1.00 PODOA 0.62 0.82 1.00 PODP 0.45 0.26 0.42 1.00 LI -0.07 -0.60 -0.60 -0.27 1.00 MI 0.33 -0.16 0.15 0.43 -0.36 1.00 HI 0.09 0.64 0.62 0.05 -0.86 -0.04 1.00 CO 0.48 -0.64 -0.17 0.09 0.21 0.58 -0.25 1.00
Bold values present the high correlation between variables
Summary
The flowchart for extracting several key bus performance indicators from AFC data of
the case study in Brisbane, Australia was introduced in this chapter. Then, based on this
process, the inputs and outputs (internal factors) of 52 key bus routes were collected at the
service level (each trip) during five continuous working days of a week (19th to 23rd August
2013). This sample dataset will be employed to estimate efficiency scores of bus routes using
DEA models in the next chapters. By this, temporal and spatial performance of selected bus
routes will be explored.
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Applying a stop buffering method for building up the service corridor of a single bus
route and using ABS 2011 Census at SA1, selected EVs were collected sufficiently within the
service areas of each bus route. Here, Pop is categorised into four age groups, and individual
income is clustered into three levels. Those EVs are employed in Chapter 7 for regression
analysis. One of the limitations is that the ABS 2011 Census does not correspond with 2013
AFC data. However, assuming that the changes of those EVs are not significant over the
period of two years from 2011 to 2013, this research employs EVs from ABS 2011 and 2013
AFC data for empirical analysis.
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6 Data Analysis for Individual Bus Route of the Case Study
Introduction
Before comparing the temporal and spatial performance of 52 bus routes in the case
study, exploring the temporal performance of a single route is essential. This helps to verify
the proposed framework and models applied, and to gain more understanding of a single bus
route operation over the time period of a day, and different days of a week without the impact
of external factors on the results obtained. The temporal performance investigation of a single
bus route provides the changes of efficiency score of the corresponding route across the
daytime and over weekdays. The most and the least efficient periods of time of a given route
can be identified. Transit operator may easily further discuss the operating issues leading to
the performance of a given route during the least efficient periods of time.
This chapter, therefore, first examines the temporal performance of bus route 111 (a
busy spine bus route on the South-East Busway corridor) during a working day (19th August
2013), and verifies results by comparing the DEA efficiency scores obtained with the two
transit productiveness indexes introduced in Chapter 3. Here, two basic transit
productiveness indexes are used to present the application of two measures in TCQSM 2013
(load factor and travel time). Then, the temporal performance of individual bus routes of the
sample is investigated and clustered during five continuous working days of a week, from 19th
(Monday) to 23rd (Friday) August 2013.
Section 6.2 represents the data analysis of bus route 111, which includes the
comparison of DEA efficiency scores and two transit productiveness indexes presented in
Chapter 3. Section 6.3 analyses and clusters the temporal performance of individual bus
routes of the sample. Finally, this chapter is concluded in section 6.4, where a summary of
findings is provided.
Data Analysis for Bus Route 111
Bus route 111 is one of the major spine bus routes in Brisbane with high passenger
demand. It connects the south side suburbs between Eight Mile Plains and the Brisbane CBD
(see Figure 6-1) along a continuous Bus Rapid Transit corridor. The date 19th August 2103
is adopted for temporal performance analysis of route 111. There are a total of 11 bus stops
along this route for each direction (inbound or outbound). The inbound direction (toward CBD)
commences at Eight Mile Plains Busway Station and terminates at Roma Street Busway
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Station. The total length of the route is 17 km, and the average schedule travel time is 27
minutes.
6.2.1 DEA-based performance evaluation of route 111
To evaluate the temporal performance of one route, the operational effectiveness is
applied for measurement only, because on a single route, DMUs have a similar scale of
service inputs and outputs. Therefore, inputs are Number of services and Total travel time,
and outputs are OTP and Transit work. The performance indicators (OTP, Transit work, and
Total travel time) of route 111 have been extracted for both inbound and outbound directions
from the raw smart-card data of 19th Aug 2013. The operation of route 111 during an hour is
regarded as a DMU in the DEA model. For example, hour 8 includes all services with a start
time from 7:00 to 8:00.
Table 6-1 and Table 6-2 summarise the statistics of the inputs (Number of services
and Total travel time) and outputs (OTP and Transit work) of route 111 for inbound and
outbound direction, respectively. The Hour starts from 6 because there is no bus service from
0:00 to 5:00. In some hours (such as from 22:00 to 24:00 for inbound direction), no services
arrive at the destination on time, so the value of OTP equals 0. In the evening, the arrival time
of bus services at the destination is normally earlier than scheduled time, but more than 1
minute earlier.
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Figure 6-1: Bus route 111 map (Source: Google map)
Table 6-1: Statistical description of the inputs and outputs of route 111 for inbound direction
Variables Mean Minimum Maximum Standard deviation
Number of services 4 1 11 2.74
Total travel time (hour) 1.73 0.32 6.52 1.54
Average travel time (hour) 0.43 0.32 0.59 0.06
OTP (%) 25 0 82 22.99
Transit work (p-km) 1193 46 7832 1975
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Table 6-2: Statistical description of the inputs and outputs of route 111 for outbound direction
Variables Mean Minimum Maximum Standard deviation
Number of services 4 1 10 2.32
Total travel time (hour) 1.65 0.5 4.87 1.23
Average travel time (hour) 0.41 0.36 0.54 0.05
OTP (%) 33 0 100 25.32
Transit work (p-km) 767 86 5649 1546
Both CRS and VRS-DEA are used for examination. To demonstrate the influence of
variables to the DEA efficiency scores of DMUs, the CRS-DEA efficiency scores are
estimated for three cases, whereby each case has a different combination between input and
output variables. Here, case 1 (with one input and one output) illustrates the direct
relationship between bus capacity and actual bus loading; case 2 considers the influence of
travel time on the efficiency score of DMUs; and case 3 takes travel time as the second input
and the OTP as the second output into account. Case 4 uses the VRS-DEA model with two
inputs and two outputs. Table 6-3 illustrates the inputs and outputs of those four cases.
Table 6-3: Inputs and outputs using for DEA models in cases 1, 2, 3, and 4
Case DEA model Orientation Input variables Output variables
1 CCR (CRS) output Number of service Transit work
2 CCR (CRS) output No of service, Total travel time Transit work
3 CCR (CRS) output No of service, Total travel time Transit work, OTP
4 BCC (VRS) output No of service, Total travel time Transit work, OTP
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Inbound direction: The results obtained from the efficiency analysis of the four cases
are expressed in Figure 6-2; here, the score axis illustrates the efficiency scores of DMUs
(hourly operation of bus route). A DMU is efficient if its score equals 1, whereas a lower score
indicates that it is more inefficient. For instance, hour 8 in case 1 is efficient (score equals to
1) and becomes the benchmark for other inefficient DMUs (score < 1), whereas hour 6 with
a score of 0.56 is inefficient against hour 8. It is possible to increase the output of hour 6 by
78.6% (= (1-0.56)/0.56), using the similar inputs.
Figure 6-2: The DEA efficiency score of the case 1, 2, and 3 for inbound direction
In cases 1 and 2, there is only one efficient DMU at hour 8 (from 7:00 to 8:00), which
is a morning peak hour with the highest passenger demand. However, case 2 witnesses a
slight increase of efficiency scores of DMUs during the afternoon time (between 12:00 and
16:00) compared to case 1 because they experience the lower travel time. Case 3 shows a
significant increase of efficiency scores of most DMUs with two efficient DMUs at hours 8 and
10. It also expresses the significant growth of efficiency scores at hours 10 and 22 because
at these two hours the OTP values are notably higher than the average value of the sample
(25%). Those results indicate that OTP significantly influences the DEA efficiency scores,
and the DEA efficiency scores of inefficient DMUs are relative to the best performing DMUs
(hours 8 and 10). Case 4 illustrates the DMUs’ efficiency scores under VRS assumption with
6 efficient DMUs (Hours 7, 8, 9, 10, 23, and 24) and higher efficiency scores for most DMUs
compared to those in case 3. This demonstrates that the VRS model generates higher
efficiency scores than the CRS model.
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Sco
re
Time
DEA efficiency score
Efficiency score of case 1 Efficiency score of case 2
Efficiency score of case 3 Efficiency score of case 4
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Outbound direction: The results obtained from the efficiency analysis of the four
cases are expressed in Figure 6-3. Both case 1 and 2 have one efficient DMU at hour 17
(from 16:00 to 17:00), which drops in the afternoon peak period with the highest passenger
demand. Similar to the inbound direction, case 2 witnesses a slight increase of efficiency
scores of DMUs during the off-peak morning and evening time compared to case 1, due to
lower travel time. Case 3 shows a significant increase of efficiency scores of most DMUs with
two efficient DMUs at hours 6 and 17. Here, hour 6 is efficient because its OTP value obtains
100%. Case 4, including three efficient DMUs at hours 6, 17, and 18, experiences the higher
efficiency scores for all DMUs compared to case 3, especially in the evening.
Figure 6-3: The DEA efficiency score of the case 1, 2, and 3 for outbound direction
Both directions: Figure 6-4 and Figure 6-5 present the efficiency scores of DMUs
under CRS and VRS assumption (with two inputs and two outputs), respectively, for inbound,
outbound, and both directions of route 111. It can be seen that 111 is efficient during the
morning peak period for the inbound direction, and is efficient during the afternoon peak
period for the outbound direction. Those results are appropriate to the variation of actual
travel demand in a day, in that it normally reaches a peak during the morning peak period for
the inbound direction and during the afternoon peak period for the outbound direction.
For both inbound and outbound directions (combined directions), the operation during
the morning and afternoon peak period (hours from 6 to 9, and from 15 to 18) is more efficient
than off-peak periods (hours 10 to 14, and from 19 to 23). It is notable that hour 24 is the
most inefficient DMU under the CRS assumption (efficiency score equals to 0.209) whereas
it is efficient under the VRS assumption (efficiency score equals to 1).
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Sco
re
Time
DEA efficiency score
Efficiency score of case 1 Efficiency score of case 2
Efficiency score of case 3 Efficiency score of case 4
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To clarify the difference between CRS and VRS models, the scale efficiency is
calculated. The scale efficiency is the ratio of efficiency scores of CRS/VRS (Banker, Charnes
et al. 1984). The results of the measures of scale efficiency are depicted in Table 6-4. It can
be seen that of seven efficient DMUs under VRS assumption, only two DMUs (hours 6 and
8) are scale efficient. This illustrates that hours 6 and 8 operate at an appropriate scale of
operations (neither too big nor too small). There are 6 DMUs displaying increasing returns-
to-scale, including hours 7, 13, 14, 20, 23, and 24. The scale of operations of those DMUs is
too small, and needs to expand the operation by possibly increasing the frequency. The
remaining DMUs, on the other hand, exhibit decreasing returns-to-scale, suggesting that its
operations are too large and need to be downsized. The possible way is to reduce the
frequency or travel time.
Figure 6-4: The CRS-DEA efficiency score of the inbound, outbound, and combined directions
Figure 6-5: The VRS-DEA efficiency score of the inbound, outbound, and combined directions
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Sco
re
Time
CRS-DEA efficiency score
Efficiency score for inbound Efficiency score for outbound
Efficiency score for both directions
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Sco
re
Time
VRS-DEA efficiency score
Efficiency score for inbound Efficiency score for outbound
Efficiency score for both directions
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 75
Table 6-4: Efficiency scores and scale efficiency of route 111 (combined directions)
DMU CRS VRS
Scale
efficiency
Returns to
scale
6 1 1 1 Constant
7 0.841 0.951 0.884 Increasing
8 1 1 1 Constant
9 0.866 1 0.866 Decreasing
10 0.739 0.857 0.862 Decreasing
11 0.573 0.615 0.932 Decreasing
12 0.712 0.809 0.88 Decreasing
13 0.829 0.848 0.978 Increasing
14 0.613 0.697 0.879 Increasing
15 0.894 1 0.894 Decreasing
16 0.871 1 0.871 Decreasing
17 0.891 1 0.891 Decreasing
18 0.798 0.983 0.812 Decreasing
19 0.693 0.755 0.919 Decreasing
20 0.597 0.685 0.871 Increasing
21 0.558 0.681 0.82 Decreasing
22 0.552 0.679 0.812 Decreasing
23 0.197 0.388 0.507 Increasing
24 0.209 1 0.209 Increasing
6.2.2 Comparison between DEA efficiency score and basic transit productiveness
indexes
This section compared the DEA efficiency scores of 111 for inbound direction with
two basic transit productiveness indexes introduced in Chapter 3: transit work load factor;
and passenger transmission efficiency. Figure 6-6 illustrates the results of those two indexes
for inbound direction of 111 on 19th August 2013. Here, maximum schedule load is 85 spaces,
and schedule time to complete a trip is 27 minutes. The correlation coefficient between those
two indexes is significantly high, at 0.979.
Figure 6-7 illustrates the comparison between transit work load factor and DEA
efficiency score in case 1 based on the similar variables used. The correlation coefficient
between those two indexes is 1.00 representing the similar result when using those two
indexes to rank the performance of a bus route. Figure 6-8 illustrates the comparison between
passenger transmission efficiency and DEA efficiency score in case 2 based on the similar
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 76
variables used. The correlation coefficient between those two indexes is 0.992. Those results
provide the valid argument to substantiate the usefulness of DEA in measuring the
operational efficiency of DMUs with multiple input and output variables in general and bus
routes in particular.
Figure 6-9 shows the comparison between passenger transmission efficiency and
DEA efficiency score in case 3, in which DEA efficiency score considers OTP as the second
output variable. The correlation coefficient between those two indexes (r= 0.884) is
significantly lower than the result obtained in Figure 6-8. Those results are evident to state
that OTP significantly influences the DEA scores, and DEA provides additional advantages
in that it deals with DMUs consisting of multiple input and output variables.
The comparison between passenger transmission efficiency and VRS-DEA efficiency
score in case 4 (expressed in Figure 6-10) represents a noticeable decrease of the correlation
between those two indexes (r= 0.553). Those results indicate that the CRS-DEA efficiency
score is closer to basic transit productiveness indexes than VRS-DEA efficiency score in
measuring the temporal performance of one bus route for one direction during a working day.
The reason why the DEA efficiency scores in Figure 6-7 and Figure 6-8 are different
from the values of the two transit productiveness indexes is because those indexes compare
the actual work to the ideal work of transit, whereas DEA compares each DMU to the most
productive DMUs (production frontier) in the existing production possibility set. Therefore, the
two basic transit productiveness indexes can only compare the performance of a bus route
for one direction in different time-space windows, or different bus routes with similar features
such as schedule time, fleet size, and the length of route. On the other hand, the DEA
approach provides the opportunity to compare the performance of different bus routes with
different features and multiple variables.
Regarding the above usefulness of the DEA model and the high correlation of CRS-
DEA efficiency scores and transit productiveness indexes, the CRS-DEA model is employed
to analyse the temporal performance of individual bus routes in section 6.3. In transit, due to
capacity constraints (bus station capacity) the output (on time performance, transit work)
might not have a constant increase by increasing the inputs (the size of the bus, service
frequency etc.). Therefore, the return to scale might not always be constant. However, the
next section (6.3) can consider CRS under the assumption that the system is operating below
capacity. For comparing the performance of different bus routes in Chapter 7, it needs to
consider VRS so as to reflect the transit capacity constraint.
Data Analysis for Individual Bus Route of the Case Study
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Figure 6-6: Transit work load factor and Passenger transmission efficiency of 111
Figure 6-7: Correlation of Transit work load factor and DEA efficiency scores in case 1
Figure 6-8: Correlation of Transit passenger transmission efficiency and DEA efficiency scores
in case 2
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Pearson's correlation coefficient, r = 0.979
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Pearson's correlation coefficient, r = 0.992
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 78
Figure 6-9: Correlation of Transit passenger transmission efficiency and DEA efficiency scores
in case 3
Figure 6-10: Correlation of Transit passenger transmission efficiency and DEA efficiency scores
in case 4
DEA-based Performance Analysis of Individual Routes
Most bus routes of the sample taken from the Brisbane area are located mainly on
the south east and north corridors, with the exception of routes 200 and 222 running along
the east corridor, and route 444 running along the west corridor. Regarding bus frequency,
those routes can be categorised into two clusters: high frequency (the headway for one
direction is equal or less than 15 minutes) and low frequency (the headway for one direction
is over 15 minutes). Across a working day, high frequency bus routes normally serve between
5:00 and 00:00, whereas low frequency bus routes have two patterns of service time period:
short service period (between 6:00 and 20:00); and long service period (between 5:00 and
00:00).
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Efficiency score of case 3 Passenger transmission efficiency
Pearson's correlation coefficient, r = 0.884
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Efficiency score of case 4 Passenger transmission efficiency
Pearson's correlation coefficient, r = 0.553
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 79
The framework for fixed-route quality of service (QOS) measures in TCQSM (2013)
indicates that frequency and service span are core measures for transit availability (refer to
Table 2-1). Therefore, bus frequency and service span may influence the ridership and the
efficiency level of bus routes. The results obtained from the empirical analysis of 52 individual
bus routes of the case study also illustrate that there is a significant difference between the
temporal performance of high or low frequency bus routes, and long or short service period.
Hence, in this research, bus routes are categorised into three clusters:
1) High frequency;
2) Low frequency for long service period; and
3) Low frequency for short service period.
In this section, the performance of those three clusters of bus routes is introduced.
Additionally, some patterns of the changes of efficiency scores over different weekdays are
calculated.
6.3.1 High frequency bus routes
The results obtained from CRS-DEA based data analysis of a single bus route across
the time of a working week indicate that efficiency scores of different days follow a similar
pattern during the daytime (by 20:00), while those vary significantly over the evening time.
This demonstrates that each route attracts a stable number of regular passengers during the
daytime, while they have a larger number of irregular passengers during the evening. Regular
passengers are defined as workers and/or students that regularly travel to the same
destination on regular time basis. Irregular passengers are those who are less frequent and
have more irregular travel patterns (Pitstick, Siddall et al. 2006, Krizek and El-Geneidy 2007,
Le Minh Kieu, Bhaskar et al. 2015). Therefore, the travel demand in the evening fluctuating
randomly leads to the variations of efficiency scores during the evening time. For each bus
route, there are variations of efficiency scores on different working days of the week (see
Figure 6-11 for an example) because the actual travel demand changes over daytime and
different working days of the week.
Based on the variations of efficiency scores of each route over the daytime, some
patterns of the operation of bus routes can be reasoned, as follows:
• Pattern 1: efficiency score reaches the highest values (nearly 1) during the
morning and afternoon peak period, and has the lowest values during off-peak
period (from 10am to 1pm). This is the major pattern of the given sample. Bus
routes typically following this pattern are 100, 111, 180, 222, and 333. Figure 6-11
and Figure 6-12, present efficiency scores of routes 100 and 111, respectively.
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 80
This pattern possibly represents the travel pattern of people working eight hours
a day, such as officers and students. They travel to the work place during the
morning peak hours and return home during the afternoon peak hours on a similar
bus route.
• Pattern 2: efficiency score reaches the highest values during the afternoon peak
period, while it achieves modest values for the morning peak period. Routes 140
and 150 are examples for this pattern. Figure 6-13 presents efficiency scores of
route 140. This phenomenon can be interpreted as regular passengers mainly use
those bus routes for return trips during the afternoon peak hours. For inbound
trips, they may use other routes or transit modes for travelling, or the time for
inbound trips varies across the morning time.
• Pattern 3: the first service hours reach the highest efficiency scores. For example,
routes 330, 340, 345, and 444. Figure 6-14 presents efficiency scores of route
444. This pattern represents the early travel to work of a large number of
passengers within the service corridor of these bus routes, and the appropriate
bus schedule (bus frequency) for the first service hours.
• Pattern 4: off-peak hours (between 10:00 and 13:00) experience high efficiency
scores. Route 200 is an example for this pattern. The efficiency score of route 200
is illustrated in Figure 6-15. This indicates that travel demand is significantly high
at midday because regular passengers of those routes may work mainly in the
morning or afternoon. This travel behaviour leads to the high travel demand at
midday.
Figure 6-11: CRS-DEA efficiency score of route 100 (follows pattern 1)
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 81
Figure 6-12: CRS-DEA efficiency score of route 333 (follows pattern 1)
Figure 6-13: CRS-DEA efficiency score of route 140 (follows pattern 2)
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 82
Figure 6-14: CRS-DEA efficiency score of route 444 (follows pattern 3)
Figure 6-15: CRS-DEA efficiency score of route 200 (follows pattern 4)
6.3.2 Low frequency bus routes for long service period
The results obtained from empirical analysis of low frequency bus routes indicate that
within the daytime, efficiency scores of a given hour across different days vary significantly
compared to those of high frequency bus routes. For example, the averages of standard
deviations of efficiency scores of routes 333 and 444 during the daytime are 0.051 and 0.048,
respectively, while those of routes 124 and 125 are 0.105 and 0.115, respectively. Efficiency
scores of routes 124 and 125 are presented in Figure 6-16 and Figure 6-17, respectively.
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 83
This can be evidence to state that high frequency bus routes attract a more stable number of
regular passengers daily than low frequency bus routes.
It is notable that some bus routes become efficient during the late evening time
(between 21:00 and 00:00), such as routes 125 and 220. The reason is because there is only
one service per hour (the headway is 60 minutes) during this period of time, so the ridership
increases considerably for each service. Additionally, the low traffic flow rate on the bus
corridor at this time leads to high value of OTP.
Figure 6-16: CRS-DEA efficiency score of route 124
Figure 6-17: CRS-DEA efficiency score of route 125
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CRS-DEA efficiency score of 125
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 84
The changes of efficiency score over the daytime follow the typical patterns given in
the previous section. For example, route 185 follows pattern 1 (see Figure 6-18); route 230
follows pattern 2 (see Figure 6-19); routes 170, 220, and 310 introduce pattern 3 (Figure 6-20
and Figure 6-21 represents efficiency scores of routes 170 and 220, respectively); and route
335 follows pattern 4 (see Figure 6-22). However, there is a new pattern of the changes of
bus route efficiency scores (named pattern 5), which reaches a peak during the morning peak
hours and achieves modest values during the afternoon peak hours. Pattern 5 is illustrated
in efficiency scores of routes 135 and 210. Figure 6-23 shows the efficiency scores of routes
135. Regular passengers mainly use those routes for inbound trips during the morning peak
hours, and then the time for outbound trips varies broadly during the daytime and evening.
Figure 6-18: CRS-DEA efficiency score of route 185 (follows pattern 1)
Figure 6-19: CRS-DEA efficiency score of route 230 (follows pattern 2)
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 85
Figure 6-20: CRS-DEA efficiency score of route 170 (follows pattern 3)
Figure 6-21: CRS-DEA efficiency score of route 220 (follows pattern 3)
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 86
Figure 6-22: CRS-DEA efficiency score of route 335 (follows pattern 4)
Figure 6-23: CRS-DEA efficiency score of route 135 (follows pattern 5)
6.3.3 Low frequency bus routes for short service period
The efficiency analysis results for this bus group show that efficiency scores of a given
hour vary significantly across different days. For example, the average of standard deviation
of route 113 is 0.158 (see Figure 6-24). This indicates that the operation of those bus routes
is unstable for different days. Due to low bus frequency (normally only one service per hour),
those bus routes attract a limited number of regular daily passengers.
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 87
Figure 6-24: CRS-DEA efficiency score of route 113
On some bus routes, the efficiency scores over the daytime follow the pattern (named
pattern 6) in that it reaches the highest value for starting and ending hours of the service
period, while it experiences modest values for the remaining hours. Routes 115 and 116
follow this pattern. The efficiency scores of route 115 is expressed in Figure 6-25.
Figure 6-25: CRS-DEA efficiency score of route 115 (follows pattern 6)
Over the daytime, the changes of efficiency scores of some routes follow pattern 2
(such as route 184), pattern 3 (such as routes 192 and 202), and pattern 5 (such as routes
155 and 203). The efficiency scores of routes 192 and 155 are illustrated in Figure 6-26 and
Error! Reference source not found., respectively.
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 88
Figure 6-26: CRS-DEA efficiency score of route 192 (follows pattern 3)
Figure 6-27: CRS-DEA efficiency score of route 155 (follows pattern 5)
From the temporal performance evaluation of individual bus routes within the sample,
six patterns of the changes of efficiency scores across the daytime were figured out. Table
6-5 introduces these six patterns along with their features and several bus routes following
each pattern. The efficiency scores of other bus routes within the given sample are presented
in Appendix A.
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Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 89
Table 6-5: Typical patterns describing the changes of efficiency scores of bus routes during a day
Pattern Features Typical bus routes
Pattern 1 Efficiency score reaches the highest values (nearly
1) during the morning and afternoon peak period,
and the lowest values during off-peak period
(between 10:00 and 13:00)
1Routes 100, 111, 180,
222, and 333;
2Routes 185 and 370
Pattern 2 Efficiency score reaches the highest values during
the afternoon peak period, while it has modest values
for the morning peak period.
1Routes 140 and 150;
2Route 230
3Routes 184
Pattern 3 The first service hours reach the highest efficiency
scores.
1Routes 330, 340, 345,
and 444;
2Routes 170, 220, and
310;
3Routes 192 and 202
Pattern 4 Off-peak hours (between 10:00 and 13:00) achieve
high efficiency scores.
1Route 200;
2Route 335
Pattern 5 Efficiency score reaches a peak during the morning
peak hours and achieves modest values during the
afternoon peak hours.
2Routes 135, 212, 210,
and 325;
3Routes 155, 203, 321,
and 334
Pattern 6 Efficiency score reaches the highest values for
starting and ending hours of the service period.
3Routes 115, 116, and
353
1, 2, 3 are three clusters of bus routes
Summary of Findings
The temporal performance analysis of bus route 111 has indicated that bus route
performance becomes efficient during the morning peak hours for the inbound direction and
becomes efficient during the afternoon peak hours for the outbound direction. For the
combined directions, bus performance during peak hours is more efficient than that during
off-peak hours. It has also confirmed that DEA provides additional advantages in dealing with
DMUs consisting of multiple input and output variables. In measuring the temporal
performance of a bus route for one direction, CRS-DEA efficiency score is closer to basic
transit productiveness indexes than VRS-DEA efficiency score.
Data Analysis for Individual Bus Route of the Case Study
Khac Duong Tran Page 90
Applying the DEA model under the CRS assumption for analysing the temporal
performance of a single bus route over the five continuous working days helps to characterise
the performance of each route. Bus routes are categorised into three clusters: (1) high
frequency; (2) low frequency for a long service period; and (3) low frequency for a short
service period. Within the daytime, cluster 1 shows that efficiency score of a given hour
remains constant over different weekdays, whereas clusters 2 and 3 experience significant
variations in efficiency scores of DMUs across different weekdays. Those results
demonstrate that bus frequency possibly affects the service consumption of each bus
route. Here, high frequency bus routes may attract a more consistent number of regular
passengers daily, so their operations remain stable during a week.
The changes of efficiency scores of each route across the daytime differentiate, so
six different patterns of bus routes operation were figured out. Pattern 1 is popular for most
bus routes in cluster 1 and 2. Pattern 5 only appears in cluster 2 and 3. Regarding the
operation of bus routes during the evening (after 20:00), efficiency scores change significantly
among different hours and days, suggesting that there are greater numbers of irregular
passengers who use bus services during the evening time.
The performance during peak periods typically presents the peak performance of a
bus route and could be used for comparing the performance of different bus routes. However,
for testing the sensitivity of external factors to efficiency scores of bus routes, bus
performance of a working day should be used to provide more appropriate results.
Empirical Analysis for Bus System in the Case Study
Khac Duong Tran Page 91
7 Empirical Analysis for Bus System in the Case Study
Introduction
This chapter aims to examine the temporal and spatial performance of 52 key bus
routes of the case study, and to identify underlying reasons leading to the poor performance
of some bus routes.
To investigate the internal sources of inefficiency of those bus routes, empirical
analysis is conducted separately for node 1 and 2 in the proposed framework in Chapter 4.
This allows one to identify sources of inefficiency related to different performance concepts:
(1) technical efficiency for service production process; and (2) service effectiveness for
service consumption process. Here, empirical analysis for nodes 1 and 2 are termed as model
1 and model 2, respectively. Network DEA is employed to generate an overall efficiency score
of each DMU, accounting for both nodes 1 and 2.
To identify the external sources of inefficiency of those bus routes, the sensitivity
analysis is conducted for node 2 using the double bootstrap model presented in Chapter 3.
Here, efficiency scores obtained from model 2 are dependent variables, while EVs are
independent variables. Results obtained are useful for policy makers to improve the operating
environment of inefficient routes.
Section 7.2 presents the empirical analysis of nodes 1 and 2 for three typical hours (a
morning and an afternoon peak hour, and an off-peak hour) using the VRS model. Section
7.3 analyses the performance of bus routes for three typical hours using the NDEA model.
Section 7.4 represents the empirical analysis of bus routes at three scales of time: every hour;
different periods of time within a day; and on a daily basis. Based on the obtained results, the
ranking of bus routes is also provided in this section. The sensitivity analysis of model 2
efficiency scores to EVs are given in section 7.5. This chapter concludes in section 7.6 with
a summary of findings.
Efficiency Analysis of Key Bus Routes for Separate Node
The technical efficiency and service effectiveness of 52 bus routes of the case study
are estimated based on maximising the outputs. The output-oriented VRS-DEA model is
adopted to calculate the efficiency scores of DMUs for two nodes (two models) expressed in
Table 4-2. A DMU, as mentioned in Chapter 4, is the performance of each bus route during
a given hour (all bus services of the corresponding route with start time falling in an hour for
both inbound and outbound directions). Three typical hours are selected in this section to
Empirical Analysis for Bus System in the Case Study
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compare the performance of those routes to explore the influences of internal variables on
the efficiency level of DMUs, including:
• A morning peak hour (7:00 to 8:00);
• An afternoon peak hour (16:00 to 17:00); and
• An off-peak hour (10:00 to 11:00).
Table 7-1 presents the summary statistics of the results obtained from two nodes
across the three given hours. A DMU is efficient if its score equals to 1, whereas a lower
score indicates that it is inefficient compared to the one with higher score. It could be noted
that the mean efficiency score in model 1 is remarkably high over the three hours (score >
0.85) and the minimum score is greater than 0.6, suggesting that all bus routes considered
have fairly good performance in terms of technical efficiency. However, model 2 witnesses
wide dispersion of efficiency scores because some bus routes have an efficiency score lower
than 0.5. Of the three given hours, the afternoon peak hour in both model 1 and model 2
experiences the higher standard deviation of efficiency scores, which reflects the wide spread
of efficiency scores during the afternoon peak hour compared to other hours.
Table 7-1: The summary statistics of efficiency scores obtained through DEA for models 1 and 2
Model Time Mean Minimum Maximum Standard
deviation
Model 1 Morning peak hour 0.881 0.694 1 0.111
Off-peak hour 0.877 0.633 1 0.12
Afternoon peak hour 0.869 0.629 1 0.127
Model 2 Morning peak hour 0.746 0.218 1 0.227
Off-peak hour 0.585 0.074 1 0.249
Afternoon peak hour 0.669 0.059 1 0.261
The results obtained from the efficiency analysis of the aforementioned models for
three given hours are presented in Figure 7-1 and Figure 7-2, respectively. The score axis
illustrates the efficiency scores of DMUs. For the VRS model, some efficient DMUs in the
given sample become benchmarks for some inefficient DMUs that have similar input and
output characteristics compared with those efficient DMUs. For instance, considering route
175 in model 1 for the morning peak hour, its score of 0.73 indicates that it is possible to
increase the outputs by 37% (=1−0.73
0.73) using similar inputs. Its benchmarks are routes 130
(𝜆130 = 0.145), 321 (𝜆321 = 0.405), 334 (𝜆334 = 0.361), and 444 (𝜆444 = 0.088). Here, 𝜆𝑖 is the
weight for 𝐷𝑀𝑈𝑖. The combination of 14.5%, 40.5%, 36.1%, and 8.8% inputs and outputs of
Empirical Analysis for Bus System in the Case Study
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routes 130, 321, 334, and 444, respectively, can build up the virtual DMU of route 175, which
locates on the production frontier. The input and output values needed to bring route 175 into
efficient status can be expressed as:
(Input of 175) = 0.145 x (Input of 130) + 0.405 x (Input of 321) + 0.361 x (Input of 334)
+ 0.088 x (Input of 444); and Equation 7-1
1.37 x (Output of 175) = 0.145 x (Output of 130) + 0.405 x (Output of 321) + 0.361 x
(Output of 334) + 0.088 x (Output of 444). Equation 7-2
a) The VRS-DEA efficiency score of the first 26 routes (model 1)
b) The VRS-DEA efficiency score of the last 26 routes (model 1)
Figure 7-1: The VRS-DEA efficiency score of bus routes in model 1
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Empirical Analysis for Bus System in the Case Study
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a) The VRS-DEA efficiency score of the first 26 routes (model 2)
b) The VRS-DEA efficiency score of the last 26 routes (model 2)
Figure 7-2: The VRS-DEA efficiency score of bus routes in model 2
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Table 7-2: Inputs and outputs of a) route 175 and its benchmarks in model 1; and b) route 220 and its
benchmarks in model 2 during the morning peak hour
a) Inputs and outputs of route 175 and its benchmarks in model 1
DMUs Inputs Outputs
No of services
Route length (km)
Service duration (hour)
Busway length (km)
Space-km
(p-km)
Route 175 5 16.87 4.93 2.93 5622
Route 130 15 27 12.83 11.46 31195
Route 321 3 13.20 2.25 1.42 2334
Route 334 2 14.37 1.83 1.42 1781
Route 444 10 27.20 12.68 2.04 17736
b) Inputs and outputs of route 220 and its benchmarks in model 2
DMUs Inputs Outputs Other variables
Space-km
(p-km)
Average vehicle speed (km/h)
Transit work
(p-km)
OTP (%) No of services
Lane priority (%)
Stops
Route 220 1732 27 113 0 1 11 38
Route 115 1675 22 454 100 1 11 36
Route 334 1781 16 578 50 2 32 48
Model 1: Figure 7-1 illustrating the results from model 1 shows that among the three
given hours there are 10 efficient DMUs (routes 111, 130, 150, 161, 192, 200, 202, 220, 321,
and 325), while routes 124, 170, 174, 175, and 230 typically have the lowest efficiency scores
(lower than 0.85). A comparative analysis of characteristics of the best and the worst
performance routes can help to explain why some routes are efficient whereas others are
inefficient. For instance, comparing route 175 and its benchmarks (routes 130, 321, 334, 444)
for the morning peak hour (see Table 7-2a), route 321 is efficient compared to 175 because
of its moderate use of busway length (only 1.42 km for route 321 compared to 2.93 km for
route 175) to produce output.
For the morning peak hour, Table 7-3 illustrates that the slacks (input slack is the
amount of input that one DMU could reduce to produce the similar output) mostly occur for
service duration. Thus, reducing the service duration can be one of the possible solutions to
Empirical Analysis for Bus System in the Case Study
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improve performance of inefficient routes. For instance, route 185 and 204 can reduce by
1.38 and 1.45 hours, respectively.
Table 7-3: Slacks for inefficient routes in model 1 during the morning peak hour
DMU
Efficiency
score
Route
length
Service
duration Services
Priority
lane
Space-
km
Route 105 0.865 0 0 0 0 0 Route 110 0.798 0 0 0 0 0
Route 112 0.699 0 -0.23 0 0 0
Route 113 0.864 0 -0.535 0 0 0
Route 116 0.754 0 -0.756 0 0 0
Route 120 0.831 0 -0.59 0 0 0
Route 124 0.726 0 -0.536 0 0 0
Route 125 0.807 0 -0.176 0 0 0
Route 135 0.822 -0.42 0 0 -6.51 0
Route 155 0.855 -0.8 -0.028 0 -5.02 0
Route 170 0.705 0 0 0 -1.8 0
Route 172 0.744 0 -0.001 0 0 0
Route 174 0.742 0 -1.304 0 0 0
Route 175 0.731 0 -0.375 0 0 0
Route 180 0.797 0 -0.413 0 0 0
Route 184 0.758 0 -0.691 0 0 0
Route 185 0.793 0 -1.389 0 0 0
Route 203 0.918 0 0 0 0 0
Route 204 0.873 0 -1.452 0 0 0
Route 210 0.722 0 -0.142 0 -0.51 0
Route 215 0.784 0 0 0 0 0
Route 222 0.77 0 -0.198 0 0 0
Route 230 0.765 0 -1.144 0 0 0
Route 235 0.823 0 -0.389 0 -0.89 0
Route 310 0.815 0 -0.091 0 -1.67 0
Route 325 0.882 0 -0.086 0 0 0
Route 330 0.874 0 0 0 0 0
Route 333 0.694 0 0 0 -2.27 0
Route 340 0.751 0 0 0 0 0
Route 345 0.888 0 -0.859 0 0 0
Route 346 0.981 -2.92 0 0 0 0
Route 353 0.968 -1.17 -0.294 0 0 0
Model 2: Figure 7-2 illustrates the results obtained from model 2 showing that the
effectiveness scores of DMUs vary significantly among routes and hours. Routes 111, 130,
345 and 370 are the most effective DMUs whereas routes 105, 113, 124, 155, 200, 220, and
310 have the poorest performance (scores are lower than 0.5) across the three hours. It can
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also be seen that route 115 and 155 have very low scores for the afternoon peak hour (0.07
and 0.01 respectively) because each has a very small value of transit work.
Considering route 220 for the morning peak hour, which typically has the lowest
effectiveness of the three hours, this route (score of 0.218) is able to increase the outputs by
358.7% using the similar inputs. The benchmarks for route 220 are routes 115 (𝝀𝟏𝟏𝟓 = 𝟎. 𝟒𝟔𝟖)
and 334 (𝝀𝟑𝟑𝟒 = 𝟎. 𝟓𝟑𝟐). The corresponding inputs and outputs of route 220 and its
benchmarks are depicted in Table 7-2b. It is useful to compare route 220 and route 115,
which have similar inputs: the former is inefficient because its outputs are remarkably low
(accounting for 113 and 0 of transit work and OTP, respectively).
In this model, the slacks mainly occur for space-km and OTP. Therefore, reducing
space-km and increasing OTP of inefficient routes may help to improve the performance of
inefficient routes. Table 7-4 presents the slacks of inputs and outputs during the morning
peak hour. Here, route 150 can reduce 6,242 units of space-km and increase 8.45 units of
OTP. The decrease of space-km can be achieved by reducing the capacity of dispatched
vehicles or shortening route length. However, it is not always feasible to modify such variables
because this action may have adverse impacts on broader quality of service objectives
including span of service, and connection to suburban areas. Transit agencies may consider
analysing onboard passenger loading of low performance routes with respect to frequencies
and bus models applied.
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Table 7-4: Slacks for some inefficient routes in model 2 during the morning peak hour
DMU Efficiency
score Space-km
Average
vehicle Speed
Transit
work OTP
Route 100 0.913 -1935 0 0 0 Route 105 0.5 -1414 -2.9 13.62 0 Route 110 0.843 -1290 0 0 0 Route 112 0.54 -729 0 132.43 0 Route 113 0.389 0 0 0 33.47 Route 120 0.961 -4311 0 0 0 Route 124 0.452 0 0 0 0 Route 125 0.439 0 -1.2 0 40.54 Route 130 0.935 -7921 0 0 9.44 Route 140 0.389 0 0 0 40.17 Route 150 0.88 -6202 0 0 8.45 Route 155 0.522 0 -1.8 0 0 Route 160 0.617 -2846 -5.3 0 0 Route 170 0.681 0 -1.5 0 0 Route 172 0.77 -919 0 37.71 0 Route 174 0.526 0 0 0 0 Route 175 0.502 0 0 0 0 Route 180 0.868 0 0 0 0 Route 184 0.586 -880 0 0 0 Route 185 0.64 0 0 0 42.1 Route 192 0.277 0 0 0 0 Route 200 0.454 0 0 0 0 Route 202 0.554 0 0 121.88 0 Route 203 0.699 0 0 0 0 Route 204 0.778 -1975 0 0 17 Route 210 0.48 0 0 0 3.13 Route 212 0.788 0 0 0 49.14 Route 215 0.5 -836 0 192.52 0 Route 220 0.218 0 -8.1 0 73.41 Route 235 0.907 0 0 0 0 Route 310 0.609 0 0 0 0 Route 325 0.743 0 -3.8 0 46.19 Route 340 0.668 0 0 0 0 Route 346 0.667 -2040 -1.3 0 0 Route 353 0.835 -567 0 0 0 Route 359 0.895 0 -4.2 0 44.31 Route 370 0.886 0 0 0 0 Route 390 0.993 0 0 0 22.62
For this reason, attracting more ridership and enhancing schedule reliability are
possible ways for performance improvement of inefficient bus routes. To increase ridership,
the external and environmental factors of the best and the worst DMUs need to be further
investigated, with comparative analysis between them to identify the source of inefficiency.
For instance, route 220 connects Wynnum (a coastal suburb in Brisbane’s east) to the CBD
whilst route 115 connects Calamvale (southern suburb of Brisbane) to the CBD. Wynnum
Empirical Analysis for Bus System in the Case Study
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has lower population density with high proportion of retirees, while Calamvale and
intermediate areas crossed by route 115 have higher population density with ages between
15 and 65 dominant (ABS, June 2014). Further, more shopping centres and schools located
in the south of Brisbane possibly contribute to the higher ridership of 115.
This empirical analysis indicates the actual performance of 52 bus routes of the case
study in Brisbane, Australia, suggesting the following messages for the operator: (1) it should
be useful to reduce service duration of some inefficient routes in model 1 (see Table 7-3),
and (2) there is a great need to investigate the influences of external factors on the efficiency
scores of inefficient routes in model 2, especially geographic information, and then to adjust
the current bus schedule to meet the actual demand of residents within the service areas of
each route.
Efficiency Analysis of Key Bus Routes Using Network model
The network technology of bus routes performance is illustrated in Figure 7-3,
including two linked sub-technologies (nodes 1 and 2). Node 1 represents the production
process, while node 2 presents the consumption process of bus routes. Node 1 and node 2
are linked by an intermediate variable, which is output of node 1 and input of node 2. Here,
space-km is used as an intermediate variable. Input 1 presents inputs of node 1, including
route length, service duration, number of services, and busway length. Output 2 introduces
outputs of node 2, including Transit work and OTP. Node 2 uses its own inputs (named as
input 2) and intermediate variables to produce its outputs (output 2). Here, Inputs of node 2
include space-km (an intermediate variable) and average vehicle speed (its own input).
In the network model, the intermediate inputs/outputs are called link flows. Let the link
leading from node 𝑘 to node ℎ be denoted by (𝑘, ℎ), and the number of items in link (𝑘, ℎ) by
𝑡(𝑘,ℎ). The intermediate inputs/outputs from node 𝑘 to node ℎ: {𝑧𝑗(𝑘,ℎ)
∈ 𝑅+
𝑡(𝑘,ℎ)} (𝑗 = 1, … , 𝑛),
where 𝑛 is the number of DMUs in the production possibility set. As regard to the link flow
constraints, two possible cases are proposed (Tone and Tsutsui 2009):
• Discretionary link flow constraints: the flow between nodes is determined freely
while keeping continuity between input and output (the link values may increase
or decrease in the optimal solution of the linear programming formulation).
𝒁(𝒌,𝒉) 𝝀𝒉 = 𝒁(𝒌,𝒉) 𝝀𝒌, (∀(𝒌, 𝒉)) Equation 7-3
• Non-discretionary link flow constraints: the flow between nodes is kept unchanged
(the link values are fixed).
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𝑧0(𝑘,ℎ) = 𝑍(𝑘,ℎ) 𝜆ℎ, (∀(𝑘, ℎ))
𝒛𝟎(𝒌,𝒉) = 𝒁(𝒌,𝒉) 𝝀𝒌, (∀(𝒌, 𝒉)) Equation 7-4
This research uses the discretionary case for empirical analysis because it does not
restrict the flow between nodes. The sample of 52 bus routes used in the previous section is
employed for empirical analysis in this section. The morning peak hour (7am to 8am) is opted
for empirical data analysis in this section only. In order to present the work of the NDEA
model, network efficiency scores are compared with the efficiency scores of each node (1
and 2) obtained in the section 7.2.
Figure 7-3: The network technology of bus route performance
Figure 7-4 illustrates the efficiency scores of the network model, and efficiency scores of node
1 (model 1) and node 2 (model 2) for the morning peak hour (7:00 to 8:00) on 21st Sep 2013.
Results from network efficiency analysis show that there are 11 efficient DMUs, including
routes 111, 115, 116, 135, 222, 230, 321, 334, 335, 345, and 444, and that the most inefficient
DMUs (scores ≤ 0.4) are routes 113, 125, 140, 192, and 220.
Production process
Consumption process
(technical efficiency measure)Node 1
Node 2
Input 1
Output 2
Intermediate variable
(output 1/input 2)Input 2
(service effectiveness measure)
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a) The efficiency score of the first 26 routes
a) The efficiency score of the last 26 routes
Figure 7-4: DEA efficiency scores of network and separate nodes (the morning peak hour)
Results obtained from correlation analysis between efficiency scores of network and
nodes 1 and 2 for the morning peak hour indicate that efficiency scores of the network and
those of node 2 represent a strong correlation (correlation coefficient equals to 0.98), whereas
the correlation between efficiency scores of node 1 and those of the network is positively
weak (correlation coefficient is 0.25). This indicates that node 2 is the most important node
in the proposed network framework. The value of the node 2 efficiency score greatly
influences the network efficiency score of DMUs.
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Table 7-5 and Table 7-6 show the input and output slacks, respectively, of the most
inefficient routes in the network model for morning peak hour. Results in Table 7-5 indicate
that the slacks mostly occur for service duration and lane priority, suggesting similar results
obtained from efficiency analysis for separate nodes in the previous section. Those inefficient
DMUs can be improved by reducing the service duration and Busway length. Table 7-6
illustrates that slacks mainly occur for OTP, which coincides with the results obtained from
data analysis of separate nodes (models 1 and 2). Increasing OTP can be a solution for
efficiency improvement of those inefficient DMUs.
Table 7-5: Input slacks for the most inefficient routes in the NDEA model during the morning peak hour
DMU Efficiency
score
Number of
services
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length
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duration
Busway
length
Space-
km
Ave. vehicle
speed
Route 220 0.218 0 0 0 0 0 -8.15
Route 192 0.277 0 0 0 0 0 0
Route 113 0.35 0 0 -0.535 0 411 0
Route 125 0.352 0 0 -0.176 0 1131 0
Route 140 0.389 0 0 0 0 0 0
Route 124 0.406 0 0 -0.886 0 1715 0
Route 210 0.438 0 0 -0.142 -0.51 1421 0
Route 175 0.448 0 0 -0.676 0 1709 0
Route 200 0.454 0 0 0 0 0 0
Route 174 0.473 0 0 -1.053 0 1384 0
Route 170 0.494 0 0 0 -1.80 2138 -0.57
Route 105 0.5 0 0 -0.026 -2.97 257 -3.65
Route 155 0.5 0 -1.277 0 -5.15 435 -0.8
Table 7-6: Output slacks for the most inefficient routes in the NDEA model during the morning peak
hour
DMU Efficiency score Transit work OTP (%)
Route 220 0.218 0 73.41
Route 192 0.277 0 0
Route 113 0.35 0 25.45
Route 125 0.352 0 43.21
Route 140 0.389 0 40.17
Route 124 0.406 0 0
Route 210 0.438 0 0
Route 175 0.448 0 0
Route 200 0.454 0 0
Route 174 0.473 0 0
Route 170 0.494 0 0
Route 105 0.5 161.23 0
Route 155 0.5 0 0
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To highlight the usefulness of this network DEA model, an aggregate model is applied
for empirical analysis of this sample, and then the results obtained are compared with network
DEA efficiency scores of DMUs. The aggregate model (termed as operational effectiveness),
used broadly by preceding studies, represents the direct relationship between service inputs
and service consumption, but neglects the role of service outputs (space-km and Average
vehicle speed). Here, for the aggregate model, inputs are number of services, route length,
Busway length, and service duration, and outputs are transit work and OTP. Figure 7-5
presents the efficiency scores of the network model and aggregate model. The correlation
coefficient between efficiency scores obtained from those two models (r= 0.623) is not high,
suggesting that results of the network model are significantly different from those of the
aggregate model. The reason is because the network model accounts for the performance of
linked sub-processes within the overall production process in its optimal solution.
Routes 100 and 353 are good examples for the comparison of those two models. In
the aggregate model, routes 100 and 353 are efficient (the efficiency score equals to 1),
whereas in the network model those routes are inefficient (efficiency scores of routes 100
and 353 are 0.91 and 0.84, respectively). This means that those routes convert inputs into
outputs optimally in the aggregate model, but do not in the network model.
Table 7-7 shows the results obtained from the efficiency analysis of those routes for
the network DEA model. Here, original outputs present the actual values of output variables,
and projection of an output illustrates its optimal value in the DEA corresponding to the
projected point of this DMU on the production frontier. Proportionate movement presents the
difference between original and projected value of an output. The results indicate that routes
100 and 353 should increase 481 and 125 units of transit work, respectively, and increase 4
and 13 units of OTP, respectively, for efficiency improvement. Furthermore, input slacks also
indicate that those routes can reduce inputs for performance improvement. For instance,
routes 100 and 353 are able to reduce 1.12 and 0.18 units of service duration or reduce 1935
and 567 units of space-km, respectively. In the aggregate model, routes 100 and 353 are
efficient, so there is no need to increase outputs or reduce inputs of those routes. From this
investigation, it can be seen that the network model is more comprehensive than the
aggregate model for bus route performance evaluation, because it takes all linked nodes and
intermediate/linked variables in the network technology into account.
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Table 7-7: Efficiency analysis of routes 100 and 353 for the morning peak hour using the NDEA model
a) Statistics of inputs
DMU
Efficiency
score
Slack
movement of
route length
(km)
Slack
movement of
service duration
(hour)
Slack movement
of number of
services
(service)
Slack
movement of
space-km
(space-km)
Route 100 0.91 -0.909 -1.115 -0.972 -1935.21
Route 353 0.84 -3.655 -0.897 -0.184 -566.91
b) Statistics of outputs
DMU
Original
transit
work
Proportionate
movement of
transit work
Projection
of transit
work
Original
OTP
(%)
Proportionate
movement of
OTP (%)
Projection
of OTP (%)
Route 100 5034.13 481.35 5515.48 40 3.83 43.83
Route 353 635.34 125.17 760.51 66.67 13.13 79.80
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a) The efficiency score of the first 26 routes
b) The efficiency score of the last 26 routes
Figure 7-5: Efficiency score of the network and aggregate model (the morning peak hour)
Ranking the Performance of 52 Bus Routes
This section employs the proposed approach for empirical analysis of 52 bus routes
of the case study of Brisbane to provide insights into the temporal and spatial performance
of those routes. Based on the efficiency scores obtained, bus routes are ranked to identify
the benchmarks and the least efficient routes within the sample. The date of 21st August 2013
(Wednesday), which is a working day, is opted for empirical analysis.
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Network model Aggregate model
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7.4.1 Technical efficiency measure for bus routes (Model 1)
This section employs model 1 (refer to section 7.2) for empirical analysis of the sample
for different time windows (an hour, peak or off-peak periods, and a day). Model 1 separately
uses an output-oriented VRS model for empirical analysis of node 1.
Table 7-8 and Table 7-9 illustrate the efficiency scores of those bus routes hourly,
from hour 7 (between 6:00 and 7:00) to hour 19 (between 18:00 and 19:00). Blank cells mean
that the data for these cells are unavailable. Based on these results, one can rank the
performance of those routes at the hourly level.
Table 7-10 shows the efficiency scores of those bus routes for key periods of time
within a working day, including:
• Morning peak period (from 5:00 to 9:00);
• Off-peak period (from 9:00 to 15:00);
• Afternoon peak period (from 15:00 to 21:00); and
• Evening period (from 21:00 to 00:00)
Based on the results in Table 7-10, one can rank the performance of those bus routes
for different key periods of time across a working day.
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Table 7-8: Efficiency scores of 52 bus routes in model 1 from hour 7 to hour 13
NO DMU Hour 7 Hour 8 Hour 9 Hour 10 Hour 11 Hour 12 Hour 13
1 Route 100 1 1 0.99 0.937 0.972 0.967 0.993 2 Route 105 1 0.865 0.794 0.831 0.789 0.886 1 3 Route 110 0.912 0.798 0.81 0.845 0.797 0.836 0.854 4 Route 111 1 1 1 1 1 1 1 5 Route 112 0.646 0.699 1 1 0.732 0.704 0.89 6 Route 113 0.727 0.864 0.808 1 0.711 0.923 7 Route 115 1 1 0.867 0.978 0.983 0.788 0.901 8 Route 116 0.695 0.754 0.824 1 1 0.697 0.886 9 Route 120 0.855 0.831 0.811 0.803 0.875 0.882 0.945
10 Route 124 0.979 0.726 0.691 0.78 0.714 0.885 0.816 11 Route 125 0.865 0.807 0.828 0.928 0.844 0.847 0.847 12 Route 130 1 1 1 0.969 1 1 1 13 Route 135 0.842 0.822 0.809 0.858 0.85 0.823 0.885 14 Route 140 0.929 1 0.99 0.884 0.898 0.946 1 15 Route 150 1 1 1 1 1 1 1 16 Route 155 0.855 0.817 1 0.851 0.822 0.971 17 Route 160 1 1 1 1 0.918 1 1 18 Route 161 1 1 1 1 1 1 19 Route 170 0.79 0.705 0.678 0.979 0.633 0.708 0.711 20 Route 172 0.737 0.744 0.699 0.737 0.73 0.684 0.82 21 Route 174 0.695 0.742 0.717 0.728 0.719 0.74 0.839 22 Route 175 0.738 0.731 0.655 0.708 0.7 0.731 0.802 23 Route 180 0.926 0.797 0.798 0.836 0.758 0.911 0.837 24 Route 184 0.758 0.758 0.728 0.755 0.754 0.703 0.829 25 Route 185 0.811 0.793 0.798 0.836 0.786 0.911 0.829 26 Route 192 1 1 1 1 1 1 1 27 Route 200 0.899 1 1 1 0.986 0.963 0.982 28 Route 202 1 1 1 1 1 1 1 29 Route 203 0.652 0.918 0.657 0.717 0.688 0.607 0.858 30 Route 204 0.825 0.873 0.98 0.928 0.993 0.979 1 31 Route 210 0.975 0.722 0.81 0.871 0.734 0.778 0.781 32 Route 212 0.851 1 0.739 1 0.878 0.656 1 33 Route 215 1 0.784 0.77 0.828 0.779 0.802 0.832 34 Route 220 1 1 1 1 1 0.864 0.928 35 Route 222 1 0.77 0.808 1 1 1 1 36 Route 230 0.57 0.765 0.699 0.694 0.668 0.67 0.737 37 Route 235 0.664 0.823 0.812 0.732 0.721 0.693 0.77 38 Route 310 0.873 0.815 0.808 0.846 0.956 0.774 0.893 39 Route 321 0.909 1 1 0.994 0.997 1 1 40 Route 325 0.875 0.882 0.923 0.898 0.898 0.855 0.876 41 Route 330 0.853 0.874 0.851 0.818 0.839 0.886 0.921 42 Route 333 0.953 0.694 0.697 0.882 0.911 0.838 0.827 43 Route 334 1 1 1 1 1 0.839 0.999 44 Route 335 1 1 1 1 1 1 1 45 Route 340 0.784 0.751 0.705 0.671 0.696 0.727 0.843 46 Route 345 1 0.888 0.897 1 1 0.941 1 47 Route 346 1 0.981 1 1 0.967 1 1 48 Route 353 0.954 0.968 1 1 1 1 1 49 Route 359 0.922 1 1 1 0.907 1 1 50 Route 370 1 1 1 1 1 1 1 51 Route 390 0.71 1 1 0.962 0.993 0.95 1 52 Route 444 1 1 1 1 1 1 1
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Table 7-9: Efficiency scores of 52 bus routes in model 1 from hour 14 to hour 19
NO DMU Hour 14 Hour 15 Hour 16 Hour 17 Hour 18 Hour 19
1 Route 100 1 0.967 1 1 1 1 2 Route 105 1 0.789 0.787 1 0.98 1 3 Route 110 0.824 0.822 0.766 0.834 0.88 0.858 4 Route 111 1 1 1 1 1 1 5 Route 112 0.754 0.971 0.925 0.649 0.756 0.942 6 Route 113 0.737 0.899 0.811 0.723 0.738 7 Route 115 0.941 0.903 0.97 0.946 1 1 8 Route 116 0.697 0.941 0.734 0.701 0.67 1 9 Route 120 0.917 0.88 0.756 0.793 0.794 0.884
10 Route 124 0.726 0.881 0.767 0.704 0.69 0.689 11 Route 125 0.858 0.866 0.815 0.834 0.866 0.829 12 Route 130 0.999 0.937 1 0.96 1 0.952 13 Route 135 0.885 1 0.894 0.83 0.842 0.793 14 Route 140 1 0.898 0.897 0.863 1 1 15 Route 150 1 1 1 1 1 1 16 Route 155 0.886 1 0.956 0.931 1 17 Route 160 1 1 1 1 1 1 18 Route 161 1 1 1 1 1 1 19 Route 170 0.731 0.701 0.73 0.64 0.674 0.656 20 Route 172 0.744 0.888 0.749 0.718 0.733 0.961 21 Route 174 0.707 0.763 0.764 0.661 0.685 0.766 22 Route 175 0.729 0.746 0.735 0.719 0.634 0.607 23 Route 180 0.958 0.808 0.713 0.804 0.805 0.999 24 Route 184 0.771 0.769 0.733 0.74 0.741 0.721 25 Route 185 0.81 0.789 0.786 0.762 0.893 0.987 26 Route 192 1 1 1 1 1 1 27 Route 200 0.953 0.969 1 1 1 0.896 28 Route 202 1 1 1 1 1 1 29 Route 203 0.633 0.898 0.68 0.655 0.613 0.964 30 Route 204 1 0.947 0.915 0.868 0.906 0.762 31 Route 210 0.816 0.731 0.767 0.736 0.892 32 Route 212 0.724 0.913 0.731 0.794 0.699 1 33 Route 215 0.8 0.931 0.924 1 1 1 34 Route 220 0.967 1 0.99 0.906 0.904 0.891 35 Route 222 1 1 0.976 0.965 0.945 1 36 Route 230 0.723 0.703 0.741 0.629 0.649 0.63 37 Route 235 0.768 0.734 0.689 0.778 0.717 38 Route 310 0.836 1 1 0.809 0.856 1 39 Route 321 1 1 1 0.998 1 1 40 Route 325 0.915 0.899 0.912 0.872 0.886 1 41 Route 330 0.913 0.836 0.789 0.815 0.899 1 42 Route 333 0.892 0.806 0.896 1 1 0.897 43 Route 334 1 1 1 1 1 0.946 44 Route 335 1 1 1 1 1 1 45 Route 340 0.824 0.731 0.69 0.694 0.727 1 46 Route 345 0.968 0.918 0.873 0.942 1 0.819 47 Route 346 1 0.943 0.953 1 1 1 48 Route 353 1 1 1 0.993 1 1 49 Route 359 1 1 1 1 1 0.924 50 Route 370 1 1 1 1 1 1 51 Route 390 1 1 0.979 0.923 0.87 0.913 52 Route 444 1 1 1 1 1 1
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Table 7-10: Efficiency scores of 52 bus routes in model 1 for different periods of time and a day
NO DMU Hour 6-9 Hour 10-15 Hour 16-19 Hour 20-24 Day
1 Route 100 1 0.97 1 0.984 1 2 Route 105 0.997 0.925 0.927 1 1 3 Route 110 0.818 0.869 0.82 0.708 0.779 4 Route 111 1 1 1 1 1 5 Route 112 0.716 0.877 0.711 0.748 0.774 6 Route 113 0.763 1 0.833 0.886 7 Route 115 0.946 0.962 1 1 8 Route 116 0.778 1 0.71 0.706 0.763 9 Route 120 0.781 0.881 0.805 0.855 0.845
10 Route 124 0.732 0.911 0.702 0.595 0.726 11 Route 125 0.849 0.858 0.843 0.746 0.827 12 Route 130 1 0.987 1 1 1 13 Route 135 0.82 0.954 0.831 0.897 0.867 14 Route 140 1 0.909 0.936 0.976 0.952 15 Route 150 1 1 1 1 1 16 Route 155 0.887 0.996 1 1 17 Route 160 1 1 1 0.799 1 18 Route 161 1 1 1 1 19 Route 170 0.713 0.719 0.679 0.605 0.698 20 Route 172 0.745 0.839 0.754 0.792 21 Route 174 0.715 0.76 0.723 0.588 0.72 22 Route 175 0.737 0.736 0.692 0.583 0.701 23 Route 180 0.878 0.85 0.822 0.83 0.852 24 Route 184 0.788 0.83 0.717 0.693 0.768 25 Route 185 0.806 0.913 0.757 0.745 0.778 26 Route 192 1 1 1 1 1 27 Route 200 0.973 0.988 1 0.967 1 28 Route 202 1 1 1 1 1 29 Route 203 0.72 0.82 0.643 0.75 30 Route 204 0.932 0.981 0.874 0.586 0.85 31 Route 210 0.725 0.765 0.8 0.628 0.731 32 Route 212 0.848 0.996 0.7 0.674 0.754 33 Route 215 0.922 0.913 1 0.693 0.955 34 Route 220 1 1 0.917 0.78 0.954 35 Route 222 0.975 1 1 1 1 36 Route 230 0.681 0.701 0.643 0.674 0.649 37 Route 235 0.736 0.725 0.766 0.508 0.68 38 Route 310 0.841 0.934 0.881 0.89 0.907 39 Route 321 1 1 1 1 40 Route 325 0.91 0.893 0.877 0.898 0.911 41 Route 330 0.857 0.859 0.824 0.902 0.849 42 Route 333 0.81 0.858 0.982 1 0.946 43 Route 334 1 1 1 1 44 Route 335 1 1 1 0.964 1 45 Route 340 0.703 0.729 0.697 0.795 0.715 46 Route 345 0.989 1 0.996 1 1 47 Route 346 1 1 1 1 48 Route 353 0.971 1 1 1 1 49 Route 359 1 1 1 0.777 1 50 Route 370 1 1 1 1 1 51 Route 390 1 1 0.908 0.803 0.985 52 Route 444 1 1 1 1 1
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Table 7-11: Ranking of 52 bus routes in model 1 for a day (21 Aug 2013)
Ranking DMU Efficiency
scores
Ranking DMU Efficiency
scores
1 Route 100 1 6 Route 333 0.946 1 Route 105 1 7 Route 325 0.911
1 Route 111 1 8 Route 310 0.907
1 Route 115 1 9 Route 113 0.886
1 Route 130 1 10 Route 135 0.867
1 Route 150 1 11 Route 180 0.852
1 Route 155 1 12 Route 204 0.85
1 Route 160 1 13 Route 330 0.849
1 Route 161 1 14 Route 120 0.845
1 Route 192 1 15 Route 125 0.827
1 Route 200 1 16 Route 172 0.792
1 Route 202 1 17 Route 110 0.779
1 Route 222 1 18 Route 185 0.778
1 Route 321 1 19 Route 112 0.774
1 Route 334 1 20 Route 184 0.768
1 Route 335 1 21 Route 116 0.763
1 Route 345 1 22 Route 212 0.754
1 Route 346 1 23 Route 203 0.75
1 Route 353 1 24 Route 210 0.731
1 Route 359 1 25 Route 124 0.726
1 Route 370 1 26 Route 174 0.72
1 Route 444 1 27 Route 340 0.715
2 Route 390 0.985 28 Route 175 0.701
3 Route 215 0.955 29 Route 170 0.698
4 Route 220 0.954 30 Route 235 0.68
5 Route 140 0.952 31 Route 230 0.649
Table 7-11 illustrates the ranking of given bus routes based on the efficiency scores
obtained from the empirical analysis for the time window of a day (21 Aug 2013). Here, there
are 22 efficient DMUs (such as routes 100, 105, and 111) and 30 inefficient DMUs (such as
routes 170, 175, 230 and 235).
Figure 7-6 presents the variations of efficiency scores of routes for the time window
of a day and of different periods of time within a day, with the gradual decrease of a day’s
efficiency scores. Here, the efficiency scores of some routes like 155, 161, and 172 are
unavailable for the time period between 21:00 and 0:00. The results indicate that of 22 first
ranking routes from Table 7-11, 10 routes are efficient for all time periods within a day,
which are 111, 150, 161, 192, 202, 321, 334, 346, 370, and 444 (see Table 7-10 or Figure
7-6a). Those bus routes are the benchmarks of this sample.
Table 7-12 illustrates the correlation relationship between efficiency scores of different
time periods within a day, and a day. Results indicate that efficiency scores of both morning
Empirical Analysis for Bus System in the Case Study
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and afternoon peak periods experience a high correlation with those of a day (correlation
coefficients are 0.84 and 0.90, respectively), while efficiency scores between the off-peak
period and a day have a lower correlation (which is 0.68 for the period from 9:00 to 15:00).
This demonstrates that the technical efficiency of bus routes during peak periods, especially
the afternoon peak period, is significantly related to the daily efficiency.
Table 7-12: Correlation analysis results of efficiency scores of different periods of time
5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day
5:00-9:00 1
9:00-15:00 0.66 1
15:00-21:00 0.78 0.49 1
21:00-0:00 0.46 0.36 0.57 1
Day 0.84 0.68 0.90 0.71 1
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a) Efficiency scores of the first 20 routes for different periods of time
b) Efficiency scores of the last 32 routes for different periods of time
Figure 7-6: Efficiency score variations of bus routes in model 1 for different periods of time, following
the gradual decrease of a day’s efficiency scores
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5:00-9:00 9:00-15:00 15:00-19:00 19:00-24:00 Day
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7.4.2 Service effectiveness measure (Model 2)
This section employs model 2 for empirical analysis of the given bus routes. Model 2
separately uses an output-oriented VRS model for empirical analysis of node 2.
Table 7-13 and Table 7-14 illustrate efficiency scores of bus routes for different hours
during the daytime (from 6:00 to 19:00) of the given date. The results indicate that efficiency
scores of a bus route change significantly between hours, because of the large variations of
travel demand across the daytime. For example, route 111 is efficient at hour 8, but its
efficiency scores reduce gradually before reaching the bottom of 0.67 at hour 12, then it is
efficient again at hours 16 and 17. On the other hand, route 140 experiences poor
performance during the peak morning hour (its efficiency score at hour 8 equals to 0.38), but
it is almost efficient at hour 12 (efficiency score equals to 0.93). Several routes in the sample,
such as routes 130 and 334, are efficient for most hours. Those routes are considered as
the benchmarks of this sample for model 2.
Table 7-15 shows the efficiency scores of the given bus routes for key periods of time
of a day and for a day. This information is useful to rank the performance of those routes for
peak periods or off-peak periods of time within a day, as well as an entire day.
Table 7-16 shows the ranking of those bus routes based on the performance of a
given day. Here, there are eight efficient routes (130, 160, 161, 192, 230, 333, 334, and 370),
which are the benchmarks of this sample for a given day. Routes 130 and 334 are efficient
for all periods of time, so those routes are the typical benchmarks of this sample. Routes
174, 200, 184, 325, 185, 335 and 155, on the contrary, are the most inefficient routes
that need further investigation to identify the sources of inefficiency. Then, possible solutions
should be made for performance improvement of those routes.
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Table 7-13: Efficiency scores of 52 bus routes in model 2 from hour 7 to hour 13
NO DMU Hour 7 Hour 8 Hour 9 Hour 10 Hour 11 Hour 12 Hour 13
1 Route 100 1 0.913 0.875 0.731 0.815 1 0.772 2 Route 105 1 0.5 0.502 0.516 0.283 1 1 3 Route 110 0.71 0.843 0.407 0.703 0.284 0.255 0.584 4 Route 111 0.653 1 0.977 0.744 0.764 0.673 0.782 5 Route 112 0.734 0.54 1 1 1 1 0.779 6 Route 113 0.299 0.389 0.221 1 0.325 1 7 Route 115 0.66 1 1 0.507 1 0.181 1 8 Route 116 1 1 0.689 1 1 0.516 1 9 Route 120 0.501 0.961 0.767 0.853 0.621 0.477 0.558
10 Route 124 1 0.452 0.323 0.668 0.57 1 0.928 11 Route 125 0.72 0.439 0.478 0.498 1 0.924 0.765 12 Route 130 1 0.935 1 1 1 1 1 13 Route 135 0.665 1 1 0.961 1 0.754 0.875 14 Route 140 0.353 0.389 0.443 0.75 0.58 0.932 0.805 15 Route 150 0.588 0.88 0.601 1 0.711 1 1 16 Route 155 0.522 0.268 0.21 0.566 0.212 0.513 17 Route 160 0.748 0.617 0.957 0.542 0.478 0.516 0.862 18 Route 161 1 0.878 0.612 0.196 1 0.513 19 Route 170 0.725 0.681 0.752 0.613 0.53 0.404 0.571 20 Route 172 0.448 0.77 1 0.363 0.328 1 0.708 21 Route 174 0.42 0.526 0.464 0.665 0.602 0.426 0.53 22 Route 175 0.378 0.502 0.598 0.531 0.52 1 0.516 23 Route 180 0.367 0.868 0.783 0.47 0.445 0.581 0.81 24 Route 184 1 0.586 0.539 0.446 0.383 0.355 0.637 25 Route 185 0.27 0.64 0.309 0.406 0.508 0.169 0.606 26 Route 192 1 0.277 0.384 0.532 0.466 1 0.931 27 Route 200 0.451 0.454 0.451 0.604 0.366 0.69 0.731 28 Route 202 0.567 0.554 0.369 0.44 0.262 0.561 0.286 29 Route 203 0.5 0.699 0.948 1 0.511 0.673 0.779 30 Route 204 0.857 0.778 0.553 0.405 0.683 0.958 0.62 31 Route 210 1 0.48 0.591 0.314 0.608 0.783 0.6 32 Route 212 0.708 0.788 0.761 0.591 0.529 1 1 33 Route 215 1 0.5 0.553 0.519 0.403 0.5 0.65 34 Route 220 1 0.218 0.292 0.535 0.163 0.562 0.545 35 Route 222 0.552 1 1 1 0.773 0.641 0.57 36 Route 230 1 1 0.728 0.785 0.701 0.883 1 37 Route 235 0.661 0.907 1 1 0.814 0.501 0.698 38 Route 310 0.73 0.609 0.288 0.363 0.201 0.561 0.543 39 Route 321 1 1 0.27 0.503 0.14 1 1 40 Route 325 0.605 0.743 0.387 0.265 0.558 0.562 0.395 41 Route 330 0.983 1 1 0.98 0.839 0.88 0.697 42 Route 333 0.807 1 1 1 0.885 1 1 43 Route 334 0.529 1 1 0.672 0.504 1 0.895 44 Route 335 0.628 1 0.368 0.242 0.506 1 0.527 45 Route 340 0.784 0.668 0.719 0.513 0.594 0.604 0.524 46 Route 345 0.873 1 0.867 0.737 0.798 0.56 0.751 47 Route 346 0.497 0.667 1 0.504 0.501 1 0.503 48 Route 353 0.485 0.835 1 0.278 0.074 0.281 0.429 49 Route 359 0.854 0.895 0.643 0.875 0.579 0.65 0.728 50 Route 370 0.365 0.886 1 0.655 0.984 0.739 0.804 51 Route 390 0.445 0.993 0.605 0.678 0.688 0.857 1 52 Route 444 0.781 1 0.793 0.907 0.785 1 0.888
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Table 7-14: Efficiency scores of 52 bus routes in model 2 from hour 14 to hour 19
NO DMU Hour 14 Hour 15 Hour 16 Hour 17 Hour 18 Hour 19
1 Route 100 0.699 1 0.92 0.773 0.903 0.719 2 Route 105 0.355 0.449 0.392 0.373 0.073 1 3 Route 110 0.521 0.374 0.535 0.686 0.674 0.363 4 Route 111 0.769 0.981 1 1 0.945 0.75 5 Route 112 1 0.937 1 0.437 0.826 0.264 6 Route 113 1 0.757 0.346 0.363 0.247 7 Route 115 0.5 0.449 0.296 0.073 1 0.003 8 Route 116 1 0.88 0.796 0.2 0.712 0.075 9 Route 120 0.488 0.559 0.658 0.744 0.637 1
10 Route 124 0.507 0.871 0.392 0.608 0.517 0.516 11 Route 125 0.342 0.755 0.35 0.483 0.645 0.705 12 Route 130 1 1 1 1 1 1 13 Route 135 0.58 1 0.41 0.363 0.226 0.5 14 Route 140 0.673 0.888 0.798 0.887 0.965 1 15 Route 150 1 1 1 0.939 1 1 16 Route 155 0.417 0.079 0.073 0.059 0.006 17 Route 160 0.857 0.473 1 0.834 0.8 0.748 18 Route 161 1 1 0.412 1 0.754 0.714 19 Route 170 0.521 0.333 0.763 0.846 0.877 0.75 20 Route 172 1 0.849 0.344 0.468 0.625 0.317 21 Route 174 0.55 1 0.374 0.398 0.586 0.36 22 Route 175 1 0.565 0.921 0.526 0.551 1 23 Route 180 0.412 0.705 0.588 0.621 0.94 0.788 24 Route 184 0.65 1 0.418 0.481 0.264 0.5 25 Route 185 0.623 1 0.704 0.591 0.261 0.419 26 Route 192 0.579 0.898 1 0.591 1 1 27 Route 200 0.318 0.291 0.429 0.414 0.437 0.377 28 Route 202 0.388 0.487 0.761 0.334 0.509 0.287 29 Route 203 0.537 1 0.573 0.82 0.341 0.157 30 Route 204 0.587 0.627 0.509 0.726 0.651 0.642 31 Route 210 0.783 1 0.784 0.804 0.27 32 Route 212 0.516 1 0.659 0.469 1 1 33 Route 215 0.245 0.486 0.694 1 1 1 34 Route 220 0.504 0.805 0.875 0.548 0.358 1 35 Route 222 0.686 0.787 0.724 0.684 1 1 36 Route 230 0.569 0.918 1 0.911 1 1 37 Route 235 0.758 0.798 0.681 1 1 1 38 Route 310 0.543 1 1 0.466 0.363 0.398 39 Route 321 0.508 1 0.36 0.982 0.709 1 40 Route 325 0.616 0.295 0.463 0.423 0.544 0.537 41 Route 330 0.622 1 1 1 0.864 0.751 42 Route 333 0.899 1 1 0.918 1 0.8 43 Route 334 1 1 1 1 1 0.428 44 Route 335 0.562 0.311 0.362 0.384 0.359 0.245 45 Route 340 0.618 0.61 0.663 0.776 0.631 0.488 46 Route 345 0.96 1 1 1 1 1 47 Route 346 1 0.888 0.26 0.926 0.287 48 Route 353 1 0.36 0.696 0.485 0.468 0.374 49 Route 359 0.745 0.557 0.533 0.716 0.627 0.616 50 Route 370 0.79 0.54 1 1 0.702 0.632 51 Route 390 0.719 0.798 0.576 0.692 0.887 0.804 52 Route 444 0.916 1 0.88 0.94 0.622 0.627
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Table 7-15: Efficiency scores of 52 bus routes in model 2 for different periods of time and a day
NO DMU Hour 6-9 Hour 10-15 Hour 16-19 Hour 20-24 Day
1 Route 100 0.948 0.879 0.834 0.701 0.877 2 Route 105 1 0.478 0.38 0.591 0.552 3 Route 110 0.603 0.446 0.731 0.339 0.612 4 Route 111 1 0.819 1 0.699 0.943 5 Route 112 0.903 1 0.573 1 0.986 6 Route 113 0.284 0.777 0.454 0.573 7 Route 115 1 0.601 0.294 0.75 8 Route 116 1 1 0.544 0.956 0.921 9 Route 120 0.871 0.587 0.702 0.714 0.716
10 Route 124 0.511 0.925 0.536 0.636 0.586 11 Route 125 0.633 0.992 0.638 0.447 0.603 12 Route 130 1 1 1 1 1 13 Route 135 1 0.942 0.417 1 0.701 14 Route 140 0.41 0.8 0.912 0.817 0.783 15 Route 150 0.672 0.968 0.937 0.955 0.873 16 Route 155 0.459 0.334 0.082 0.366 17 Route 160 0.978 0.673 1 0.802 1 18 Route 161 0.992 1 0.855 1 19 Route 170 0.797 0.526 1 0.473 0.865 20 Route 172 0.901 0.744 0.582 0.775 21 Route 174 0.486 0.803 0.401 0.539 0.546 22 Route 175 0.481 1 0.679 0.851 0.645 23 Route 180 0.67 0.592 0.68 0.542 0.641 24 Route 184 1 0.765 0.455 0.366 0.518 25 Route 185 0.402 0.491 0.583 0.472 0.467 26 Route 192 0.343 0.867 1 1 1 27 Route 200 0.469 0.55 0.539 0.274 0.541 28 Route 202 0.413 0.646 0.637 0.943 0.569 29 Route 203 0.918 0.807 0.592 0.777 30 Route 204 0.875 0.753 0.663 0.599 0.763 31 Route 210 0.578 0.766 0.976 1 0.853 32 Route 212 0.706 0.88 0.763 0.436 0.755 33 Route 215 0.8 0.514 0.797 1 0.643 34 Route 220 1 0.541 0.774 0.853 0.785 35 Route 222 0.918 0.753 0.984 0.658 0.884 36 Route 230 1 0.899 1 0.26 1 37 Route 235 0.776 0.996 1 1 0.954 38 Route 310 0.637 0.476 0.504 0.443 0.557 39 Route 321 0.823 0.661 1 0.843 40 Route 325 0.567 0.439 0.543 0.598 0.509 41 Route 330 1 0.861 0.914 0.597 0.92 42 Route 333 0.948 1 0.951 0.795 1 43 Route 334 1 1 1 1 44 Route 335 0.876 0.395 0.336 0.382 0.453 45 Route 340 0.82 0.572 0.637 0.453 0.627 46 Route 345 0.932 0.8 1 0.768 0.928 47 Route 346 0.607 0.79 0.563 0.7 48 Route 353 0.906 0.354 0.682 0.646 0.61 49 Route 359 0.908 0.781 0.717 0.808 0.868 50 Route 370 0.894 1 1 0.561 1 51 Route 390 0.668 0.938 0.781 0.68 0.804 52 Route 444 0.937 1 0.778 0.956 0.926
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Table 7-16: Ranking of 52 bus routes in model 2 for a working day (21 Aug 2013)
Ranking DMU Efficiency
scores
Ranking DMU Efficiency
scores
1 Route 130 1 20 Route 172 0.775 1 Route 160 1 21 Route 204 0.763 1 Route 161 1 22 Route 212 0.755 1 Route 192 1 23 Route 115 0.75 1 Route 230 1 24 Route 120 0.716 1 Route 333 1 25 Route 135 0.701 1 Route 334 1 26 Route 346 0.7 1 Route 370 1 27 Route 175 0.645 2 Route 112 0.986 28 Route 215 0.643 3 Route 235 0.954 29 Route 180 0.641 4 Route 111 0.943 30 Route 340 0.627 5 Route 345 0.928 31 Route 110 0.612 6 Route 444 0.926 32 Route 353 0.61 7 Route 116 0.921 33 Route 125 0.603 8 Route 330 0.92 34 Route 124 0.586 9 Route 222 0.884 35 Route 113 0.573 10 Route 100 0.877 36 Route 202 0.569 11 Route 150 0.873 37 Route 310 0.557 12 Route 359 0.868 38 Route 105 0.552 13 Route 170 0.865 39 Route 174 0.546 14 Route 210 0.853 40 Route 200 0.541 15 Route 321 0.843 41 Route 184 0.518 16 Route 390 0.804 42 Route 325 0.509 17 Route 220 0.785 43 Route 185 0.467 18 Route 140 0.783 44 Route 335 0.453 19 Route 203 0.777 45 Route 155 0.366
Figure 7-7 presents the variations of efficiency scores of bus routes in model 2 for
different periods of time, which follow the gradual reduction of efficiency scores of a day. This
indicates that the temporal and spatial performance of bus routes vary significantly because
of the changes of travel demand over time for a single route, and among different routes. For
instance, routes 111, 222, and 345 have high efficiency scores for peak periods of time
(nearly 1) and lower efficiency scores for off-peak periods of time. On the other hand, routes
124 and 175 have higher efficiency scores of off-peak periods compared to peak periods.
Routes 112 and 116 have considerably low efficiency scores for only the afternoon peak
period, but high efficiency scores for the remaining periods of time. Routes 192 and 140, by
contrast, experience low efficiency scores for only the morning peak period, but high
efficiency scores for the remaining periods of time.
The results obtained from the correlation analysis between efficiency scores in model
2 of different periods of time are presented in Table 7-17. Here, efficiency scores of the
afternoon peak period have fairly high correlation with a day’s efficiency scores, suggesting
the important contribution of this period to the overall performance of bus routes a day.
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Table 7-17: Correlation analysis results of efficiency scores of different periods of time
5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day
Day 0.52 0.67 0.79 0.48 1
a) Efficiency scores of the first 26 routes for different periods of time
b) Efficiency scores of the last 26 routes for different periods of time
Figure 7-7: Efficiency score variations of bus routes in model 2 for different periods of time, following
the gradual decrease of a day’s efficiency scores
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7.4.3 Network performance measurement
This section employs a NDEA model for data analysis of the similar sample of 52 bus
routes. The results obtained for every single hour are expressed in Table 7-18 (hours 7 to
13) and Table 7-19 (hours 14 to 19). Those results provide information about the overall
performance of bus routes at hour level across a working day.
Table 7-20 represents the efficiency scores of bus routes for different periods of time
within a day (peak periods and off-peak periods) and for a day 21st August 2013. Based on
the efficiency scores of a day, the given bus routes are ranked and shown in Table 7-21.
The results from Table 7-21 indicate that there are seven efficient DMUs, including
routes 130, 160, 161, 192, 230, 334, and 370. Those routes are benchmarks for the given
sample. On the contrary, routes 174, 310, 325, 340, 335, 124, 185, and 155 are the most
inefficient routes (efficiency score is less than 0.5). Those inefficient routes need to be further
investigated to identify the underlying reasons for their poor performance.
Figure 7-8 presents the efficiency scores of bus routes for different periods of time
with the gradual decrease of day’s efficiency scores. The results indicate the significant
variations of efficiency scores among different routes and different time periods of a single
route. Only two routes, 130 and 334, are efficient for all periods of time.
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Table 7-18: Network efficiency scores of 52 bus routes from hour 7 to hour 13
NO DMU Hour 7 Hour 8 Hour 9 Hour 10 Hour 11 Hour 12 Hour 13
1 Route 100 1 0.913 0.873 0.697 0.795 0.998 0.769 2 Route 105 1 0.5 0.5 0.515 0.228 1 1 3 Route 110 0.645 0.843 0.342 0.588 0.219 0.201 0.538 4 Route 111 0.653 1 0.977 0.744 0.764 0.673 0.782 5 Route 112 0.734 0.54 1 1 1 1 0.65 6 Route 113 0.296 0.35 0.164 1 0.234 1 7 Route 115 0.66 1 1 0.507 1 0.134 1 8 Route 116 1 1 0.516 1 1 0.514 1 9 Route 120 0.499 0.961 0.761 0.84 0.553 0.444 0.535
10 Route 124 1 0.406 0.211 0.542 0.401 0.757 0.719 11 Route 125 0.72 0.352 0.421 0.489 1 0.91 0.765 12 Route 130 1 0.935 1 1 1 1 1 13 Route 135 0.557 1 0.81 0.797 0.923 0.679 0.725 14 Route 140 0.328 0.389 0.441 0.68 0.526 0.91 0.805 15 Route 150 0.588 0.88 0.601 1 0.711 1 1 16 Route 155 0.5 0.219 0.21 0.535 0.166 0.513 17 Route 160 0.748 0.617 0.957 0.542 0.453 0.516 0.862 18 Route 161 1 0.878 0.612 0.196 1 0.513 19 Route 170 0.567 0.494 0.687 0.594 0.53 0.37 0.556 20 Route 172 0.447 0.77 1 0.363 0.25 1 0.613 21 Route 174 0.394 0.473 0.449 0.559 0.559 0.414 0.487 22 Route 175 0.378 0.448 0.514 0.501 0.397 1 0.458 23 Route 180 0.342 0.853 0.758 0.431 0.412 0.574 0.808 24 Route 184 1 0.586 0.521 0.393 0.282 0.222 0.45 25 Route 185 0.269 0.598 0.238 0.303 0.508 0.154 0.576 26 Route 192 1 0.277 0.384 0.532 0.466 1 0.931 27 Route 200 0.404 0.454 0.451 0.604 0.362 0.681 0.731 28 Route 202 0.567 0.554 0.369 0.44 0.262 0.561 0.286 29 Route 203 0.5 0.683 0.948 1 0.511 0.586 0.623 30 Route 204 0.857 0.778 0.553 0.389 0.683 0.958 0.62 31 Route 210 1 0.438 0.489 0.287 0.545 0.765 0.577 32 Route 212 0.704 0.788 0.517 0.591 0.529 1 1 33 Route 215 1 0.5 0.545 0.515 0.332 0.5 0.471 34 Route 220 1 0.218 0.292 0.535 0.163 0.545 0.535 35 Route 222 0.552 1 0.957 1 0.773 0.641 0.57 36 Route 230 1 1 0.481 0.619 0.484 0.883 1 37 Route 235 0.447 0.906 1 1 0.705 0.41 0.663 38 Route 310 0.634 0.501 0.218 0.359 0.189 0.531 0.532 39 Route 321 1 1 0.27 0.506 0.139 1 1 40 Route 325 0.603 0.644 0.38 0.233 0.532 0.545 0.316 41 Route 330 0.838 0.972 0.955 0.839 0.718 0.874 0.664 42 Route 333 0.768 0.739 0.776 0.955 0.815 0.916 0.93 43 Route 334 0.529 1 1 0.676 0.504 1 0.893 44 Route 335 0.628 1 0.368 0.242 0.506 1 0.527 45 Route 340 0.765 0.655 0.683 0.412 0.444 0.576 0.486 46 Route 345 0.873 1 0.798 0.737 0.798 0.536 0.751 47 Route 346 0.497 0.667 1 0.506 0.501 1 0.503 48 Route 353 0.464 0.835 1 0.278 0.074 0.281 0.429 49 Route 359 0.786 0.895 0.643 0.875 0.554 0.65 0.728 50 Route 370 0.365 0.886 1 0.707 0.984 0.751 1 51 Route 390 0.442 0.993 0.605 0.665 0.683 0.828 1 52 Route 444 0.781 1 0.793 0.907 0.785 1 0.888
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Table 7-19: Network efficiency scores of 52 bus routes from hour 14 to hour 19
NO DMU Hour 14 Hour 15 Hour 16 Hour 17 Hour 18 Hour 19
1 Route 100 0.699 1 0.92 0.773 0.903 0.719 2 Route 105 0.355 0.441 0.292 0.373 0.072 1 3 Route 110 0.514 0.354 0.535 0.686 0.674 0.346 4 Route 111 0.769 0.981 1 1 0.945 0.75 5 Route 112 1 0.909 0.836 0.437 0.642 0.24 6 Route 113 1 0.717 0.344 0.363 0.179 7 Route 115 0.5 0.442 0.284 0.067 1 0.003 8 Route 116 0.741 0.857 0.796 0.117 0.712 0.075 9 Route 120 0.488 0.54 0.599 0.744 0.589 1
10 Route 124 0.335 0.812 0.279 0.488 0.454 0.369 11 Route 125 0.286 0.755 0.35 0.483 0.633 0.655 12 Route 130 1 1 1 1 1 1 13 Route 135 0.574 1 0.352 0.359 0.189 0.5 14 Route 140 0.673 0.849 0.728 0.792 0.965 1 15 Route 150 1 1 1 0.939 1 1 16 Route 155 0.358 0.079 0.069 0.054 0.006 17 Route 160 0.857 0.473 1 0.834 0.8 0.748 18 Route 161 1 1 0.412 1 0.754 0.714 19 Route 170 0.521 0.331 0.763 0.846 0.877 0.75 20 Route 172 0.939 0.81 0.344 0.468 0.613 0.3 21 Route 174 0.358 1 0.301 0.369 0.586 0.31 22 Route 175 1 0.446 0.921 0.38 0.35 1 23 Route 180 0.403 0.66 0.527 0.568 0.81 0.787 24 Route 184 0.424 1 0.355 0.47 0.202 0.5 25 Route 185 0.623 0.829 0.703 0.591 0.233 0.413 26 Route 192 0.579 0.898 1 0.591 1 1 27 Route 200 0.318 0.291 0.429 0.414 0.437 0.377 28 Route 202 0.388 0.487 0.761 0.334 0.509 0.287 29 Route 203 0.287 0.949 0.54 0.82 0.206 0.148 30 Route 204 0.587 0.627 0.505 0.726 0.651 0.57 31 Route 210 0.783 1 0.783 0.799 0.238 32 Route 212 0.516 0.725 0.441 0.413 1 1 33 Route 215 0.181 0.426 0.615 1 1 1 34 Route 220 0.504 0.805 0.862 0.513 0.323 1 35 Route 222 0.686 0.787 0.709 0.675 1 1 36 Route 230 0.496 0.745 1 0.885 0.967 1 37 Route 235 0.758 0.728 0.498 1 1 1 38 Route 310 0.535 1 1 0.423 0.352 0.398 39 Route 321 0.512 1 0.36 0.982 0.709 1 40 Route 325 0.547 0.254 0.424 0.372 0.478 0.537 41 Route 330 0.564 0.935 0.835 1 0.793 0.697 42 Route 333 0.79 0.953 0.946 0.918 1 0.758 43 Route 334 1 1 1 1 1 0.428 44 Route 335 0.562 0.311 0.362 0.384 0.359 0.245 45 Route 340 0.618 0.524 0.516 0.596 0.536 0.463 46 Route 345 0.925 0.977 0.9 0.981 1 1 47 Route 346 1 0.887 0.245 0.926 0.287 48 Route 353 1 0.36 0.696 0.481 0.468 0.374 49 Route 359 0.745 0.557 0.533 0.716 0.627 0.574 50 Route 370 0.892 0.546 1 1 0.715 0.632 51 Route 390 0.719 0.798 0.565 0.62 0.776 0.74 52 Route 444 0.916 1 0.88 0.94 0.622 0.627
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Table 7-20: Network efficiency scores of 52 bus routes for different periods of time and a day
NO DMU Hour 6-9 Hour 10-15 Hour 16-19 Hour 20-24 Day
1 Route 100 0.948 0.856 0.834 0.692 0.877 2 Route 105 1 0.435 0.339 0.591 0.552 3 Route 110 0.572 0.406 0.701 0.339 0.612 4 Route 111 1 0.819 1 0.699 0.943 5 Route 112 0.899 1 0.479 0.804 0.986 6 Route 113 0.22 0.777 0.421 0.573 7 Route 115 1 0.601 0.294 0.754 8 Route 116 1 1 0.528 0.747 0.849 9 Route 120 0.871 0.564 0.685 0.714 0.716
10 Route 124 0.496 0.724 0.366 0.38 0.421 11 Route 125 0.633 0.992 0.62 0.442 0.603 12 Route 130 1 1 1 1 1 13 Route 135 0.832 0.869 0.379 1 0.66 14 Route 140 0.41 0.734 0.863 0.798 0.748 15 Route 150 0.672 0.968 0.937 0.955 0.873 16 Route 155 0.4 0.332 0.082 0.366 17 Route 160 0.978 0.673 1 0.674 1 18 Route 161 0.992 1 0.855 1 19 Route 170 0.658 0.507 1 0.473 0.865 20 Route 172 0.901 0.744 0.563 0.775 21 Route 174 0.472 0.754 0.353 0.316 0.495 22 Route 175 0.47 1 0.603 0.851 0.62 23 Route 180 0.634 0.592 0.6 0.451 0.574 24 Route 184 1 0.619 0.432 0.247 0.511 25 Route 185 0.378 0.469 0.536 0.347 0.378 26 Route 192 0.343 0.867 1 1 1 27 Route 200 0.462 0.55 0.539 0.274 0.541 28 Route 202 0.413 0.646 0.637 0.943 0.569 29 Route 203 0.91 0.737 0.555 0.777 30 Route 204 0.875 0.753 0.663 0.599 0.763 31 Route 210 0.537 0.766 0.947 1 0.853 32 Route 212 0.696 0.88 0.698 0.353 0.755 33 Route 215 0.8 0.426 0.797 1 0.642 34 Route 220 1 0.541 0.739 0.816 0.784 35 Route 222 0.91 0.753 0.984 0.658 0.884 36 Route 230 1 0.892 0.966 0.158 1 37 Route 235 0.716 0.996 0.917 1 0.952 38 Route 310 0.525 0.459 0.476 0.392 0.489 39 Route 321 0.823 0.661 1 0.859 40 Route 325 0.554 0.366 0.498 0.598 0.488 41 Route 330 0.96 0.752 0.788 0.597 0.79 42 Route 333 0.83 0.926 0.935 0.795 0.968 43 Route 334 1 1 1 1 44 Route 335 0.876 0.395 0.336 0.376 0.453 45 Route 340 0.756 0.47 0.487 0.395 0.479 46 Route 345 0.929 0.8 0.998 0.768 0.928 47 Route 346 0.607 0.796 0.563 0.701 48 Route 353 0.906 0.354 0.682 0.646 0.61 49 Route 359 0.908 0.781 0.717 0.643 0.868 50 Route 370 0.91 1 1 0.561 1 51 Route 390 0.668 0.938 0.709 0.67 0.793 52 Route 444 0.937 1 0.778 0.956 0.926
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Table 7-21: Ranking of 52 bus routes in network model for a working day (21 Aug 2013)
Ranking DMU Efficiency
scores
Ranking DMU Efficiency
scores 1 Route 130 1 21 Route 204 0.763
1 Route 160 1 22 Route 212 0.755
1 Route 161 1 23 Route 115 0.754
1 Route 192 1 24 Route 140 0.748
1 Route 230 1 25 Route 120 0.716
1 Route 334 1 26 Route 346 0.701
1 Route 370 1 27 Route 135 0.66
2 Route 112 0.986 28 Route 215 0.642
3 Route 333 0.968 29 Route 175 0.62
4 Route 235 0.952 30 Route 110 0.612
5 Route 111 0.943 31 Route 353 0.61
6 Route 345 0.928 32 Route 125 0.603
7 Route 444 0.926 33 Route 180 0.574
8 Route 222 0.884 34 Route 113 0.573
9 Route 100 0.877 35 Route 202 0.569
10 Route 150 0.873 36 Route 105 0.552
11 Route 359 0.868 37 Route 200 0.541
12 Route 170 0.865 38 Route 184 0.511
13 Route 321 0.859 39 Route 174 0.495
14 Route 210 0.853 40 Route 310 0.489
15 Route 116 0.849 41 Route 325 0.488
16 Route 390 0.793 42 Route 340 0.479
17 Route 330 0.79 43 Route 335 0.453
18 Route 220 0.784 44 Route 124 0.421
19 Route 203 0.777 45 Route 185 0.378
20 Route 172 0.775 46 Route 155 0.366
The results of the correlation analysis between efficiency scores in the network model
of different periods of time are shown in Table 7-22. Among all periods of time, efficiency
scores of the afternoon peak period have the highest correlation with those of a day
(correlation coefficient is 0.8), presenting the similar result with model 1 and 2. This
demonstrates that the afternoon peak period is the most important period within a day of bus
services in the case study of Brisbane.
Table 7-22: Correlation analysis results of efficiency scores of different periods of time
5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day
Day 0.53 0.68 0.80 0.50 1
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a) Efficiency scores of the first 26 routes for different periods of time
b) Efficiency scores of the last 26 routes for different periods of time
Figure 7-8: Efficiency score variations of bus routes in network model for different periods of time,
following the gradual decrease of a day’s efficiency scores
The comparison between efficiency scores of model 1 (the Technical efficiency
measure) and model 2 (the Service effectiveness measure) for a day is shown in Figure 7-9,
with the gradual decrease of model 2 efficiency scores. The correlation coefficient between
those two models is 0.12, suggesting that there is a weak relationship between the technical
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efficiency and the service effectiveness of the given bus routes. This result supports the
findings in the literature that the efficiency and effectiveness measures are different
perspectives of transit (Chu, Fielding et al. 1992).
a) Efficiency scores of the first 26 routes of models 1 and 2
b) Efficiency scores of the last 26 routes of models 1 and 2
Figure 7-9: Efficiency score variations of bus routes in models 1 and 2 for a day following the gradual
decrease of model 2 efficiency scores
From the results in Figure 7-9, there are six efficient routes in both model 1 and 2,
while some routes have low efficiency scores for both models. Some bus routes are efficient
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in model 1, but significantly inefficient in model 2. By contrast, some routes are efficient in
model 2, but significantly inefficient in model 1. Details of those routes are presented in Table
7-23 with the six bus routes (130, 160, 161, 192, 334, and 370) being the benchmarks of the
considered sample.
Table 7-23: Efficiency scores statistics of some routes for models 1 and 2
DMU Model 1 efficiency score Model 2 efficiency score Notes
Route 130 1 1 Routes are efficient in
both models. Route 160 1 1
Route 161 1 1
Route 192 1 1
Route 334 1 1
Route 370 1 1
Route 174 0.72 0.546 Low efficiency score in
both models. Route 184 0.768 0.518
Route 185 0.778 0.467
Route 202 1 0.569 High score in model 1,
but low score in model 2. Route 105 1 0.552
Route 200 1 0.541
Route 335 1 0.453
Route 155 1 0.366
Route 230 0.649 1 Low score in model 1,
but high score in model
2 Route 235 0.68 0.954
Identification of External Sources of Inefficiency and
Recommendations
Using DEA models only helps to rank the performance of bus routes and investigate
the internal factors affecting their performance efficiency, but cannot explain the influences
of external factors on efficiency levels of DMUs. This section uses the Simar and Wilson
(2007) double bootstrap approach to examine the impact that external variables (EVs)
have on the efficiency scores obtained in model 2 (the service effectiveness measure)
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for a working day (21st Aug 2013). Bus route performance of a working day is opted for
measure because it typically presents the actual demand of residents within the service
corridor of bus routes.
Seven EVs related to population density (PODC, PODYA, PODOA, and PODP),
individual income (LI, MI, and HI), and car ownership (CO) are used in this section, which
potentially affect the bus ridership. To account for the influences of routes’ characteristics on
efficiency levels of routes, this research employs three more independent variables including
signalised intersection spacing (SIS), lane priority (LAP), and frequency (FR). SIS and LAP
may affect the delay time of buses on each route, which possibly affects the attraction of bus
service to passengers. FR is a dummy variable, which accounts for the high or low service
frequency of bus routes. Here, FR equals 1 for high frequency bus routes (headway during
peak periods for one direction is equal to or less than 15 minutes) and 0 for low frequency
bus routes (headway is greater than 15 minutes).
Table 5-2 presents the results obtained from the correlation analysis of external
variables. There is a high correlation between PODOA and PODYA (correlation coefficient
equals to 0.82), and between HI and LI (correlation coefficient is -0.86). Therefore, PODOA
and HI are rejected from the sample of EVs.
Note:
PODC: population density of people with age under 18 within service areas of bus
route
PODYA: population density of young adults with age from 18 to 34 within service
areas of bus route
PODOA: population density of people with age from 35 to 64 within service areas of
bus route
PODP: population density of old people with age 65 and older within service areas of
bus route
LI: percent of low-income group (<400 AUD/week)
MI: percent of medium income group (400-1500 AUD/week)
HI: percent of high-income group (>1500 AUD/week)
SIS: route length per total number of signalised intersections on the route
LAP: percent of Busway travel length to route length
The model can be expressed as follows:
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��𝒊 = 𝜷𝟎 + 𝜷𝟏𝑷𝑶𝑫𝑪 + 𝜷𝟐𝑷𝑶𝑷𝒀𝑨 + 𝜷𝟑𝑷𝑶𝑫𝑷 + 𝜷𝟒𝑳𝑰 + 𝜷𝟓𝑴𝑰 + 𝜷𝟔𝑪𝑶 + 𝜷𝟕𝑺𝑰𝑺 +
𝜷𝟖𝑳𝑨𝑷 + 𝜷𝟗𝑭𝑹 + 𝜺𝒊 Equation 7-5
Where: 𝛿𝑖 is the bootstrapped bias-corrected efficiency scores.
Table 7-24a presents the original and bias-corrected efficiency scores on average.
The bias-corrected estimates are less than the original estimates, suggesting that without
correcting for bias, the results would overestimate the actual efficiency of bus routes. The
results also indicate that eight of the nine given EVs have a significant impact on the efficiency
of given routes (see Table 7-24b). The output-oriented efficiency score is the dependent
variable in this model, which varies from 0 to infinity. Therefore, a positive (negative)
coefficient of EV indicates a negative (positive) marginal effect on efficiency.
The results show that PODC with an estimated negative coefficient has a positive
impact on efficiency, while PODP on the contrary negatively affects efficiency of bus routes.
This indicates that a young group of Pop (PODC) contributes to an increase in efficiency,
while older groups of Pop (PODP) contribute negatively to efficiency. This result coincides
with the comparative analysis between routes 115 and 220 in section 7.3 that route 220 is
less efficient than 115 because it crosses areas with higher density of retirees. PODYA is the
only EV that is insignificantly correlated with efficiency scores of DMUs. This suggests that
young adults may use different means for daily travelling such as bus, rail, and private car.
Bus mode seems to be an irregular choice for commuting.
Regarding individual income, the results indicate that LI negatively affects efficiency
whereas MI contributes to an increase in efficiency of DMUs. This indicates that low-income
earners may tend to use bus services less than medium-income earners. The medium-
income group may have stable jobs at fixed work places, so they may use bus services
regularly for travelling between home and the work place. On the contrary, the actual travel
demand of the low-income group for daily work may be less than the medium-income group.
Additionally, CO negatively affects the efficiency of bus routes, highlighting the finding
elsewhere that car ownership possibly has an adverse effect on transit consumption (Taylor,
Miller et al. 2009). In South East Queensland, the mode share of private motor vehicles is
significantly high (accounting for 83% in 2006), and the Queensland Government aims to
reduce the share of trips taken by private motor vehicles to 66% in 2031 (Government 2011).
This statistic for mode share of private cars may support the finding above that private car
ownership has a negative impact on bus routes’ efficiency. Therefore, encouraging residents
to change their weekday trips from private car use to transit use may be an effective solution
for bus routes performance improvement.
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Finally, SIS, LAP and FR positively affect efficiency of bus routes, suggesting that bus
routes with high frequency and better conditions for decreasing delay time may be more
efficient. This suggests that the increase of FR for some inefficiency bus routes with
significantly low frequency (such as one hour) may be essential to improve their performance.
Moreover, possible solutions should be made by transit agencies to increase SIS and LAP of
some inefficient routes of the case study. This may help to increase the operating speed of
bus vehicles, OTP, and bus LOS, which makes bus service more attractive to passengers.
These findings significantly demonstrate the contribution of the exogenous operating
environment to the efficiency of bus routes in the given case study, which appeals to transit
regulators and operators for policy making to create a better operating environment for
inefficient bus routes.
Table 7-24: a) Original and bias-corrected efficiency scores; and b) Truncated Regression
a) Original and bias-corrected efficiency scores
Number of DMUs Original DEA estimates Bias-corrected estimates
Mean Standard deviation
52 0.731 0.63 0.101
Bias-corrected estimates are based on the first stage of Algorithm #2 of Simar and Wilson
(2007).
b) Truncated regression
Variable Coefficient Confidence Interval
Lower bound Upper bound
Constant -1.859462 -3.851271 -0.216262
PODC -0.003560* -0.005480 -0.000712
PODYA 0.000054 -0.000131 0.000149
PODP 0.006640** 0.002014 0.010353
LI 0.085844** 0.049474 0.131246
MI -0.044075* -0.084589 -0.004426
CO 4.542467** 1.089310 7.847107
SIS -0.137264* -0.297773 -0.036946
LAP -0.014555** -0.027754 -0.007861
FR -0.366482* -0.517776 -0.119881
** Significant at 1% confidence interval; * Significant at 5% confidence interval;
Total number of iterations = 2000; Bold values present significant variables.
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From this investigation of external sources of inefficiency of bus routes and the
identification of internal factors (service duration, space-km, and OTP) significantly
influencing the efficiency level of bus routes in sections 7.2 and 7.3, some recommendations
are provided in Table 7-25.
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Table 7-25: Recommendations for performance improvement of inefficient bus routes
Recommendation Rationale Further considerations
Decrease service duration of inefficient bus routes in model 1 (technical efficiency measure) by increasing the operating speed of bus vehicles (or reducing the travel time of trips).
Slack variables in model 1 mainly occur for service duration (see Table 7-3).
Transit agencies need to consider the signalised intersection spacing, stop spacing, and transit priority system. Those factors potentially affect bus service duration.
Reduce the number of bus stops along some routes to ensure the appropriate distance between them (which varies from 0.4 to 0.6 km for urban area (Alterkawi 2006)).
Buses’ delay time at signalised intersections can be reduced by using transit signal priority on arterial roads.
The most inefficient bus routes for model 1 (such as routes 174, 175, 230, and 235) in the sample show that its signalised intersection spacing (less than 0.55) and stop spacing (less than 0.35) are significantly lower than the mean of the sample (which are 0.88 and 0.64 for signalised intersection spacing and stop spacing, respectively).
Reducing the total number of stops will help to decrease the total dwell time at stops, and then reduce the travel time of trips. However, it possibly has adverse effect on the route accessibility of passengers.
The service effectiveness can be improved for the most inefficient routes by reducing space-km and increase OTP.
Slack variables in model 2 mainly occur for space-km and OTP (see Table 7-4).
It is hard to reduce the number of trips per day, so smaller bus size should be applied on those routes to be appropriate to actual demand.
Bus routes on the street (such as routes 184 and 185) can be provided with separate lane on arterial roads by road marking to ensure the operating speed and increase OTP.
LAP positively affects the efficiency of bus routes in model 2 (see Table 7-24b).
Transit agencies need to balance the road space for other modes such as private cars and bicycle.
The timetable of bus routes should be adjusted to accommodate the actual congestion on the road.
Inefficient routes with an hour headway should be considered to increase its frequency to at least two trips per hour. Such as routes 113, 185, 310, 325, and 335.
Bus frequency (FR) was demonstrated to positively contribute the efficiency of bus routes (see Table 7-24b).
Transit agencies need to consider the overlap of these routes with rail and other high frequency bus routes, such as 111, 180, 330, and 333.
The timetable of some routes should be further investigated and modified to be more appropriate to the actual demand of residents within their service areas.
Route 200 following pattern 4 (see Table 6-5) has the highest efficiency scores at middle noon (which offers 4 trips per hour for a direction) and lower efficiency scores for peak periods. This route offers 7 trips per hour during the morning peak period for inbound and 9 trips per hour during the afternoon peak period for outbound.
Route 200 has a significant overlap with route 222, so further study should be conducted to examine whether this overlap has a negative impact on its inefficient performance, and whether there is a need to reduce the frequency of this route to save resources and make it more efficient during peak periods.
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Transit operators are able to consider the recommendations proposed in Table 7-25
with further considerations to achieve the performance improvement of inefficient bus routes.
For example, for the morning peak hour (21st Aug 2013), the service duration that should be
reduced to improve the performance of inefficient bus routes regarding the technical
efficiency (model 1) is presented in Table 7-26. The space-km that should be reduced to
improve the performance of inefficient bus routes regarding the service effectiveness (model
2) is presented in Table 7-27
Table 7-26: Reduction of service duration for inefficient bus routes in model 1 (the morning peak hour)
DMU Efficiency
score
Reduction of service
duration (hour)
Route 112 0.699 0.23
Route 113 0.864 0.535
Route 116 0.754 0.756
Route 120 0.831 0.59
Route 124 0.726 0.536
Route 125 0.807 0.176
Route 155 0.855 0.028
Route 172 0.744 0.001
Route 174 0.742 1.304
Route 175 0.731 0.375
Route 180 0.797 0.413
Route 184 0.758 0.691
Route 185 0.793 1.389
Route 204 0.873 1.452
Route 210 0.722 0.142
Route 222 0.77 0.198
Route 230 0.765 1.144
Route 235 0.823 0.389
Route 310 0.815 0.091
Route 325 0.882 0.086
Route 345 0.888 0.859
Route 353 0.968 0.294
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Table 7-27: Reduction of space-km for inefficient bus routes in model 2 (the morning peak hour)
DMU Efficiency score Reduction of
space-km
Route 100 0.913 1935
Route 105 0.5 1414
Route 110 0.843 1290
Route 112 0.54 729
Route 120 0.961 4311
Route 130 0.935 7921
Route 150 0.88 6202
Route 160 0.617 2846
Route 172 0.77 919
Route 184 0.586 880
Route 204 0.778 1975
Route 215 0.5 836
Route 346 0.667 2040
Route 353 0.835 567
Summary of Findings
The sample of the 52 bus routes in the case study of Brisbane was employed for
empirical analysis using proposed framework and NDEA models. The obtained results
indicate that bus routes have fairly good performance regarding the technical efficiency
measure (model 1), while the temporal and spatial performance varies significantly with
regards to the service effectiveness measure (model 2).
NDEA proved to be a good tool for the performance measurement of the bus routes,
including two linked sub-processes (technical efficiency and service effectiveness). Here,
node 2 plays an important role in the network model. Therefore, the performance
improvement of node 2 may significantly lead to the overall bus route performance
improvement.
Based on the efficiency scores obtained from model 1 and model 2 separately, and
for network model, 52 bus routes are ranked for every hour and key periods of time within a
day, as well as a full day. The benchmarks and the least efficient bus routes of the given
sample are identified. Furthermore, the internal factors, significantly affecting the efficiency
levels of bus routes, are identified. The empirical analyses show that, for technical efficiency
measurement (model 1) service duration is statistically associated with inefficient routes,
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while for service effectiveness (model 2), space-km and on-time performance (OTP) have a
potential role in improving the performance of ineffective routes.
The comparison between results obtained from model 1 and model 2 indicates that
there is a weak correlation between the service production process and the service
consumption process. This is explained by the significant variations of bus ridership of
different routes, and different periods of time in a day of a single bus route. Thus, it is essential
to investigate the influences of external factors on the performance of bus routes, especially
factors related to the bus ridership.
Based on the data of external factors collected within the service corridor of individual
bus routes, the sensitivity of efficiency scores in model 2 to EVs was examined using the
double bootstrap model of Simar and Wilson (2007). The results demonstrate the significant
effect of eight out of nine selected EVs on the efficiency levels of DMUs. It is notable that
private car ownership (CO) and low-income group (LI) negatively affect the efficiency,
whereas population density of people under 18 (PODC) positively contributes to the efficiency
of DMUs. Those results are similar to the findings of Taylor, Miller et al. (2009). Furthermore,
the characteristics of bus routes (SIS and LAP) and service frequency (FR) are demonstrated
to be positively significant to the efficiency of DMUs. Those findings provide transit policy
makers with additional and useful information for decision making, which helps to improve
the operating environment of inefficient routes.
Based on the investigation of both internal and external sources of inefficiency,
several recommendations are also proposed to improve the performance of bus routes in the
case study. Here, the operating environment of bus routes should be improved by bus priority
systems (lane priority and signal priority) and appropriate distance between stops. This helps
to reduce service duration and increase OTP. Additionally, FR should be increased for
several routes with only an hour headway.
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Khac Duong Tran Page 135
8 Conclusion and Recommendations
This chapter summarises the findings and contributions of this research; and provides
potential directions for future research. The main results obtained are summarised in section
8.1. Significant contributions are presented in section 8.2. Section 8.3 identifies the practical
implications and section 8.4 discusses the limitations of this research. Finally, section 8.5
provides recommendations for future research on this topic.
Summary of Research Findings
This research is carried out to evaluate the spatial and temporal performance of
individual bus routes composing a bus network, and investigate its sources of operational
inefficiency. Therefore, it is organised coherently to achieve the four research objectives
outlined in Section 1.6, Chapter 1:
Research objective 1: ‘Build up a framework to measure the operational
effectiveness of key bus routes within a bus network.’
Research objective 2: ‘Measure the temporal and spatial performance of key bus
routes within a bus network using the proposed framework in objective 1.’
Research objective 3: ‘Examine the influence of external variables on the efficiency
scores estimated in objective 2.’
Research objective 4: ‘Provide recommendations to transit agencies and policy
makers to improve bus route performance considering the knowledge generated
through the case study conducted.’
The first research objective was fulfilled by Chapter 2 (Literature review), Chapter
3 (Methodology), and Chapter 4 (Framework for bus routes performance measurement). The
role of each chapter is as follows:
o Chapter 2 first reviewed the approaches used for performance measurement of
bus systems in the literature (Section 2.1). This found that there are three main
approaches to measure the performance of a bus system, including (1)
Comparative Analysis (CA); (2) Stochastic Frontier Analysis (SFA); and (3) Data
Envelopment Analysis (DEA). Compared with CA, an approach using different
single productive ratios (an output/ an input) to compare bus route performance,
SFA and DEA are superior in dealing with DMUs with multiple inputs and outputs.
Both SFA (a parametric approach) and DEA (a non-parametric approach) are able
to generate an overall efficiency score of a given DMU based on the frontier
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production function (the best DMUs within a set of DMUs). Therefore, most recent
studies that were reviewed have employed SFA and/or DEA for performance
measurement of bus systems. Although both SFA and DEA have their own
advantages and disadvantages, it is proven by Michaelides et al. (2010) that those
two approaches generate consistent results in general terms. The DEA model
requires no specific functional form for the production function, and the sensitivity
of DEA scores to data errors can be addressed by using AFC data, a fairly
accurate data source. Furthermore, Coelli et al. (1998) indicated that the SFA
approach is only well-developed for single-output technologies, and that in the
non-profit service area where multiple-output production is important and prices
are difficult to define, the DEA approach should be applicable. Thus, DEA is
employed for empirical analysis in this research.
Second, Chapter 2 reviewed bus performance evaluation using the DEA
models (in Section 2.2). The results indicated that bus performance is measured
at both system (DMUs are bus systems) and route levels (DMUs are bus routes
within a system). However, a limited number of studies focused on measurement
at the route level. Additionally, the performance measurement is separately
performed for two major bus performance concepts defined by Fielding et al.
(1985): (1) Technical efficiency; and (2) Service effectiveness. Those
performance concepts are coincided with the definitions of ‘productivity’ and
‘utilisation’ of Vuchic (2007), respectively. Therefore, there is a need to develop
a comprehensive framework for bus route performance measurement, which
considers both of these bus route performance concepts.
o Chapter 3 provided details about the CCR-DEA model (developed by Charnes,
Cooper, and Rhodes (CCR) in 1978) and the BCC-DEA model (developed by
Banker, Charnes and Cooper in 1984), and the network DEA model (NDEA)
developed by Färe and Grosskopf (2000). NDEA illustrates its ability to look into
the internal structure of a production process consisting of several linked sub-
processes, and generates a single overall efficiency score of DMUs. Therefore, a
NDEA model was selected for the development of framework for the examination
of bus routes’ performance.
o Chapter 4 developed the framework for bus routes’ performance evaluation with
appropriate inputs and outputs. This framework, consisting of two linked nodes (1
and 2), enables one to either evaluate the performance of bus routes for each
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Khac Duong Tran Page 137
node separately (models 1 and 2 for nodes 1 and 2, respectively) or for the whole
network model. Particularly, ‘transit work’ was used to present the service
consumption in this model. This offers a more accurate output compared to the
definition of ‘passenger-km’ in preceding studies. The first research objective
was fully achieved by the development of the NDEA-based framework for bus
route performance evaluation in this chapter.
Research objective 2 was performed by Chapter 5 (data collection), Chapter 6
(Data analysis for individual bus routes of the case study), and Chapter 7 (Empirical analysis
for bus system of the case study). The achievement of this objective was established through
two stages of empirical analysis. The first stage was to understand the temporal performance
of individual bus routes (Chapter 6), and the second stage was to measure the spatial and
temporal performance of several bus routes of the case study (Chapter 7). Details are as
follows:
o Chapter 5 provided the methods for data collection of both internal (Section 5.2)
and external variables (Section 5.3). Regarding internal variables, a dataset of
52 key bus routes of the case study were collected for a period of one working
week, from Monday 19th to Friday 23rd August 2013. Bus performance indicators
were drawn from AFC data supplied by TransLink Division of Queensland
Department of Transport and Main Roads, Australia. Relevant variables such as
route length, section length between stops, and timetable were obtained from the
TransLink website (http://translink.com.au).
External variables (EVs) were collected for the sample of 52 bus routes
using ArcGIS and ABS 2011 Census. For a single bus route, the service corridor
was first created using a stop buffering method. The EVs’ data were then
calculated within the service corridor of corresponding route using ABS 2011
Census at the Statistical Areas Level 1 (SA1), which is the most detailed level of
demographic and socio-economic data. Therefore, this method offered the
opportunity to obtain the best EVs for each route.
o Chapter 6 illustrated the results obtained from the temporal performance of
individual bus routes. Here, the DMUs are the performance of a single bus route
for different hours across all working days of a week. This chapter examined the
temporal performance of Route 111 across 19th August 2013 and compared the
results obtained from DEA models (CRS and VRS model) for inbound direction
with two basic transit productiveness indexes (Transit work load factor and Transit
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passenger transmission efficiency). It was found that DEA provides additional
advantages in dealing with DMUs consisting of multiple input and output variables,
and that for one direction of a bus route, CRS-DEA efficiency score is closer to
basic transit productiveness indexes than VRS-DEA efficiency score. Additionally,
bus route performance is more efficient during peak periods than off-peak periods
across a day.
This chapter also examined the temporal performance of individual bus
routes using a CRS model. A total of 52 bus routes are categorised into three
clusters: (1) high frequency; (2) low frequency for a long service period; and (3)
low frequency for a short service period. The results indicated that cluster 1
achieves stable efficiency scores of a given hour over different days, while clusters
2 and 3 experience significant variations in efficiency scores of DMUs across
different weekdays. Thus, bus frequency possibly affects the service
consumption of each bus route, and should be examined in the second stage of
analysis. Finally, six different patterns of the changes of efficiency scores of each
route across the daytime were identified on the basis of the results.
o Chapter 7 presented the results obtained from the temporal and spatial
performance analysis of 52 bus routes. An output-oriented NDEA model was
employed for empirical analysis with DMUs being the performance of different bus
routes during a given period of time (an hour, peak/off-peak periods within a day,
and a day). The NDEA model was proven to be a good tool for bus routes’
performance measurement.
Based on the efficiency scores obtained from model 1 and model 2
separately, and from the network model, 52 bus routes were ranked for each
model for different periods of time, especially for a day. The benchmarks and the
least efficient bus routes of the given sample were identified.
Furthermore, the internal factors, significantly affecting the efficiency levels
of bus routes, were identified. The analyses showed that, for technical efficiency
(model 1), service duration is statistically associated with inefficient routes, while
for service effectiveness (model 2), space-km and on-time performance (OTP)
have a potential role in improving the performance of ineffective routes.
Research objective 3 was fulfilled by Chapter 5 (data collection) and Chapter 7
(Data analysis for bus system of the case study). Based on the data of external factors
Conclusion and Recommendations
Khac Duong Tran Page 139
collected within the service corridor of individual bus routes in Chapter 5, the sensitivity of
efficiency scores in model 2 to EVs was examined using the double bootstrap model of Simar
and Wilson (2007) in Chapter 7. The results demonstrated the significant effect of eight
out of nine selected EVs on the efficiency levels of DMUs. It was observed that private
car ownership (CO) and low-income group (LI) negatively affected the efficiency levels,
whereas population density of people under 18 (PODC) positively contributed to the efficiency
of DMUs. These results coincide with the findings in literature. Furthermore, the
characteristics of bus routes (SIS and LAP) and service frequency (FR) were demonstrated
to be positively significant to the efficiency of DMUs. This result clarified the hypothesis in
Chapter 6 that high frequency routes attract more regular passengers than low frequency
bus routes.
Research objective 4 was given by Chapter 7. Here, both internal and external
factors contributed to the performance of bus routes. Reducing service duration of inefficient
routes is one of the solutions to improve the technical efficiency of the bus route. The increase
of on-time performance (OTP) and decrease of space-km may be solutions to improve the
service effectiveness. Regarding the operating environment of bus routes, the increase of
SIS and LAP for some inefficient bus routes should be considered to reduce the delay time
and offer better LOS. Another solution is that the timetable of some inefficient routes should
be modified with the careful consideration of travel behaviour of local residents.
Research Contributions
The principal contribution of this research is that it has developed a comprehensive
approach to provide insight into the temporal and spatial performance of bus transit,
considering the influences of external factors on bus routes’ performance. Through a logical
process, the achievement of the four research objectives has made several contributions to
transit knowledge in the course of conducting. Those contributions are as below:
o This research developed a network DEA-based framework for performance
evaluation of bus routes. As indicated in the literature review chapter, bus route
performance was explicitly examined for a particular performance concept
(technical efficiency or service effectiveness). The proposed network
framework, thus, provides transit professionals with an overall and single measure
for bus route performance evaluation (operational effectiveness). It allows one
to evaluate the operational effectiveness of individual bus routes, accounting for
both linked sub-production processes: technical efficiency and service
effectiveness. Thus, the results obtained from the NDEA model were
Conclusion and Recommendations
Khac Duong Tran Page 140
demonstrated in section 7.3 to be superior to those obtained from traditional
method (aggregate model).
o This research has addressed research gaps identified in Chapter 2 by employing
AFC data and 2011 ABS Census Data at SA1. AFC data was used for extracting
actual bus performance indicators such as travel time, OTP, space-km, and
transit work. Those actual bus performance indicators were then utilised as
inputs and outputs in DEA models to generate the most reliable results. ABS
Census Data at SA1 was used to calculate EVs (socioeconomic and demographic
characteristics) within the service corridor of a single bus route. Those EVs were
used in the truncated regression model (the Bootstrap model) to investigate the
impact of EVs on the efficiency levels of bus routes (refer to table 7-24).
o This research is the first of its kind that has investigated the temporal performance
of 52 individual bus routes using the case study in Brisbane, Australia, across a
working week (from 19th to 23rd August 2013). The results provided further
understanding of the temporal performance of those bus routes as follows: the
performance of bus routes are more stable during the daytime than the evening
time; high frequency routes attract more regular passengers than low frequency
routes; the changes of efficiency scores across the daytime of given bus routes
may follow six different patterns (refer to Table 6-5); and pattern 1 is the most
popular pattern for high frequency bus routes.
o The temporal and spatial performance of 52 bus routes of the case study in
Brisbane was sufficiently evaluated in this research using a NDEA model. Those
bus routes were examined for model 1 and model 2 separately, and for the
network model across different periods of time (every hour, key periods of time
within a day, and a full day). Bus routes were ranked to identify the benchmarks
and the most inefficient routes. Furthermore, through the values of slack variables,
this model helped to identify the internal sources of inefficiency and the
quantitative reduction of inputs/increase of outputs for the performance
improvement of those bus routes (refer to tables 7-26 and 7-27).
o Using the case study in Brisbane, Australia, this research is the first of its kind that
investigated the sources of inefficiency of given bus routes related to
socioeconomic and demographic characteristics within the service corridor of a
single bus route. It identified the significant influence of eights EVs on efficiency
of bus routes. Some EVs, such as CO, PODC, and LI, illustrated the coincided
Conclusion and Recommendations
Khac Duong Tran Page 141
results with findings in preceding studies, that were implemented at the urban area
level (EVs are collected for different urban areas). Thus, the knowledge gained
help to substantiate the existing findings in literature. Moreover, the results of
other EVs, like PODP, LAP, and FR, presented the additional findings for this case
study.
o This research has provided transit agencies and regulators in Brisbane with
additional information for policy making, which helps to optimise the performance
of the current transit system of this area (refer to section 8.3).
Practical Implications
The approach developed in this research can be used by transit professionals for
developing more practical and appropriate policies, which may help to improve the
performance of the current transit system, as well as support the planning of new routes.
Figure 8-1 presents the process in which regulatory rules and policies are made based on
additional information provided by the efficiency analysis process. The regulatory rules and
socio-economic policies made by regulators have an impact on the transit operating
environment: the external factors (such as private car ownership, parking facility, transit
accessibility, road system, traffic condition, and employment distribution) and the
management behaviour of transit agencies. Within a transit agency, decision making and
actions are made to offer better services for a community, which directly relate to the internal
factors (schedule, stops, priority lane, route length, and service coverage). Both internal and
external factors then significantly affect the service consumption of a target community.
Finally, analysing the performance efficiency of routes is useful to identify the benchmarking
routes, the most inefficient routes, and sources of inefficiency, and then effectively assist
transit operators and regulators in policy making.
This approach was developed for the bus mode of the case study in Brisbane. It is
transferable to bus networks of other cities. Furthermore, this approach could be applied to
other transit modes such as ferry and rail with the availability of AFC data.
Making decision is always a complicated process in transit sector, as it belongs to
public services and relevant to political, social and economic aspects. Therefore, based on
the empirical analysis, this study proposes some possible ways to addressed operational
problems of bus routes in the case study of Brisbane. Applicable policies should be made by
each transit agency based on different information and tools. To achieve the performance
improvement of the bus network in Brisbane, transit operators are able to consider the
recommendations provided in Table 7-25, including:
Conclusion and Recommendations
Khac Duong Tran Page 142
• Decrease service duration of inefficient bus routes in model 1 (Routes 174, 175,
230, and 235) by reducing travel time of trips. The travel time of trips could be
reduced by increasing the stop spacing by increasing the stop spacing (reduce
the stops) and/or providing transit signal priority at signalised intersections on
arterial roads.
• Ensure the appropriate distance between stops from 0.4 to 0.6 km for some bus
routes crossing urban areas (Routes 174, 175, 230, and 235) to reduce the travel
time of trips.
• Use transit signal priority on arterial roads to reduce delay time at signalised
intersections of some bus routes, such as routes 184 and 185 (refer to variable
SIS in table 7-24).
• Reduce space-km and increase OTP for inefficient routes in model 2 (Routes
155, 184, 185, 200, 325, and 335).
• Provide a separate lane for buses on arterial roads by road marking (such as
routes 174 and 175).
• Increase FR of some routes (such as 113, 185, 310, 325, and 335).
• Further investigate and modify the timetable of some routes (such as route 200)
to be more appropriate to the actual demand (overlap with rail or express bus).
Figure 8-1: Policy implications of transit routes performance analysis
Regulators
Policies and
regulatory rules
Transit operating
environment(external variables)
Service
consumption
Transit
agencies
Decision making
and actions
Service outputs(internal variables)
Efficiency
analysis
DEA
models
Truncated
regression
models
Conclusion and Recommendations
Khac Duong Tran Page 143
Limitations
Below is the list of limitations for the current research, largely due to data availability
and limited resources:
o The bus network of the case study in Brisbane consists of more than 250 bus
routes, while this research only employed a sample of 52 radial bus routes of this
case study for empirical analysis. Thus, the results achieved only introduce the
performance of several key routes within the network. With the availability of data
from other routes, the research can be extended to other routes for a
comprehensive analysis of the entire Brisbane network.
o Data in this research is collected from AFC data for only one working week
(Monday to Friday) in August 2013. Thus, it excluded weekends and public
holidays, where actual bus demand may change significantly because of many
public events. The timeframe of one week could not provide a longitudinal
performance evaluation of given bus routes.
o Regarding internal variables used in the proposed framework, some service
inputs, such as fuel consumption, operating cost, and maintenance cost, were
unavailable at the route level of the case study. Therefore, this research uses
proxies to refer to those service inputs. Additionally, this research estimates the
OTP at the destination of bus routes only because of the lack of arrival time at all
intermediate stops when extracting this indicator from AFC data.
o In terms of external variables, this research employed a number of variables
related to population, individual income, car ownership, and route characteristics
only. Other factors, such as weather, employment structure, and travel behaviour
of users were not considered. Moreover, external variables are calculated by
using information from ABS 2011 Census Data while AFC data in August 2013
were employed to generate inputs and outputs for DEA models. This two-year
delay of data collection may lead to bias on the obtained results of the sensitivity
analysis of efficiency scores. To demonstrate the applicability of the proposed
methodology, it is assumed that the changes of those external variables over the
period of two years are not significant.
o This research examined the performance of bus routes without considering the
impacts of other transit modes (such as ferry and especially rail) on bus demand.
Additionally, the linkage between bus routes was not considered.
Conclusion and Recommendations
Khac Duong Tran Page 144
o There are several ‘Park and Ride’ facilities in the case study, which may influence
the ridership of some nearby bus routes. In this research, ‘Park and Ride’ near the
service corridor of some bus routes was not taken into account.
o This research provides the performance evaluation of an entire bus route based
on data of complete trips. It represents the macro level of the average
performance along the route. The micro level of performance over different
segments of a route is not considered.
Recommendation for Future Research
This research has focused on the temporal and spatial performance evaluation of bus
routes in Brisbane, Australia. There are still several areas that need to be carried out in future
studies. The most potential areas for future research are as below:
o It would be useful to conduct a similar research in the future using a larger sample
of the case study in Brisbane (greater number of bus routes and longer period of
time). This sample should consist of both radial bus routes and local routes
connecting different suburb areas with each other. Such research would provide
more comprehensive results for this case study.
o This research has considered bus routes as DMUs in the DEA model. It would be
useful to carry out similar research in the future, which considers segments
composing a route as DMUs. The performance evaluation of transit routes at the
segment level would provide insights into the performance of each segment, as
well as identify the least efficient segments along a single route. This will assist
transit agencies effectively in making accurate decisions for system optimisation.
o This research only examined the performance of bus routes across working days
of a week. Future research, thus, can upgrade the approach developed in this
research to investigate the performance of bus routes in Brisbane on weekends
and public holidays to extend the findings.
o This research has employed several EVs to investigate the external sources of
inefficiency. However, a wide range of other EVs, in reality, may affect the
efficiency of bus routes such as employment distribution, the present of railway
on the bus corridor, stops accessibility, parking space availability, and the
presence of attraction points (schools, hospitals, shopping centres, recreation
centres). Therefore, future research can apply the proposed approach to examine
the influence of other EVs on bus efficiency.
Conclusion and Recommendations
Khac Duong Tran Page 145
o Although bus mode dominates in Brisbane, rail and ferry are important transit
modes in this area. Thus, it would be useful to conduct research on rail or ferry
system using the approach developed in this research with some necessary
adjustments.
o A non-parametric approach, the DEA model, was used in this research for
empirical analysis. However, SFA (a parametric approach) was demonstrated to
be a good tool for efficiency analysis of DMUs. Thus, it would be useful to carry
out research where SFA would be employed to examine bus route performance.
Furthermore, both DEA and SFA can be used in the future research together, and
then the results obtained from those two methods can be compared to explore the
work of each method.
Reference
Khac Duong Tran Page 146
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Appendix
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SPATIAL EFFICIENCY SCORES OF INDIVIDUAL
BUS ROUTES
This appendix provides the spatial performance of remaining individual bus routes within the
given sample (Chapter 6).
Figure A 1: CRS-DEA efficiency score of route 180 (follows pattern 1)
Figure A 2: CRS-DEA efficiency score of route 222 (follows pattern 1)
0
0.2
0.4
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1
Hour6
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CRS-DEA efficiency score of 180
Mon Tue Wed Thu Fri
0
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re
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CRS-DEA efficiency score of 222
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 152
Figure A 3: CRS-DEA efficiency score of route 111 (follows pattern 1)
Figure A 4: CRS-DEA efficiency score of route 150 (follows pattern 2)
Figure A 5: CRS-DEA efficiency score of route 330 (follows pattern 3)
00.20.40.60.8
1
Sco
re
Time
CRS-DEA efficiency score of 111
Mon Tue Wed Thu Fri
0
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1
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CRS-DEA efficiency score of 150
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CRS-DEA efficiency score of 330
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 153
Figure A 6: CRS-DEA efficiency score of route 340 (follows pattern 3)
Figure A 7: CRS-DEA efficiency score of route 345 (follows pattern 3)
Figure A 8: CRS-DEA efficiency score of route 310 (follows pattern 3)
0
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CRS-DEA efficiency score of 340
Mon Tue Wed Thu Fri
0
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1
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CRS-DEA efficiency score of 345
Mon Tue Wed Thu Fri
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1
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CRS-DEA efficiency score of 310
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Appendix
Khac Duong Tran Page 154
Figure A 9: CRS-DEA efficiency score of route 370 (follows pattern 1)
Figure A 10: CRS-DEA efficiency score of route 210 (follows pattern 5)
Figure A 11: CRS-DEA efficiency score of route 212 (follows pattern 5)
0
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1
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CRS-DEA efficiency score of 370
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CRS-DEA efficiency score of 210
Mon Tue Wed Thu Fri
00.20.40.60.8
1
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CRS-DEA efficiency score of 212
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 155
Figure A 12: CRS-DEA efficiency score of route 325 (follows pattern 5)
Figure A 13: CRS-DEA efficiency score of route 116 (follows pattern 6)
Figure A 14: CRS-DEA efficiency score of route 353 (follows pattern 6)
0
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CRS-DEA efficiency score of 325
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re
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CRS-DEA efficiency score of 116
Mon Tue Wed Thu Fri
00.20.40.60.8
1
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CRS-DEA efficiency score of 353
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 156
Figure A 15: CRS-DEA efficiency score of route 184 (follows pattern 2)
Figure A 16: CRS-DEA efficiency score of route 202 (follows pattern 3)
Figure A 17: CRS-DEA efficiency score of route 203 (follows pattern 5)
0
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CRS-DEA efficiency score of 184
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CRS-DEA efficiency score of 202
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re
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CRS-DEA efficiency score of 203
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 157
Figure A 18: CRS-DEA efficiency score of route 321 (follows pattern 5)
Figure A 19: CRS-DEA efficiency score of route 334 (follows pattern 5)
0
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Hour 7 Hour 8 Hour 9 Hour10
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CRS-DEA efficiency score of 321
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CRS-DEA efficiency score of 334
Mon Tue Wed Thu Fri
Appendix
Khac Duong Tran Page 158
DISCUSSION ON SLACKS
Coelli, Prasada Rao et al. (1998) indicated that the piece-wise linear form of the non-
parametric frontier in DEA can cause a few difficulties in efficiency measurement. The
problem arises because of the sections of the piece-wise linear frontier which run parallel to
the axes (see Figure B 1) which do not occur in most parametric functions. Refer to the Figure
B 1 where the firms use two inputs (x1 and x2) to produce an output y, C and D are the two
efficient firms that define the production frontier (SS’). Firms A and B are inefficient firms
within the production possibility set T. The Farrell (1957) measure of technical efficiency gives
the efficiency level of firms A and B as OA’/OA and OB’/OB, respectively. However, it is
questionable as to whether the point A' is an efficient point since one could reduce the amount
of input x2 used (by the amount CA') and still produce the same output. This is known as
input slack (𝜽𝒙𝒊 − 𝑿𝝀 = 𝒔−) in the literature. Once one considers a case involving more
inputs and/or multiple outputs, the diagrams are no longer as simple, and the possibility of
the related concept of output slack (𝒀𝝀 − 𝒚𝒊 = 𝒔+) also occurs (for the given optimal values
of 𝜽 and 𝝀).
Some authors argue that both the Farrell measure of technical efficiency (θ) and any
non-zero input or output slacks should be reported to provide an accurate indication of
technical efficiency of a firm in a DEA analysis (Tone, Cooper et al. 1999, Cooper, Seiford et
al. 2007). Thus, it can be stated that the i-th firm is completely efficient if its efficiency score
equal 1 and the input and output slacks are equal to zero (𝒔− = 𝟎 𝒂𝒏𝒅 𝒔+ = 𝟎).
Figure B 1: Efficiency Measurement and Input Slacks (Source: Coelli, Prasada Rao et al. (1998))
A
B
D
B'C
A'
S'
S
x1/q
x2/q
0
Appendix
Khac Duong Tran Page 159
EXAMPLES FOR DETAILED SAMPLE CALCULATION USING THE DEA MODELS
This appendix presents several examples for detailed empirical analysis of the given sample, using the DEA models. This research uses
Matlab codes and MaxDEA Pro software for data empirical analysis. Here, the slack movement of inputs is presented by negative values.
Table C 1: CCR-DEA efficiency scores of route 111 obtained from temporal performance analysis in Chapter 6 (the date 19th Aug 2013)
Note: PM: proportionate movement; SLM: slack movement; PR: projection
Appendix
Khac Duong Tran Page 160
Table C 2: BCC-DEA efficiency scores of route 111 obtained from temporal performance analysis in Chapter 6 (the date 19th Aug 2013)
Note: PM: proportionate movement; SLM: slack movement; PR: projection
Appendix
Khac Duong Tran Page 161
Table C 3: BCC-DEA efficiency scores of 52 bus routes obtained from empirical analysis of node 1 (7:00 to 8:00, the date 21st Aug 2013)
Appendix
Khac Duong Tran Page 162
Note: PM: proportionate movement; SLM: slack movement; PR: projection
Appendix
Khac Duong Tran Page 163
Table C 4: BCC-DEA efficiency scores of 52 bus routes obtained from empirical analysis of node 2 (7:00 to 8:00, the date 21st Aug 2013)
Appendix
Khac Duong Tran Page 164
Note: PM: proportionate movement; SLM: slack movement; PR: projection
Appendix
Khac Duong Tran Page 165
Table C 5: NDEA efficiency scores of 52 bus routes obtained from empirical analysis (7:00 to 8:00, the date 21st Aug 2013)
Appendix
Khac Duong Tran Page 166
Note: PM: proportionate movement; SLM: slack movement; PR: projection
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