lalit sivanandan nookala - university of minnesota duluth

Weather Impact on Traffic Conditions and Travel Time Prediction

by

Lalit Sivanandan Nookala

October 2006

Submitted in partial fulfillment of the

Requirements for the degree of

Master of Science

Under the instruction of Dr. Donald Crouch

Department of Computer Science

University of Minnesota Duluth

Duluth, Minnesota 55812

U. S. A.

UNIVERSITY OF MINNESOTA DULUTH

This is to certify that I have examined this copy of master’s thesis by

Lalit Sivanandan Nookala

And have found that it is completed and satisfactory in all aspects,

and that any and all revisions required by the final examining committee have been made.

Dr. Donald Crouch

_______________________________

Name of Faculty Advisor

______________________________

Signature of Faculty Advisor

_____________________________

Date

GRADUATE SCHOOL

i

ABSTRACT

Traffic congestion is caused by various factors such as accidents, inclement

weather conditions, road maintenance work etc. In this work, the traffic congestion

caused by weather conditions is studied and the effect of weather conditions on traffic

volume and travel time is analyzed. The weather conditions are recorded by the RWIS

sites for various locations in and around twin cities metro area. The values recorded using

RWIS gives more localized weather conditions and hence is useful in assessing the effect

on traffic. Color-coded daily traffic volume graph with the corresponding color-coded

volume/occupancy graph are analyzed to study the effect of weather conditions on traffic.

It has been observed that the traffic congestion increases due to inclement weather

conditions because the freeway capacity drops and the traffic demand does not drop

accordingly. It has also been observed that during severe snow conditions the traffic

demand also drops significantly and the congestion on the freeway disappears. Further,

the short term travel time prediction using time-varying coefficients was done for the

days that had been affected by severe weather conditions. The error in the prediction was

high due to congestion caused by the weather conditions and a part of this work was

devoted to reduce this error. It had been observed that the error in prediction is related to

the change in the traffic occupancy of the road. A new prediction model that is an

extension of the time-varying prediction model has been proposed as the part of this

thesis that incorporates the change of occupancy caused due to weather conditions. It has

been observed that the prediction error reduces with the new model.

ii

ACKNOWLEDGEMENTS

I am grateful to my thesis advisor Dr. Taek Kwon for giving me an opportunity to

work under him and for guiding me. I wish to thank him for boosting my confidence with

his constant encouragement. Without his support and contribution, this thesis would not

have been possible.

I would like to thank my thesis committee members Dr. Donald Crouch and Dr.

Gary Shute for their interest in my thesis and their helpful suggestions. I am grateful to

Carol Wolosz from the NATSRL office for her help and to Linda Meek, Lori Lucia, Jim

Luttinen and the faculty at Computer Science Department at UMD for their support. Last

but not the least, I take this opportunity to thank my family and my friends.

iii

TABLE OF CONTENTS

LIST OF FIGURES ...................................................................................................................... v

LIST OF TABLES ....................................................................................................................... vi

CHAPTER 1 : INTRODUCTION............................................................................................... 1

1.1 Traffic Congestion Issues ............................................................................................... 1

1.2 Related Work on Travel Time Prediction....................................................................... 2

1.3 Road Weather Information System (RWIS) (Kwon, Fleege 2000)................................ 3

1.4 Objective of thesis........................................................................................................... 4

CHAPTER 2 : THEORETICAL BACKGROUND................................................................... 6

2.1 Traffic Parameters ................................................................................................................. 6

2.1.1 Traffic Volume .....................................................................................................6

2.1.2 Traffic Flow Rate .................................................................................................6

2.1.3 Occupancy.........................................................................................................7

2.1.4 Traffic Density ......................................................................................................7

2.1.5 Traffic Speed .......................................................................................................7

2.1.6 Travel Time ...........................................................................................................8

2.1.7 Traffic Capacity ..................................................................................................8

2.1.8 Traffic Demand ...................................................................................................9

2.2 Prediction of Travel Time ................................................................................................... 10

2.2.1 Time-varying coefficients for short-term travel time prediction (Zhang, Rice 2001)....................................................................................................................10

2.2.2 Day to day travel time trends and travel time prediction from the loop detector data (Kwon, Coifman, Bickel 2000) .......................................................12

CHAPTER 3 : DATA SOURCE AND METHODOLOGY.................................................... 14

3.1 Site Selection and Data Source ........................................................................................... 14

iv

3.2 Relational Database............................................................................................................. 15

3.3 Methodologies Used to Analyze Weather Impact on Traffic ............................................. 16

3.3.1 Correlation coefficients...................................................................................16

3.3.2 Effect of pavement conditions on daily total volume...............................17

3.3.3 Effect of pavement conditions on traffic dynamics ..................................17

3.4 Methodology to analyze weather impact on travel time prediction .................................... 20

3.4.1 Travel time estimation......................................................................................20

3.4.2 Time-varying coefficients for travel time prediction ..................................20

CHAPTER 4 : EXPERIMENTAL RESULTS......................................................................... 24

4.1 Correlation Coefficient Matrix............................................................................................ 24

4.2 Impact of Pavement Conditions on Daily Traffic Volume ................................................. 26

4.3 Impact of Pavement Conditions on Congestion.................................................................. 30

4.3.1 Case 1: Increased congestion by snow .......................................................30

4.3.2 Case2: Reduction of congestion by a severe snow event.......................32

4.3.3 Case 3: Increased congestion by damp conditions .................................33

4.3.4 Case4: Volume decrease and increase of congestion by wet conditions....................................................................................................................34

4.3.5 Case 5: Changes in pavement conditions ..................................................37

4.4 Impact of inclement weather conditions on travel time prediction..................................... 39

4.4.1 Case1: Effect of travel time prediction when weather conditions do not cause congestion......................................................................................................39

4.4.2 Case 2: Effect of travel time prediction by before-and-after weather events ..........................................................................................................................41

4.4.3 Case3: Wet and damp pavement conditions in the morning peak time......................................................................................................................................43

4.4.4 Case 4: The whole day is affected by snow................................................45

4.4.5 Case 5: Multiple changes of weather changes during the day..............47

v

CHAPTER 5 : CONCLUSION.................................................................................................. 50

5.1 Conclusion........................................................................................................................... 50

5.2 Future Recommendations.................................................................................................... 51

REFERENCES............................................................................................................................ 53

LIST OF FIGURES

Figure 3.1: Location of R/WIS sites in and around the metro area used for the study......14

Figure 4.1: Effect of pavement conditions on the traffic volume of Little Canada on January 4th and January 11th in 2005. The volume/occupancy graphs of the corresponding days are also presented.......................................................................................................31

Figure 4.2: Effect of severe snow conditions on the traffic volume. The volume/occupancy graphs of the corresponding days are also presented..........................33

Figure 4.3: Effect of damp pavement conditions on the traffic volume. ...........................34

Figure 4.4: Effect of wet pavement conditions on the traffic volume. The volume/occupancy graphs of the corresponding days are also presented..........................36

Figure 4.5: Effect of different pavement conditions on the traffic volume. The volume/occupancy graphs of the corresponding days are also presented..........................38

Figure 4.6: Travel time is affected by the snow conditions and is adjusted but the severe snow condition reduces the total traffic volume and the congestion disappears and the travel time prediction error between the baseline estimate and the prediction model is very low. ............................................................................................................................41

Figure 4.7: Travel time is affected by the snow conditions and is adjusted by the formula given in the equation. The change in the weather condition though reduces the traffic volume but also increases the congestion which increases the travel time. The PPE graphs shows the error that occurs due to the change in weather..................................................42

Figure 4.8: Travel time is affected by the damp conditions and is adjusted. The damp conditions increases congestion and travel time that is underestimated by the prediction model..................................................................................................................................44

vi

Figure 4.9: Travel time is affected by the snow conditions and the weather condition does not change. The snow conditions increases the travel time and the prediction model is erroneous due to the weather condition. ............................................................................46

Figure 4.10: Travel time prediction is severely affected by changing weather conditions and the prediction model is unable to predict the travel time accurately. The TVWI equation computes the travel time and the error in prediction are reduced. ......................48

LIST OF TABLES

Table 2.1: Length Based Classification Boundaries ............................................................8

Table 3.1: R/WIS sites and detectors in the proximity .....................................................15

Table 4.1: The correlation coefficient matrix for January 2005 at the Little Canada site .25

Table 4.2: The correlation coefficient matrix for June 2005 at the Little Canada site ......26

Table 4.3: Surface Conditions in Number of Hours and Traffic Volume at the Little Canada Site in January 2005..............................................................................................28

1

CHAPTER 1 : INTRODUCTION

1.1 Traffic Congestion Issues

As the number of vehicles on the road steadily increases and the expansion of

roadways is remained static, congestion on urban freeways became one of the major

transportation issues in US. Urban traffic costs 3.7 billion hours of travel delay and $63

billion per annum in the USA (Shrank, Lomax, 2005). Two ways can be considered to

reduce congestion on urban freeways; one is to increase the total freeway capacity by

expanding the number of lanes on the existing roads or new roads, but this requires extra

lands and enormous expenditure on the infrastructure which is often not viable in many

urban areas. Another solution is to use various traffic control strategies in order to

efficiently use the existing freeways. The control strategies often involve predicting

congestion levels and proactively managing the traffic before congestion is reached.

Among many parameters, travel time is one of the indicators that helps in determining the

future states of the freeway sections (Ben-Avika et al, 1992)

Congestion can happen due to various conditions such as road work, peak hour

traffic, accidents, and inclement weather conditions (Chin et al 2004). The primary

objective of this thesis is to analyze the effect of inclement weather conditions on traffic.

It is known that inclement weather conditions decrease traffic demand while they also

decrease the freeway capacity (Goodwin, 2002). If the decrease rate of the freeway

capacity is faster than the decrease of the traffic demand, traffic congestion is bound to

occur. It has been noted that 15% of the congestion occur due to bad weather conditions

(Cambridge Systematics, 2005). However, it is still unclear on how much traffic

demand and freeway capacity decreases occur under adverse weather conditions. It is

also unknown what level of the demand/capacity imbalance causes the congestion and

how much the travel time is affected. This thesis will attempt to answer some of these

questions by analyzing the Twin Cities’ freeway and Road Weather Information System

(RWIS) data.

2

1.2 Related Work on Travel Time Prediction

Predicting travel time is difficult for various reasons. To predict travel time for a

section of a road, traffic conditions or the speed changes of the vehicles along the section

must be estimated. It is difficult to accurately estimate the traffic conditions since they

can widely vary in spatial and time domain (Hall, Persaud 1989).

In order to predict travel time, past history of travel time is one of the most

important measures. Several ways of collecting travel time data exist. The Automated

Vehicle Identification (AVI) is a recent technology that is being used to measuring travel

time (Dion, Rakha, TRB 2003). The AVI system has various AVI tags and AVI reader

system and a computer system to store the data that is required for processing. The AVI

data processing system computes the travel time. Several research programs presently try

to utilize cell phones in the vehicles for measuring the travel time (Yim et. Al 2000).

Video-based signature analysis for computation of travel time where the vehicle is

tracked by analyzing the video images and the speed is measured using laser detection

has also been proposed (Tam 1999/2000). Many other studies have focused on the widely

available loop detector data from the freeway network for estimating travel time. Studies

also include methods for vehicle re-identification based on sub-sampling of the freeway

loop detector data and using it for travel time measurement (Coifman, 1998), a more

recent study uses re-identification of vehicle signatures obtained from loop detectors for

travel time measurements using blind de-convolution (Parsekar, 2004;Kwon, Parsekar,

2005). Another study includes using inductive waveform for estimating travel time from

the loop detectors (Sun, Ritchie, 1999).

The flow and occupancy data available from the loop detectors placed in the

freeways is widely available; hence, many travel time prediction models make use of this

data. Spectral analysis has been suggested for predicting traffic flow (Nicholson, Swann

1974). Kalman filtering theory has been used to predict traffic flow in the immediate

future (Okutani, Stephanades 1984). Though traffic flow prediction may help in

predicting travel time, it does not necessarily lead to travel time prediction. Therefore,

recent research efforts mostly focus on direct prediction of travel time using the historic

3

and current levels of flow and occupancy data. Historical travel time information has

been used initially to predict the travel time (Schrader et al 2004). The time-varying

coefficient method utilizes a linear time-varying regression model and the coefficients are

estimated through historical travel time (Rice, van Zweet 2004, Zhang, Rice, 2001).

Another approach suggests a stepwise multiple regression model (Kwon, et. al 2000).

This model utilizes the volume and occupancy vector and the estimated travel time vector

for the given time to develop the model. The estimated travel time that the above two

approaches suggest is calculated by estimating the speed based on the volume and the

occupancy data collected by single loop detectors or speed data collected between a pair

of loop detector stations. These studies typically use artificial neural networks, support

vector machines, and regression trees for the prediction models (Kwon et. al 2000).

Studies also suggest that under various conditions these machine learning algorithms can

perform with varied degrees of success (Kwon et al 2000). Though it is still a debatable

issue whether to use neural network or statistical methods for traffic forecasting (Kirby et

al 1999).

Most of the models mentioned above use historical travel time, but do not utilize

road weather conditions on the freeway section. Several research results on weather

impact on traffic have been published, but none was directed towards incorporating the

impact of weather conditions to a travel-time prediction model (Pisano, Goodwin 2002).

To the best of the author’s knowledge, none of today’s travel time prediction models

incorporates weather conditions into their predicted travel time.

1.3 Road Weather Information System (RWIS) (Kwon, Fleege 2000)

Traditionally the weather conditions available to researchers and engineers were

the data from the National Weather Service (NWS) that does not provide the weather

condition specific to a particular segment of a freeway (Federal Highway Administration

2005). It has been frequently observed by transportation departments that freeway driving

conditions (pavement conditions) can be significantly different from one section to

4

another section within the same freeway especially during the winter storms, i.e., NWS

data in general is not detailed enough for learning the present pavement conditions.

Therefore, a relatively new system called the Road Weather Information System (RWIS)

has been implemented in many states, which reports the micro climatic conditions at a

specific location. This information is representative of the road weather conditions where

the RWIS station is located.

RWIS is a sensor network that collects sub-surface, surface and atmospheric

weather information on roadways, and has been mainly used for freeway winter

maintenance (i.e., snow/ice removal). The environmental and the road conditions are

collected by Environmental Sensors Systems (ESS). Some common parameters for which

data is collected are air temperature, dew temperature, visibility, pavement condition,

surface temperature etc. The atmospheric sensors are placed on a tower near the roadway;

the pavement sensors are embedded in the roadway; and the sub-surface sensors are

buried under the pavement. The data collected for the road and the weather conditions are

usually stored at the Remote Processing Unit (RPU). A sever (or servers) typically

located at a central facility of transportation departments pulls data from RPU’s at a

regular interval. The collected data are saved in a database and used for real-time

monitoring. It is also used to build models that forecast the location specific weather

conditions. Forecasts of weather and pavement conditions specific to the site are used in

planning winter freeway maintenance (Goodwin, 2003)

The availability of weather conditions specific to a road segment from RWIS

presents a new opportunity to study weather impacts on the traffic which was not feasible

in the past (Pisano, Ficek, Taylor, 2004). This thesis utilizes the Mn/DOT RWIS data to

study the weather impact on traffic and travel time.

1.4 Objective of thesis

The objective of this thesis is to study the impact of weather conditions on the

traffic flow, the capacity of a freeway section, and the travel time. Inclement weather

5

conditions can cause congestion thereby affecting the travel time. However, most of the

existing travel time prediction models do not incorporate the weather or pavement

conditions and they mainly rely on the traffic patterns and trends. Exclusion of traffic

conditions on travel time prediction potentially has an adverse effect on the prediction

accuracy. This thesis attempts to incorporate the pavement conditions obtainable from

RWIS into a travel time prediction model in order to improve the prediction accuracy.

6

CHAPTER 2 : THEORETICAL BACKGROUND

In this chapter the theoretical background, the basic traffic parameters and

terminologies are reviewed, and the theory related to this thesis is explained. An

overview of travel time prediction is given, and the challenges in quantifying them are

explained.

2.1 Traffic Parameters

Counting of vehicles is the most fundamental parameter in traffic, and most of the

studies that are done in traffic engineering use this count to quantify traffic volume, flow

and capacity of a section of a lane. Another important parameter is the occupancy of loop

detectors, which is the percent of time vehicles are present on the detector. Traffic speeds

measured at a single location are highly variable and not widely used. Speeds can be

averaged over time (time mean speed) or space (space mean speed), but space mean

speed is more meaningful in traffic analysis (Roess et al 1997). Another important

parameter is the travel time and commonly estimated from the flow and occupancy data.

This section describes the basic traffic parameters.

2.1.1 Traffic Volume Traffic volume is defined as the number of vehicles passing through a point of a

lane or a freeway in a given time interval (Transportation Engineers 1999). Traffic

volume is one of the measures that estimate the amount of traffic flow at a given point.

The volume of the traffic is often measured on annual, monthly, daily, hourly or sub-

minute intervals.

2.1.2 Traffic Flow Rate Traffic flow is the estimation of the number of vehicles that will pass through a

point or a section of the freeway in one hour based on the count of the vehicles in the

given interval. Flow rate is equivalent to hourly rate at which vehicles pass over a given

point of a lane or a roadway at a given time instance (Roess et al 1997).

7

Volume differs from flow rate in that volume is the actual count of the vehicles

that have passed through the point or the section of the freeway during a given time

interval whereas traffic flow represents the number of vehicles that could pass in one

hour at a time instance. Flow is a concept borrowed from the hydrodynamic theory and

frequently used to model traffic dynamics.

2.1.3 Occupancy Occupancy is the percentage of time vehicles are present at a given point (traffic

detector) during the given time interval. For example, 10% of occupancy in a 30 second

interval means that vehicles were present on the detector for 3 seconds during the 30

second interval.

2.1.4 Traffic Density Density is defined as the number of vehicles per mile for a section of a lane or a

roadway for the given time interval. Density is computed by,

( ) ( ) / ( )density k flow q speed u= (2.1)

where denotes flow in vehicles/hr, and denotes space mean speed in mph. If speed is

unknown, it is often estimated by,

/k o g= , (2.2)

where is the occupancy observed and g is a constant that quantifies an average vehicle

length.

2.1.5 Traffic Speed Traffic speed for a given time interval is the average speed of every vehicle

traveled in a section of the lane or the roadway. It is a space mean speed and computed as

the ratio of traffic flow with the corresponding density for the given time interval, that is

from Eq. (2.1).

( ) ( ) / ( )speed u flow q density k=

8

The speed that is estimated using this formula is often not accurate as the

computation of density from occupancy uses inaccurate average vehicle length (g) (Sun,

Ritchie, 1999). Accuracy of vehicle length measurements could increase the speed

computation but such measurements are rarely available. In general the average vehicle

length is estimated during the free flow condition in which the speed is more or less a

constant (usually the speed limit enforced at the section). The following table gives the

list of vehicle lengths as defined by the Federal Highway Administration (FHWA).

Table 2.1: Length Based Classification Boundaries

Primary Description of

Vehicles Included in the

class

Lower Length > Upper Length ≤

Passenger Vehicles(PV) 0ft 13ft

Single Unit Trucks(SU) 13ft 35ft

Combination Trucks(CU) 35ft 61ft

Multi-Trailer Trucks(MU) 61ft 120ft

Since different class of vehicles have different lengths and the mix of vehicles can

differ from time to time, the average vehicle length will not remain constant for a

particular section of a freeway. Without a reliable source for average vehicle length,

density calculation is not reliable and hence the average traffic speed computed from

flow and density has a margin of errors.

2.1.6 Travel Time Travel time is the time that it takes an individual vehicle to traverse a unit length

of roadway. Total travel time (TTT) is the sum of the individual travel times of all the

vehicles crossing a length of roadway.

2.1.7 Traffic Capacity Capacity of a section of a freeway is the maximum traffic flow that can pass

through the section without causing congestion (Transportation Research Board 1998).

9

Accidents, construction or repair of lanes, peak hour traffic and weather conditions affect

the capacity of the section. Capacity may be estimated from the free flow condition by

searching the maximum flow rate.

2.1.8 Traffic Demand Traffic demand is the number of vehicles that would be entering the section of a

lane or freeway. During traffic congestion the demand exceeds the capacity of the section

of the freeway.

10

2.2 Prediction of Travel Time

In this section we will discuss few travel time prediction approaches that have

been used in the past. These approaches use the historical data that has been collected by

the loop detectors. The approaches differ in their mathematical models and how they

incorporate the historical data for estimating future travel time.

2.2.1 Time-varying coefficients for short-term travel time prediction (Zhang, Rice 2001) Short term travel time prediction is helpful in congestion management, route

guidance and various other traffic management issues (Zhang, Rice 2001). This model

tries to fit predicted travel time for the freeway trip with the parameters estimated using

the freeway sensor data. The model uses a varying linear regression as stated below

(Hastie, Tibshirani 1993). The linear regression fits the curve between the travel times of

a section ( )T t with travel time predictor *( , )T t Δ which is the snapshot prediction travel

time for the section recorded at t −Δ time. Let ( ,tα Δ) and ( ,tβ Δ) be the linear

coefficients of which are function of departure time t andΔ . Δ is the parameter through

which one can specify how much time prior to the departure time the travel time is being

predicted. Based on these definitions, the travel time at future time t is modeled as:

( ) , , *( ,T t t t T tα β ε= ( Δ)+ ( Δ). Δ) + (2.3)

The data available from the freeway sensors may have a certain lag, which is

determined by the external parameterΔ . Assume that ( )nT t is the travel time that it will

take to travel in future from origin s0 to destination sn. The sensor data is recorded at s0,

s1, s2,…, sn.. Assuming that the data is available until t-Δ we can estimate the space mean

velocity of the vehicles based on the volume and the occupancy recorded at sensors.

These speed estimates are directly used in the model, i.e., the travel time predictor

*( ,T t Δ) , which is the travel time reported when the velocity profile does not change

over the period of time of t-Δ, is given as:

11

,

1

10

*( , ( ) / (i

n

i li

T t s s v x t−

+

=

Δ) = − −Δ)∑ (2.4)

where 1i is s+ − is the length of the link between two stations and ( ,.)iv s is the speed

calculated at the start of the link. This approach assumes that weighted linear

combination of the historical travel time and the current travel time predict the future

travel time. The regression model described in Eq (2.3) has the coefficients α, β as a

function of time t . This suggests that the values of the coefficients in the linear regression

can change as the time changes. This approach is intuitive as the traffic pattern changes

time-to-time and a model with constant coefficients will not be able to capture the time-

varying nature of the travel time. There is no specific function for ,tα( Δ) and ,tβ( Δ) but

we could utilize the relationship between ( )T t and *( , )T t Δ which in general does not

abruptly change from t and Δ.

The estimation of coefficients is based on the historical data. Let the set of

historical data be represented as H where a trip hn for all 1,...,n N= within the set H is

defined as

max( , ( ), *( , ),0 )n n n nh t T t T t= Δ ≤ Δ ≤ Δ (2.5)

where nt is the departure time for the trip nh , ( )nT t is the trip travel time and the

*( , )nT t Δ is the current travel time where the velocity profile remains unchanged for the

trip. In this context Δ can be regarded as the time into future we predict the travel time

based on the currently available information about the trip travel time. maxΔ is the

maximum time in the future for which the predicted travel time based on the historical

travel time data set H is still meaningful. The estimate of ,tα( Δ) and ,tβ( Δ) are then

computed by minimizing the cost function:

2[ ( ) , , . *( , ] . ( )n

n n nh H

T t t t T t w t tα β∈

− ( Δ) − ( Δ) Δ) −∑ (2.6)

The weight function (.)w is a strictly decreasing function in | |nt t− and hence the trips

which are near to the trip for which the travel time is to be predicted has a higher weight

12

assigned to it. An example for the weight function is 1 .(.) ( )w φσ σ

= . Weighted Least

Squares method is used to solve for α and β coefficients in Eq. (2.6).

2.2.2 Day to day travel time trends and travel time prediction from the loop detector data (Kwon, Coifman, Bickel 2000) Another approach also suggests the use of historical travel time information for

predicting future travel time but also uses flow and the occupancy values available from

the freeway loop detector data. The method suggests the use of linear regression with

stepwise variable selection. It uses departure time it , day of departure id , day of the week

of the trip iw , flow if and occupancy io . The if and io are flow and occupancy vectors that

have all the flow and occupancy values recorded at the loop detectors that are in place at

the section for which the travel time is to be predicted.

Since the loop detector data is inherently noisy this method suggests that a low

pass filter should be used to eliminate the noisy data. The following filtering method was

suggested:

2

2

/54

4/50

0

, , 0,1,...4i

t i t iji

j

ez a y a ie

−

−=

=

= = =∑∑

(2.7)

where ty is the original data and tz is the processed data.

This method also suggests creating ten virtual detectors stations instead of the

original ones on the section of the road for the trip. The original loop detector data is

interpolated to give the flow and occupancy data for each of the virtual station.

Henceforth, these virtual stations are treated as original stations and the flow and the

occupancy values reported by these stations are used to form the flow and the occupancy

vector. Flow and occupancy at time t and location x and on day d is denoted

by{ ( , )}df x t and{ ( , )}do x t . Hence the vector ( )df t and ( )do t represent

( ) { (1, ), (2, ),..., (10, )}d d d df t f t f t f t= (2.8)

( ) { (1, ), (2, ),..., (10, )}d d d do t o t o t o t= (2.9)

13

With the data that is collected as specified above we try to predict the travel

timeτ (sec) using the information available at t −Δ where t is the departure time for the

trip for which the travel time is being predicted. To build the regression model we use

historical information of the flow and occupancy vectors and the actual travel time for

given day and time. Therefore, (i d if f t= −Δ) is the flow vector and similarly

(i d io o t= −Δ) is the occupancy vector. Hence, the input ( , , , )i i i i iX o f t w= to the model is

the covariate vector and iτ is the response variable. These input and response vectors can

be used to build the stepwise regression model (Kwon et al) that can be used to predict

travel time for a section on a given time of the day. Further, the decision trees or neural

networks can also be used with these variables to build a model for travel time prediction.

14

CHAPTER 3: DATA SOURCE AND METHODOLOGY

The objective of this thesis is to investigate how weather conditions on freeways

impact traffic dynamics, and can be applied in future predictions. This chapter describes

the basic methodologies of the study and the data source used for the experiments and

analysis.

3.1 Site Selection and Data Source The site selection criterion used for this study was based on the availability of

RWIS sites since they are sparsely located in terms of geographical distribution. In the

Twin Cities’ freeway network, only six RWIS sites are available while more than 5,000

detectors exist for traffic monitoring. The map of the selected sites is shown in Figure

3.1. Table 3.1 shows the address of the RWIS station and freeway loop detectors in the

proximity. The detector numbers shown follow the standard loop detector identification

system used in Mn/DOT. The RWIS data was downloaded from the Mn/DOT RWIS ftp

server, and the traffic data was obtained from the data archives kept at UMD. UTSDF

format is used to archive the RWIS data (Kwon, Dhruv, 2004).

Figure 3.1: Location of RWIS sites in and around the metro area used for the study

4

3

1

6

2

5

15

Table 3.1: R/WIS sites and detectors in the proximity

Site Name

(RWIS)

Location Description Detector IDs

1 Mississippi River

I-35W over Mississippi River 2224,2225,2226, 2149,2150,2151

2 Burnsville I-35W near Exit 4B, Minnesota River

1006,1007,1008,494,495,496

3 Maple Grove

I-94 near 494/694 Split 907,908,909, 910,911,912

4 Little Canada

I-694 and I-35E 2419,2420,2421, 2426,2427,2428

5 Cayuga St. Bridge

I-35E Mile Point 108 2465,2466,2467, 2386,2387,2388

6 Minnetonka Blvd

I-494 & Minnetonka Blvd 1877,1878, 1851,1852

3.2 Relational Database A relational database was created as a part of another project at the Transportation

Data Research Laboratory (TDRL) data center. Due to the volume of data that needs to

be stored and analyzed, a database partitioning method based on monthly partition was

developed for fast retrieval and efficient management of the overall data. The partition

was done by automatically creating a new database table for each month.

The raw RWIS data from Mn/DOT system is recorded at every 10 minutes

whereas the raw loop data is recorded at every 30 seconds. Due to the discrepancy in the

time interval, one-to-one mapping or correlation study cannot be done using the original

data. Hence, the traffic data was aggregated for 10 minutes by combining 20 traffic data

points. The volume was summed up and the occupancy was averaged. After this

conversion, the timestamp for every data is in 10 minute interval and a query based on

time returns the data occurred within the same period for the analysis.

16

3.3 Methodologies Used to Analyze Weather Impact on Traffic In order to analyze how the weather conditions affect the traffic flow, several

analysis methods were employed. The methods used are correlation coefficient analysis

to understand which weather parameter affects the traffic, daily traffic volume variability

under different weather conditions to study on the influence on trip demands, congestion

analysis to gauge how severe the weather impact is on traffic. This section describes

those methods used for the analysis. The experimental results using real data are

discussed in Chapter 4.

3.3.1 Correlation coefficients Correlation coefficients for two variables signify the degree of linearity between

them. For sufficient amount of data the degree of linearity can be measured as strong,

positive, negative or no correlation (Devore, 1995). Correlation coefficient ρ for two

variable x and y is defined as:

2

1 1 1

2 2 2

1 1 1 1

( )( )

( ) ( )

n n n

i i i ii i i

n n n n

i i i ii i i i

n x y x y

n x x n y yρ = = =

= = = =

−=

− −

∑ ∑ ∑

∑ ∑ ∑ ∑ (3.1)

The correlation coefficient is computed between two variables using a set of

paired data ( , )i ix y . If there is no paired data available then an interpolation could be used

to establish the paired data or the pair could be removed from the set.

There are few properties on correlation coefficient ρ that has to be noted. Firstly,

ρ does not depend on the ordering of pair of data, i.e. correlation coefficient for paired

data ( , )i ix y is identical to that of paired data ( , )i iy x . Secondly, ρ is independent of the

units of x and y. The square of the correlation coefficient gives coefficient of

determination which is the extent of variation of the response variable due to the fitting of

the linear curve. For example ρ = 0.25 explains 25% of variation in the response variable

by the linear model. Moreover, 1 ρ− ≤ ≤1 , the value of 1 indicates that the sample data

points of ( , )i ix y lie on a straight line with a positive slope whereas the value of -1

indicates that the data points lie on a straight line with a negative slope. For analysis,

17

following rule of thumb is used; correlation is said to be weak if 0 | ρ≤ |≤ 0.5 ; the

correlation is said to be strong if 0.8 | ρ≤ |≤1.

As a first part of the analysis, we wish to examine whether a correlation exists

between weather and traffic parameters or not. The set of RWIS parameters included in

the study are: air temperature, dew temperature, relative humidity, average air speed, wet

bulb temperature, surface temperature, and sub-surface moisture. The traffic parameters

are volume and occupancy. Months used for analysis was chosen based on months with

typical winter and typical summer to observe seasonal effects.

3.3.2 Effect of pavement conditions on daily total volume Traffic patterns are similar at a given location on the same weekday unless either

one of them is affected by conditions such as holidays, traffic incidents, road

construction, etc. For example, January 10th 2005 which is a Monday and January 17th

2005 which is again a Monday on the subsequent week will have similar traffic trends if

the location is the same and they are affected by special conditions mentioned above.

This type of trend was used in data imputation in the past (Kwon, 2004). By observing

whether this similarity in traffic trend holds under different weather condition or not, we

could measure how much weather affected the traffic. It should be noted that the

information about the pavement conditions in RWIS is not numeric and hence the

correlation coefficient can not be computed.

For this analysis, five classes of pavement conditions are used, i.e., dry, snow,

frost, damp and wet. The daily traffic volume totals are then computed and compared to

observe whether snow or wet weather events reduced the total daily traffic volume. If the

daily traffic volume was reduced due to weather conditions, it indicates that trip demand

was reduced, i.e., people were discouraged from driving by weather conditions.

3.3.3 Effect of pavement conditions on traffic dynamics The trends observed in the daily volume in a given month as explained in the

previous subsection will be unable to capture information about the effect of the various

inclement conditions on traffic patterns observed at different time of the day. In order to

18

study the effect of pavement conditions on traffic dynamics, data visualization

approaches were devised.

In this approach, traffic volume is observed for the same time span of the day, for

same weekdays in different weeks in a given month for the same location to identify

traffic volume changes under different pavement conditions. The total traffic volume

recorded for every ten minute is plotted against the time of the day. Different color is

used to plot traffic volume count with different weather conditions that are recorded by

the R/WIS station at the location. For example, the traffic volume count is plotted with

green color if the pavement condition is reported to be dry by the R/WIS station. If the

pavement condition changes to damp in the next time instance, the traffic volume count

recorded at that time instance is plotted with red color. The advantage of using different

color codes to plot the traffic volume count is that it gives a visual representation of how

traffic volume is affected by the pavement conditions. In addition, volume/occupancy

scatter graphs for the corresponding days are plotted to measure the traffic congestion.

For analysis a single day is divided into three periods. They are morning peak

hour which is from 6:00AM to 9:00AM; afternoon peak hour which is from 3:00PM to

6:00PM and the rest of the time is the off-peak hours. The scatter plot points are drawn

with different colors for each of the time periods. In general, the traffic demands increase

during peak hours, and thus congestion may occur if the increase in the traffic exceeds

the capacity of the freeway section. Inclement weather conditions can reduce the capacity

of the freeway section and can add more congestion at the location. In some cases a drop

in demand can also be noticed due to inclement weather conditions, this would happen as

some people may be discouraged from driving in the inclement weather conditions. In

some cases a drastic drop in the traffic demand can be observed such that the demand is

still within the highway capacity that the freeway section can handle, hence the

congestion is eliminated.

For the analysis of weather impact we first observe the changes in traffic volume

count during the morning peak and afternoon peak for different weekdays in the same

month where the weather conditions are different. The volume vs. occupancy scatter plot

is then drawn using different colors for morning peak, afternoon peak and off peak points

19

to observe congestion levels. The percentage change in the peak hour traffic volume and

change of congestion levels together give a measure to analyze the weather impact on the

traffic conditions on the freeway.

20

3.4 Methodology to analyze weather impact on travel time prediction

Motorists experience that inclement weather conditions generally increase travel

time. This section describes the methodologies on how to analyze weather impact of

travel time and application to travel time prediction.

3.4.1 Travel time estimation Travel time estimation is computation of an average travel time for a time period

in the past at a specific location (Cortes et al 2001). The traffic data archive gives us

information about the volume and occupancy at the traffic detectors for a given date and

time and the location. A group of detectors at a location in a freeway makes up a station.

The speed at a station is then estimated by the station volume and the occupancy values

using the techniques discussed in Chapter 2. These speed values are used to compute the

travel time between each station using the known distance information. In order to more

accurately estimate the travel time, the distance between a pair of stations (origin and

destination stations) is split in three equal sections. For the first section the speed of the

origin station is used. For the final section the speed of the destination station is used. The

average of the first and last section speeds is used for the middle section. Since the

volume and occupancy data is in thirty-second interval, the speed is computed for every

thirty seconds. This three section approach was developed by Mn/DOT and used to

compute travel time notification in the Twin Cities’ freeways. The estimated travel time

is later used in the time-varying regression model to compute the coefficients which are

described in the subsequent subsection.

3.4.2 Time-varying coefficients for travel time prediction The estimated travel time ( )T t and the snapshot travel time prediction

*( ,T t Δ) can be fitted to a linear curve as the relationship between ( )T t and

*( ,T t Δ) since both are expected to slowly vary with respect to t and Δ. Snapshot

21

prediction is the future estimate of the travel time for a section of a freeway given that the

speed with which the traffic traverses the freeway remains unchanged for the time. Since

the relationship varies with time, the coefficients also vary with respect to time. Hence it

is called a time-varying regression model (Zhang, Rice; 2001) and can be expressed using

a weighted least squares cost function as follows.

2[ ( ) , . *( , )] . ( )n n nT t t t T t w t tα β− ( Δ) − ( ,Δ) Δ −∑ (3.2)

The coefficients ( , )tα Δ and ( , )tβ Δ in this model is computed by minimizing the

objective function given in Eq. (3.2). A standard solution of Eq. (3.2) in a matrix form is

given by

1( ) .( *)T TA wA A wTαβ

−⎡ ⎤=⎢ ⎥

⎣ ⎦ (3.3)

where

*1 1 1

*2 2 2

* * *1 2

*

1 1 1T

n

n n n

w w Tw w T

A wAT T T

w w T

⎡ ⎤⎢ ⎥⎡ ⎤ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

L

L M and

1

1 2 2** * *

1 1 2 2

nT

n n

n

Tw w w T

A wTwT w T w T

T

⎡ ⎤⎢ ⎥⎡ ⎤ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦

L

L M

The above equation computes ( , )tα Δ and ( , )tβ Δ . The weight is the weight

assigned for each value of the snapshot prediction and the estimated travel time. This

weight function is chosen as a normal distribution since the travel time values that are

closer to the time for which the prediction is computed has a higher correlation.

Incorporating this idea all of the weight values in this thesis are computed using the

following function.

22

2( )12

x

eμσ

σ π2

−−

2

The mean is time instance for which the prediction is being done and the value

σ controls the decay rate and was chosen using the time window.

The travel time is predicted by using the snapshot travel time that has been

recorded Δ time before. In the experimentsΔ is set to 5, 15, 30 and 60 minutes. A time

lagΔ = 5 or 15 minutes would be applicable for real-time travel time prediction while

time lag Δ of 30 or 60 minutes is useful for trip planning. The accuracy of the predicted

travel time in Eq. (3.2) depends on the value of the Δ since traffic patterns are less

correlated as time lag Δ becomes large.

The hypothesis of this thesis is that the error in prediction of travel time will

increase during inclement weather conditions. The travel time prediction using time-

varying coefficients uses travel time information of the previous hours. Based on this

historical travel time the travel time for the next hour is predicted. The prediction of

travel time for the beginning of the hour will have error if the previous hour that has been

used as historical information for computing the coefficients was affected by weather

conditions. To reduce the error in the travel time prediction we propose to use the

changes in volume and occupancy to compute the calibration factor so that the travel time

predicted using the time-varying coefficients can be adjusted to reduce error caused by

the inclement weather conditions. We assume that the change in the occupancy and

volume can be estimated using the weather prediction.

The freeway capacity will decrease as the inclement weather conditions occurs

and the capacity also increases when the pavement conditions is normal, that is dry. The

congestion on the freeway depends on the demand by the traffic to use the freeway. If

demand does not drop considerably during this inclement pavement condition, then

congestion occurs on the freeway as the occupancy by the traffic increases. In essence,

occupancy could play an important role in travel time during the inclement weather

conditions. After numerous experiments, the following formula was devised to calibrate

the predicted travel time.

23

' ( , ( , ). ( , ). ( ,predpred predT t T t t W t T tω οΔ) = Δ) + ( Δ Δ) (3.4)

where )tω( is the coefficient that changes with time, ( , )predT t Δ is the travel time

predicted by the time varying coefficient approach, ' ( , )predT t Δ is the adjusted result, and

, )W tοΔ ( is the change in the occupancy for weather W at time instance t , the change in

occupancy is computed on hourly basis. )tω( decreases monotonically with time between

0 and 1.

For comparison of the predicted travel time, a measure of error on the prediction

is needed. The percentage prediction error (PPE) is given by (Zhang, Rice 2001) was

used in this thesis, i.e.,

( ) ( )( )

predT t T tPPET t−

= (3.5)

24

CHAPTER 4: EXPERIMENTAL RESULTS

This chapter presents experimental results of the methodologies discussed in

Chapter 4. The first section describes the results of correlation coefficient matrix. The

second section describes the experimentation results on weather impact on daily traffic

volume. In the third section, experimental results on weather impacts on traffic

congestion are presented. In the last section, a comparative study on travel prediction

incorporating weather impact is presented.

3.1 Correlation Coefficient Matrix In order to investigate which RWIS parameter (i.e., weather factor) has

correlation to traffic parameters, correlation coefficient matrices were constructed. A

correlation coefficient matrix is a table that shows the degree of linear correlation

between all possible pairs of two parameters within the set of parameters chosen. In this

case, the random variables are the parameters of RWIS and traffic from which we wish to

identify strongly correlated parameters. For the RWIS parameters, only the sensor

parameters that are recorded as numerical values were chosen since non-numerical

parameters cannot be used for computing the correlation coefficients.

Two months of 2005, January and June, each representing typical winter and

summer months were selected and tabulated. Table 4.1 shows the correlation coefficient

matrix computed for January 2005, and Table 4.2 shows the coefficients for June 2005 at

the Little Canada site. From the two tables, it can be observed that air temperature

(atemp) and dew temperature (dtemp) have a strong correlation (0.908) so as the wet bulb

temperature (wbtemp) and air temperature (atemp). Also notice that relative humidity

(relhum) has a strong correlation to dew temperature (dtemp). These strong correlations

within atmospheric parameters are expected since they are dependent variables.

Correlation between traffic parameters, i.e., occupancy (occ) and volume (vol), is also

shown strong, as expected. Another interesting observation is that wind speed showed

almost no correlation to any other weather or traffic parameters.

25

The correlations between traffic and RWIS parameters were shown to be very

weak. With respect to seasonal differences (differences between Table 2 and 3), slightly

stronger correlations between traffic and RWIS parameters were shown in the summer,

but both of them had weak correlations and the difference was insignificant. Similar

results were observed from other sites and months. From this experiment, it was clear that

no clear linear correlation exists between the traffic and quantifiable RWIS parameters. It

also suggests that predicting traffic conditions based on air temperature, humidity, or dew

temperature would be highly unreliable. However, this does not suggest that RWIS data

should not be used in traffic analysis as it will be apparent from the proceeding sections.

Especially, non-quantifiable parameters such as pavement conditions were not used in the

correlation study, but are likely to have a stronger relation to the traffic dynamics.

Table 4.1: The correlation coefficient matrix for January 2005 at the Little Canada site

atemp dtemp relhum avgspd wbtemp sur-temp

sub-moist

vol Occ

atemp 0.908 0.418 -0.002 0.995 0.865 0.003 0.028 -0.252

dtemp 0.737 -0.044 0.939 0.662 0.028 -0.087 -0.183

relhum -0.025 0.462 0.117 0.206 -0.286 0.083

avgspd -0.019 0.107 -0.174 0.109 -0.207

wbtemp 0.823 0.0599 -0.000 -0.182

sur-temp

0.065 0.136 -0.208

sub-moist

0.197 0.149

vol 0.706

Notation: atemp= “air temperature”; dtemp= “dew temperature”; relhum= “relative humidity”; avgspd= “average wind speed”; wbtemp= “wet bulb temperature”; surtemp= “surface temperature”; submoist= “sub-surface moisture”; vol= “traffic volume”; occ= “loop occupancy”

26

Table 4.2: The correlation coefficient matrix for June 2005 at the Little Canada site

atemp dtemp relhum avgspd wbtemp sur-temp

sub-moist

vol occ

atemp 0.387 -0.666 0.338 0.811 0.879 0.353 -0.068 0.038

dtemp 0.470 0.086 0.816 0.085 0.535 -0.340 -0.314

relhum -0.263 -0.025 -0.787 0.086 -0.226 -0.089

avgspd 0.245 0.380 0.126 0.015 -0.217

wbtemp 0.520 0.406 -0.239 -0.138

sur-temp

0.087 0.098 0.121

sub-most

-0.562 -0.346

vol 0.942

3.2 Impact of Pavement Conditions on Daily Traffic Volume As shown in the previous section, RWIS atmospheric parameters (air temperature,

humidity, wind speed etc.) showed weak correlations to traffic volume or occupancy. On

the other hand, we hypothesize that RWIS pavement surface conditions may have

stronger correlations to the traffic parameters. Pavement conditions in RWIS are typically

recorded in non-numeric descriptive terms, such as dry, snow, damp and wet. One way of

looking at the relationship between the RWIS pavement conditions and traffic data would

be comparing daily traffic volumes under different pavement conditions. If the traffic

volume was reduced and no other special events occurred, it would indicate reduction of

trip demand, i.e., trips were discouraged by the weather events.

Table 4 summarizes the daily traffic volumes of the same day of the week

according to the pavement conditions in number of hours in January 2005 at the Little

Canada site. January was chosen since constructions do not occur in January in

Minnesota but the month has many snow events that result in a wide range of driving

conditions on the pavement. The idea here is that the same day of the week within

27

consecutive weeks should have similar volume counts in urban freeways unless they are

affected by special events such as inclement weather conditions, accidents, or holidays.

The similarity in the same day of the week traffic trends was observed in other studies

and commonly used in data imputation (4). The basic methodology of analysis used is

thus a comparison of daily traffic volumes on the days with weather events against a

comparable dry. From Table 4, the first week of January 1st – 3rd should be excluded from

the analysis since the daily volume could be abnormal affected by a holiday.

From Table 4.3, a clear case of volume reduction by snow events is observed

from January 21st by comparing the volume with January 14th. It is a clear case since

January 14th had dry conditions while January 21st had snow presence on the pavement

all day (24 hours). According to these two same days of the weekly comparison, the daily

traffic volume on the snow day was reduced by 20%. Another case of volume reduction

by snow and frost can be observed from January 12th. However, in other cases volume

reduction is not obvious, which we believe are due to time shift (or delays) in trips to dry

conditions within the same day if the weather event does not sustain extended hours.

In general, according to the data reviewed from the table given and the other sites

under this study unless snow is present on the pavement for extensive hours, reduction of

daily traffic volume was not significant. In another perspective of the analysis, a regional

characteristic may play a role, i.e., snow removal in Minnesota is fairly effective and

timely so that motorists in Minnesota may delay the essential trips within the same day

but do not abandon them. Another factor might be that motorists in Minnesota are used to

snowy pavement conditions that they are less discouraged from daily trips. In any case,

the main observation from this experiment is that, unless the snow events are severe and

last for extensive hours, daily total traffic volumes were not significantly reduced.

28

Table 4.3: Surface Conditions in Number of Hours and Traffic Volume at the Little Canada Site in January 2005

Surface conditions in number of hours

Day Weekday Daily Traffic Volume Dry Wet Snow Frost Damp

3 Monday 105494 24 0 0 0 0

10 Monday 111185 9.17 0 14.83 0 0

17 Monday 101698 13.17 0 10.83 0 0

24 Monday 109490 5 0 10.83 0 8.17

31 Monday 108200 24 0 0 0 0

4 Tuesday 111863 24 0 0 0 0

11 Tuesday 112362 4 0 20 0 0

18 Tuesday 107450 13.5 0 9.5 1 0

25 Tuesday 112567 6 0 8.83 0 9.17

5 Wednesday 113963 24 0 0 0 0

12 Wednesday 107765 0 0 15.5 4 4.5

19 Wednesday 113696 12.5 0 11.5 0 0

26 Wednesday 114215 17.83 0 3.83 0 2.33

6 Thursday 115646 24 0 0 0 0

13 Thursday 113157 17.83 0 6.17 0 0

20 Thursday 110750 0 0 24 0 0

27 Thursday 116972 23.83 0 0.17 0 0

7 Friday 118569 0.33 0 23.67 0 0

14 Friday 114673 24 0 0 0 0

29

21 Friday 91260 0 0 24 0 0

28 Friday 122897 18.17 0 5.83 0 0

8 Saturday 88326 12.33 0 11.67 0 0

15 Saturday 80185 24 0 0 0 0

22 Saturday 73764 9.17 0 14.5 0 0.33

29 Saturday 73764 24 0 0 0 0

2 Sunday 66020 12.33 0 9.33 2.33 0

9 Sunday 71561 0 0 23.83 0.17 0

16 Sunday 66464 8.17 0 15.83 0 0

23 Sunday 71857 14.5 0 9.5 0 0

30 Sunday 77639 24 0 0 0 0

30

4.3 Impact of Pavement Conditions on Congestion In the previous section, it was observed that winter weather events do not

significantly affect the daily traffic volume unless they are extensive. However, we

hypothesize that the weather impact on traffic might be more significant during the peak

traffic hours since small variance in road capacity by inclement weather conditions

should affect the congestion dynamics. This section investigates the effect of pavement

conditions on traffic in peak hours.

In order to analyze the impact of pavement conditions on traffic in peak hours,

two types of graphs are employed. The first type is a line graph of volume changes in

time using a color code that changes according to different surface conditions. This graph

gives information on when the weather event occurred and what the traffic level was at

that time. The traffic conditions in a dry day on the same day of consecutive weeks are

again used as the baseline comparison. The second type of graphs is the

volume/occupancy scatter graphs with color coded data points for off-peak, morning

peak, and afternoon peak hours. The morning peak hours were defined as 6:00-9:00AM

and the afternoon peak hours as 3:00-6:00PM. The color-coded scatter graphs provide the

effects on congestion by the weather events identifiable to morning and afternoon peak

hours. Analysis was shown case by case, each case representing one type of traffic impact

patterns.

4.3.1 Case 1: Increased congestion by snow This is the case where the peak hour traffic volume is slightly reduced but

congestion increases. The example is taken from January 4th 2005 and January 11th

2005; both dates are one week apart and are Tuesdays. The resulting graphs are shown in

Figure 4.1. The left side shows traffic on a dry condition which is used as the baseline for

comparison, and the right side represent the case in which snow event affected the traffic.

In the morning peak of snow pavement conditions, an insignificant drop of traffic volume

is clearly observed. From the scatter graph, increase of congestion is also observed. In

the afternoon peak hours, although pavement conditions are partially dry, similar

congestion increase is observed. These observations may be explained in the following

way. The snowy pavement conditions on the freeway may have caused reduction of the

31

freeway capacity and the traffic volume. However, the reduction in freeway capacity was

not sufficient to provide the capacity required by the level of the snow event volume even

though it was reduced. Indeed the volume (or demand) reduction was minuscule, i.e. 2%,

and thus the cause of increased congestion is considered due to reduction in the freeway

capacity by a snow event in this case.

Figure 4.1: Effect of pavement conditions on the traffic volume of Little Canada. The volume/occupancy graphs of the corresponding days are shown below each line graph.

32

Little Canada January 4th 2005 January 11th 2005 % change in traffic

Total traffic volume 111863 112362

Morning peak traffic 23998 23462 Decrease by 2.23

Evening peak traffic 27387 26658 Decrease by 2.26

4.3.2 Case2: Reduction of congestion by a severe snow event This is the case where snow event actually reduces congestion. In this case the

snow event may have been severe and reduced the volume significantly during the

morning peak in comparison to a normal dry day. From Figure 4.2, we can observe that

traffic congestion was actually reduced during the snow event according to the

volume/occupancy scatter graph. A logical explanation in this case is that the capacity of

the freeway was not significantly reduced by snow as most motorists expected or the road

was quickly cleared by snow plow.

33

Figure 4.2: Effect of severe snow conditions on the traffic volume. The volume/occupancy graphs of the corresponding days are shown below each line graph.

Little Canada January 17th 2005 January 31st 2005 % change in traffic


Morning peak traffic 18596 21601 Increase by 14

Evening peak traffic 24924 27150 Increase by 8.1

4.3.3 Case 3: Increased congestion by damp conditions It was observed that damp condition also reduces peak hour traffic volume and

can cause increase in traffic congestion. The effect was similar to snowy conditions. In

Figure 4.3, the morning peak hour volume was reduced, and increased congestion

occurred due to a damp condition.

34

Figure 4.3: Effect of damp pavement conditions on traffic.

Little Canada July 13th 2005 July 20th 2005 % change in traffic



Evening peak traffic 26611 26885 Decrease by 1

4.3.4 Case4: Volume decrease and increase of congestion by wet conditions

Wet conditions were investigated to see how they affect traffic volume and

congestion. The example is shown in Figure 4.4. Similarly to damp conditions, traffic

volume was reduced and congestion was increased. Also notice from graph that

35

congestion begins to occur at a lower volume which indicates reduction in the freeway

capacity. This reduction in capacity appears the cause of increased congestion.

36

Figure 4.4: Effect of wet pavement conditions on traffic.

37

Burnsville February 2nd 2005 February 14th 2005 % change of traffic


Morning peak traffic 21284 19793 Decrease by 7

Afternoon peak traffic 25003 25793 Increase by 3.1

4.3.5 Case 5: Changes in pavement conditions This is the case where changes from one kind of weather to another affected the

traffic volume and the congestion. From Figure 4.5, the morning and afternoon peak hour

volumes were reduced by 13.7% and 9.2%, respectively. The scatter graphs show that the

change in weather events increased congestion. This experiment suggests that any type of

weather events except dry conditions can affect traffic dynamics causing congestion.

38

Figure 4.5: Effect of different pavement conditions on the traffic volume. The volume/occupancy graphs of the corresponding days are also presented.

Little Canada January 5th 2005 January 12th 2005 % change of traffic



Afternoon peak traffic 27565 25007 Decrease by 9.2

In summary, inclement weather conditions reduced the traffic volume while

increasing congestion during the peak hours. Traffic was not affected during the off-peak

hours. It was also observed that if the snow conditions are very severe, the traffic volume

drops considerably and the congestion was actually reduced or disappeared. The effect

damp and wet conditions were similar to snow conditions but a drastic drop of volume

that causes reduction in congestion was not observed. Finally, it was observed that when

the traffic volume was reduced during the peak hours by weather events, then more

traffic volume during the following off-peak hour was observed. This indicates that the

traffic flow shifts towards non-peak hour when weather events occur.

39

4.4 Impact of inclement weather conditions on travel time prediction

In order to analyze the impact of pavement conditions on travel time prediction, a

section of 17.5 miles from Maple Grove to Little Canada was used. Eq. 3.5 was used for

the computation of the percentage prediction error (PPE). The hypothesis is that PPE of

the time varying linear coefficient approach would be higher when inclement weather

conditions impacts the traffic dynamics. To analyze the travel time affected by weather

conditions, line graphs for the predicted travel time and the baseline travel time estimate

and its corresponding PPE values are compared. The calibrated travel time estimates (Eq.

3.4) at the same time are then plotted along with the predicted travel time values and the

baseline estimate of travel time to note any improvements. The weather impact on traffic

volume and volume/occupancy scatter graphs are presented to show the traffic

conditions.

In the following subsections, case by case analyses of various examples on

weather impact on travel time are shown. In all graphs, the legend “TV” denotes the time

varying linear coefficient approach, “Baseline” denotes actual travel time estimates, and

“TVWI” denotes travel time estimates with weather impact incorporated. The current

travel time predictor *( , )T t Δ in Eq. (2.3) is used to predict the travel time. In the

experiments, Δ was set to 5, 15, or 30 minutes, i.e., travel time prediction at 5, 15, or 30

minutes ahead. In the proceeding cases, only the prediction examples with 15Δ =

minutes are presented since the differences in performance can be more clearly observed

from the graphs. The historical information of 3 hours prior to the hour of prediction was

used to compute the time varying coefficients.

4.4.1 Case1: Effect of travel time prediction when weather conditions do not cause congestion As discussed in the previous section, severe snow conditions significantly

decrease the volume but reduction in the freeway capacity is not sufficient to cause

congestion. This case is shown in Figure 4.6. Once the traffic drops significantly the TV

travel time prediction model starts performing better sine the traffic is in a free flow state.

40

However it can be seen from the graph that during 5:00-6:00AM the traffic has not

dropped considerably, and thus the effect of weather impact can be seen on travel time

prediction for the hour. In the TVWI model, the change in the occupancy is used to adjust

the impact of inclement weather condition on travel time and the accuracy closely

approaches the baseline. The overall effect of significant drop in traffic due to severe

snow conditions is that the accuracy of travel time prediction by the TV model is well

maintained. The current travel time predictor is being used to predict the travel time 15

minutes into the future (Δ=15 minutes).

Effect of pavement conditions on travel time prediction for 01/17/2005

500

750

1000

1250

1500

5:00

5:20

5:40

6:00

6:20

6:40

7:00

7:20

7:40

8:00

8:20

8:40

9:00

Time instance

Trav

el ti

me

in s

econ

ds

TVBaselineTVWI

41

Figure 4.6: Traffic is affected by severe snow conditions that reduces the volume and avoids congestion and hence facilitates free flow conditions. The percentage prediction error of travel time is also negligible.

4.4.2 Case 2: Effect of travel time prediction by before-and-after weather events

The change in the pavement conditions can cause error in the prediction of travel

time as the prediction depends on the previous travel time information. If the weather

event changes from dry to snow, the TV prediction model underestimates the travel time

during the snow event. To illustrate this, note from Figure 4.7 that the pavement

conditions in the afternoon changes from dry conditions to snow. Congestion occurred

during the afternoon peak hours. Note from the travel time performance graph that TVWI

model performs better in comparison to the TV model under the change of weather

conditions since it incorporates the weather conditions.

42

Figure 4.7: Travel time prediction is affected by the snow conditions which causes congestion. The PPE graphs shows the error that occurs due to the change in weather.


500

750

1000

1250

1500

1750

15:00

15:25

15:50

16:15

16:40

17:05

17:30

17:55

18:20

18:45

Time instance of the day

Trav

el ti

me

in s

econ

ds

TV

Baseline

TVWI

Effect of calibration of weather impact on travel time prediction

-0.3-0.2

-0.10

0.10.2

0.30.4

15:00

15:25

15:50

16:15

16:40

17:05

17:30

17:55

18:20

18:45

Time instance

Perc

enta

ge p

redi

ctio

n er

ror PPETV

PPETVWI

43

4.4.3 Case3: Wet and damp pavement conditions in the morning peak time This case illustrates how the wet condition impacts travel time prediction. In

Figure 4.8, during the morning peak hours traffic volume was reduced due to wet

conditions but it caused congestion (significant increase of occupancy). As shown in the

travel time performance graphs of Figure 4.8, the TV prediction model underestimates

the travel time during the weather event and overestimates after the weather events. This

makes sense since it predicts the travel time based on the past data. Note from the TVWI

model that the rate of under and over estimate is significantly reduced since it

incorporates the weather condition. This case again demonstrates that incorporation of

weather impact to travel time prediction improves the accuracy of travel time prediction.

44

Figure 4.8: Travel time was affected by damp conditions. The damp conditions increase the travel time, and the TV prediction model underestimates the travel time. The TVWI model corrects the difference and improves the prediction accuracy.


500

750

1000

1250

1500

1750

5:00

5:20

5:40

6:00

6:20

6:40

7:00

7:20

7:40

8:00

8:20

8:40

9:00

Time instance

Trav

el ti

me

in s

econ

ds

TVBaselineTVWI


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

5:00

5:25

5:50

6:15

6:40

7:05

7:30

7:55

8:20

8:45

9:10

Time instance

Perc

enta

ge p

redi

ctio

n er

ror PPETV

PPETVWI

45

4.4.4 Case 4: The whole day is affected by snow Inclement weather conditions occur the whole day and can affect the travel time

prediction. As shown in Figure 4.9, traffic volume in this case tends to drop while

increasing travel time and congestion during the peak traffic hours. Note from the

performance graph that the TV prediction model consistently underestimates the travel

time in this case. The TVWI model corrects the error by incorporating the weather

conditions but it still underestimates the travel time in some instances.

46

Figure 4.9: Travel time is affected by snow conditions whole day. The snow conditions increases the travel time and the prediction tends to underestimate the travel time.


500750

10001250150017502000

5:00

5:30

6:00

6:30

7:00

7:30

8:00

8:30

9:00

16:05

16:35

17:05

17:35

18:05

18:35

Time instance

Trav

el ti

me

in s

econ

ds

TV

Baseline

TVWI


-0.4-0.3-0.2-0.1

00.10.20.30.4

5:00

5:30

6:00

6:30

7:00

7:30

8:00

8:30

9:00

16:0

5

16:3

5

17:0

5

17:3

5

18:0

5

18:3

5

Time instance

Perc

enta

ge p

redi

ctio

n er

ror PPETV

PPETVWI

47

4.4.5 Case 5: Multiple changes of weather changes during the day In this case, weather conditions vary during the day and change traffic conditions

and travel time. Figure 4.10 shows the condition changes from frost to snow, snow to

wet, and then wet to snow that occurs at the Little Canada site on Jan 12th 2005. The TV

model underestimated the travel time during the morning peak hours and overestimated

during the afternoon peak hours. This inconsistency is due to varying conditions. The

TVWI model corrects this error and closely approximates to the baseline estimates.

48

Figure 4.10: The TV travel time prediction is affected by changing weather conditions and is unable to predict the travel time accurately. The TVWI model reduces the error by incorporating the weather conditions.


500750

10001250150017502000225025002750

4:45

5:30

6:15

7:00

7:45

8:30

15:3

5

16:2

0

17:0

5

17:5

0

18:3

5

Time instance

Trav

el ti

me

in s

econ

ds

TV

Baseline

TVWI


-0.6

-0.4

-0.2

0

0.2

0.4

4:45

5:35

6:25

7:15

8:05

8:55

16:05

16:55

17:45

18:35

Time instance

Perc

enta

ge p

redi

ctio

n er

ror PPETV

PPETVWI

49

As shown through several cases the travel time is affected by changing weather

conditions. The error in the TV prediction model increases if the change in weather

conditions affects occupancy, since the TV prediction model uses past history to predict

future travel time. Weather is one of the factors that can change over time and affect the

travel time prediction. In this thesis it was demonstrated that the travel time predicted by

the TV model can be adjusted to incorporate weather impacts. In the formulation the

weather impact was estimated through increased occupancy and it was shown though

examples that the prediction error can be significantly reduced. Since all of our

experiments were done using past data, we were able to estimate and incorporate the

change of traffic conditions into the travel time prediction. In real world data, we assume

that the weather predictions can be obtained through the National Weather Service and

can be incorporated into the prediction model in terms of occupancy increase or decrease.

50

CHAPTER 5 : CONCLUSION

5.1 Conclusion The thesis first presented analyses on the weather impact on traffic utilizing

Mn/DOT RWIS and traffic data. According to the correlation coefficient study presented,

no strong correlation between the traffic and RWIS parameters was found. Next, the

effect of daily traffic volume was investigated. It was found that daily total volume under

weather events was only marginally affected (decreased). In most cases, the peak hour

traffic volume was reduced but reduced volume appeared during the off-peak hours as an

increase in volume. In order to study how weather impacts traffic during peak hours,

color coded visualization techniques were used, i.e., the traffic volume graphs were

generated with different color codes representing different pavement conditions and the

volume/occupancy scatter graphs were color coded according to morning and afternoon

peak hours and off-peak hours. The analysis of these graphs suggests that the traffic

volume generally drops during peak hours if a weather event occurs. The drop in the

traffic volume depends on the kind of weather event and the severity of the weather. It

was also observed that freeway capacity was reduced under weather events. In most

cases, congestion was increased during a weather event although the volume drops. This

happens because the weather event has reduced the freeway capacity but the trip demand

to use the freeway has not decreased accordingly. One exception was also observed.

During severe snow conditions the traffic volume drops considerably due to significant

reduction in trip demands. In those cases, congestion on the freeway was actually

reduced. The wet and damp conditions did not sufficiently reduce the trip demands

enough to ease congestion but the freeway capacity was reduced enough to cause a higher

level of congestion.

As the second part, the impact of weather events on the travel time prediction was

investigated using a time-varying linear coefficient (TV) model. Since the TV travel time

prediction model relies on the historical travel time information to estimate the future

travel time, the prediction errors were more significant under changing weather

conditions. It was observed that if the pavement conditions change from snow, damp or

wet to normal dry conditions then the TV model tends to overestimates the travel time.

51

On the other hand, if the pavement conditions change from dry to snow, damp or wet

conditions then the TV model tends to underestimates the travel time. This happens

because the prediction model assume the future travel condition is identical to the past

travel condition. In this thesis, an attempt was made to reduce the error induced by the

impact of weather changes. It was found that when the changes in occupancy of the

freeway under weather events and was compared to that of the normal dry conditions a

more accurate prediction of travel time was obtained. The calibration factor that has been

proposed in this thesis is based on the change in the occupancy that will occur due to the

impact of weather events. Various experiments that have been conducted for different

cases based on the theory and the experiments, it has been concluded that the error in the

travel time prediction increases during weather event and the travel time prediction can

be made more accurate if the change in estimated occupancy due to the weather event is

incorporated into the model.

5.2 Future Recommendations The weather impact on travel time was investigated using the color code for

different weather events and it showed the trends of traffic impact. However, one can also

try using the precipitation intensity and other weather related information to more

accurately model the impact of the weather events on traffic. Future work can also

include more specific studies on the measure of the severity of the weather events in

response to traffic impact. Such a measure would help formulate the drop in freeway

capacity and effect on congestion and could lead to more reliable prediction of future trip

times.

In the other part of this thesis we have used the change of occupancy as one of the

factors that can be used to adjust the travel time prediction during the change in weather

event. Another important area of for future work would be to predict the change in

occupancy if there is a change in weather events that are being predicted from such as the

National Weather Service. Once the change in occupancy can be predicted then the trip

time prediction can be done more reliably and this can help in trip planning. This also

relates to understanding of changes of trip demands and high way capacity by weather

52

events. If we can accurately predict the trip demands and the highway capacity, the

dependency of travel time prediction on the historical travel time can be avoided.

53

REFERENCES

Cambridge Systematics, Inc., Texas Transportation Institute 2005, Traffic congestion and

reliability: trends and advanced strategies for congestion mitigation, Federal highway

administration, Cambridge Systematics, Inc., Texas transportation institute, September

2005.

Chin, S. M., Franzese, O., Greene, D. L., Hwang, H. L., Gibson, R. C. (2004), Temporary

loss of highway capacity and impact on performance: phase 2, Oak ridge national

laboratory, Report no. ORLNL: TM-2004/209, November 2004.

Coifman, B. (1998), Vehicle reidentification and travel time measurement in real-time on

freeways using the existing loop detector infrastructure, Transportation Research Record

(1643):181-191, 1998

Cortes, C. E, Lavanya, R., Oh, J., Jayakrishnan, R. (2001), A general purpose

methodology for link travel time estimation using multiple point detection of traffic,

Department of Civil Engineering and institute of transportation studies, University of

California, Irvine, 2001.

Devore, J. L. (1995), Probability and Statistics for Engineering and the Sciences, 4th Ed,

Brooks/Cole Publishing Company, CA, USA, 1995.

Dion, F., Rakha H. (2003), Estimating Spatial Travel Time using Automatic Vehicle

Identification Data, Transportation Research Board (TRB) 2003

Goodwin, L. C., Best Practices for Road Weather Management, Federal Highway

Administration; May 2003.

Hall, F. and Persaud, B. N. (1989), Evaluation of speed estimates made with single-

detector data from freeway traffic management systems. Transportation Research Record,

1232:9-16, 1989.

Hastie, T., Tibshirani R., (1993), Varying coefficient models, Journal of the Royal

Statistical Society Series B, 55(4):757-796, 1993

54

Kirby, H. R., Watson, S. M., Dougherty, M. S. (1997), Should we use neural network or

statistical models for short-term motorway traffic forecasting?, International Journal of

Forecasting, 13(1):43-50, March 1997.

Kwon J., Coifman B., Bickel P. (2000), Day to day travel time trends and travel time

prediction from loop detector data, Transportation Research Record, 2000.

Kwon, T. M. (2004), TMC Traffic Data Automation for Mn/DOT’s Traffic Monitoring

Program, Mn/DOT; Report No. MN-RC-02004-29, July 2004.

Kwon T., Dhruv N. (2004), “Unified transportation sensor data format (UTSDF) for

efficient archiving and sharing of statewide transportation sensor data,” Proc. of the

Transportation Research Board 83nd Annual Meeting, Washington D.C., Jan. 2004.

Kwon T.M., Fleege E. (2000), “R/WIS Architecture for Integration and Expansion,”

Journal of the Transportation Research Board: Transportation Research Record 1700, pp.

1-4, The National Research Council, The National Academies, 2000.

Kwon, T. and Parsekar A. (2005), Deconvolution of vehicle inductance signature for

vehicle reidentification, Transportation Research Board 83nd Annual Meeting,

Washington D.C., Jan. 2005.

Nicholson, H., Swann, C. (1974), The prediction of traffic flow volumes based on

spectral analysis, Transportation Research, 8:533-538, 1974

Okutani I., Stephenades Y. J. (1984), Dynamic prediction of traffic volume through

Kalman Filtering, Transportation Research, 18(B):1-11, 1984

Lomax, T., Schrank, D. (2005), The 2005 urban mobility report, Texas Transportation

Institute, May 2005

Parsekar, A. (2004), Blind deconvolution of vehicle signature for travel time estimation,

November 2004.

Pisano, P., Goodwin, L.C. (2002), Surface transportation weather applications, ITE

2002Annual Meeting and Exhibit Compendium of Papers, 2002.

55

http://ops.fhwa.dot.gov/weather/best_practices/ITE2002_SurfTransWxAppl.pdf

Pisano, P. Ficek, M., Taylor, R (2004), Resources and further information: Weather and

ITS, U.S. Department of Transportation (US DoT), Federal Highway Administration

(FHWA), American Meteorological Society(AMS), Intelligent Transportation Society of

America (ITS America), January 2004

Rice, J., van Zweet, E. (2004), A simple and effective way for predicting travel times on

freeways, IEEE transactions on Intelligent Transportation Systems, 5(3):200-207,

September 2004.

Roess, R. P., McShane W. R., Prassas E. S. (1997), Traffic Engineering 2nd Edition,

Prentice-Hall, December 1997.

Schrader, C. C., Kornhauser, A. L., Friese, L. M. (2004), Using historical information in

forecasting travel times, Transportation Research Board, 2004.

Sun, C., Ritchie, S.G. (1999), Individual vehicle speed estimation using single loop

inductive waveform, Journal of Transportation Engineering, 1999.

Torday, A., Dumont, A. 2003, Link travel time estimation with probe vehicles in

signalized networks, SRTC, March 2003.

Transportation Engineers, Institute of (1999), Traffic Engineering Handbook 5th Edition,

Institute of Transportation Engineers, September 1999.

Transportation Research Board (1998), Special report 209: Highway capacity manual,

Transportation Research Board, 1998.

Yim, Y., Ygance, J., Drane, C. (2000), Travel Time Estimation on the San Francisco Bay

Area Network Using Cellular Phones as Probes, California PATH Draft Report D2000-

43.

Zhang, X., Rice, J. A. (2001), Short Term Travel Time Prediction Model using Time

Varying Coefficient Linear Model, Elsevier Reprint, March 2001.

lalit sivanandan nookala - university of minnesota duluth

Documents