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Establishing speed-flow-density relationships for exclusive motorcyclelanesH. Hussaina; R.S. Radin Umarb; M.S. Ahmad Farhanc
a Department of Civil Engineering, Faculty of Engineering, Universiti Putra Malaysia, Serdang,Selangor, Malaysia b Department of Higher Education, Ministry of Higher Education, Putrajaya,Malaysia c Malaysian Institute of Road Safety Research, Kajang, Selangor, Malaysia
Online publication date: 14 April 2011
To cite this Article Hussain, H. , Radin Umar, R.S. and Ahmad Farhan, M.S.(2011) 'Establishing speed-flow-densityrelationships for exclusive motorcycle lanes', Transportation Planning and Technology, 34: 3, 245 — 257To link to this Article: DOI: 10.1080/03081060.2011.565175URL: http://dx.doi.org/10.1080/03081060.2011.565175
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Establishing speed�flow�density relationships for exclusive motorcyclelanes
H. Hussaina*, R.S. Radin Umarb and M.S. Ahmad Farhanc
aDepartment of Civil Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400,Serdang, Selangor, Malaysia; bDepartment of Higher Education, Ministry of Higher Education,Level 3, Block E9, Parcel E, 62505, Putrajaya, Malaysia; cMalaysian Institute of Road SafetyResearch, Lot 125-135, Jalan TKS 1, Taman Kajang Sentral, 43000, Kajang, Selangor, Malaysia
(Received 4 November 2009; final version received 1 February 2011)
The motorcycle is a popular mode of transport in Malaysia and developing Asiancountries, but its significant representation in the traffic mix results in high ratesof motorcycle accidents. As a result, the Malaysian Government decided tosegregate motorcycle traffic along its new federal roads as an engineeringapproach to reduce accidents. However, traffic engineers needed to know themaximum traffic a motorcycle lane could accommodate. Despite substantialliterature related to speed�flow�density relationships and capacities of varioustransport facilities, there is a knowledge gap regarding motorcycle lanes. Thispaper establishes motorcycle speed�flow�density relationships and capacities ofexclusive motorcycle lanes in Malaysia. Observations of motorcycle flows andspeeds were conducted along existing and experimental motorcycle lanes.Motorcycle speed�density data were aggregated and plotted for two types ofobservable motorcycle riding behaviour patterns that were influenced by thewidths of a motorcycle lane: the headway pattern (lane width 5 1.7 m) and thespace pattern (lane width � 1.7 m). For both riding patterns, regression analysisof motorcycle speed�density data best fits the logarithmic model and conse-quently the motorcycle flow�density and speed�flow models are derived.Motorcycle lane capacities for headway and space riding patterns are estimatedas 3300 mc/hr/lane and 2200 mc/hr/m, respectively.
Keywords: motorcycle; accidents; motorcycle lane facility; motorcycle speed�flow�density relationships; motorcycle lane capacity
1. Introduction
As a result of the low socioeconomic status of its people and relatively poor public
transport services, especially in busy urban areas, motorcycle riding is an alternative
and cheaper mode of transport which provides the freedom of door-to to door travel
in countries such as Malaysia and other developing Asian countries. In addition, it is
part of the travelling culture in these hot climate countries. The motorcycle
population in Malaysia represents 47% of the total vehicle mix (Malaysian Road
Transport Department 2007), and motorcycle riders and pillion passengers account
*Corresponding author. Email: [email protected]
Transportation Planning and Technology
Vol. 34, No. 3, April 2011, 245�257
ISSN 0308-1060 print/ISSN 1029-0354 online
# 2011 Taylor & Francis
DOI: 10.1080/03081060.2011.565175
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for 57% of road accident fatalities (Royal Malaysian Police 2007). It clearly indicates
that motorcycle accidents are a key accident problem in the country and that
something must be done to tackle the road safety problem of this major and
vulnerable road user.
The idea of segregating motorcycles from the traffic mix in Malaysia was initiated
during the early 1970s. The first exclusive motorcycle lane was constructed along
Federal Highway Route 2 (F02) in the state of Selangor. But as there were no proper
guidelines available at that time, the geometric design of this facility was based on a
‘rule-of-thumb’ approach. Studies later showed that the introduction of this 30-km-
long (per direction) exclusive motorcycle lane led to a significant reduction in
motorcycle accidents � by 39% on that stretch (Radin Umar et al. 1995, 2000). This
supported the notion that segregation is the best engineering approach to avoid
conflicts between motorcyclists and other vehicles in the traffic mix, thus reducing
serious injuries and fatalities.
Recently, the Malaysian Government decided to adopt a policy to provide
exclusive motorcycle lanes along its new federal roads as part of its engineering
approach to reduce motorcycle accidents (The Star Newspaper 2007). This policy
involves a large-scale project with usually limited financial resources. Therefore, it is
essential for traffic engineers to have some idea regarding the maximum number of
motorcycles that can be accommodated in a motorcycle lane (i.e. its capacity) in their
attempt to minimise the costs of construction and to maximise the operating
performance of the motorcycle lane.
Despite the widely available literature related to the fundamental speed�flow�density relationships, capacity and level of service for roadways, pedestrians and
bicycle lane facilities (HCM 2000), there has been a knowledge gap for motorcycle
lanes. This paper is seen as an initial effort towards a better understanding
of motorcycle traffic science, operations and facility design. It attempts to
develop motorcycle speed�flow�density relationships along an uninterrupted
exclusive motorcycle lane from which the values of critical density, critical speed
and capacity may be determined.
2. Related motorcycle traffic studies
The most relevant available literature to motorcycle traffic science and facilities is the
guidelines for the design of a cycle track published by the Malaysian Ministry of
Works (Public Works Department 1986). Although the design elements of this cycle
track seem to be a cross between a highway and a bicycle track, there is no mention
of the capacity of this facility and it is not known if the lane width recommendations
(minimum 2.0 m and maximum 3.5 m) were actually derived from any scientific
studies.
In a recent study that relates to motorcycle/rider characteristics, it was reported
that small- and medium-sized motorcycles (less than 150 c.c. engine) represented
99% of all motorcycles in Malaysia (Hussain et al. 2005). The static handlebar width
of a motorcycle/rider unit is 0.8 m, while the operating width ranged from 0.9 to
1.7 m (a mean width of 1.3 m). There are two observable behaviour patterns with
regard to motorcyclists’ riding manner, which are influenced by the width of the
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motorcycle lane. The first pattern is for situations when the motorcycle lane width is
1.7 m or less, thus constraining the available riding space of the motorcyclists and as
a consequence forcing them to ride in a single file regardless of low- or high-flow
traffic conditions. This riding behaviour is known as headway (or platoon) behaviour
and the motorcycle flow is measured in mc/hr/lane. For the second riding pattern,
motorcyclists are able to pass other motorcyclists as the width is more than 1.7 m.
The formation of two lines during low- or high-flow traffic conditions is observable
and this pattern is referred to as the space pattern and the motorcycle flow is
expressed in mc/hr/m width.
2.1. Speed�density models from past studies
There have been various established forms for the shape of the speed�density
relationships covering the linear as well as various logarithmic and exponential
curves. Greenshields (1934) first proposed the linear speed�density model, which is
simple and straightforward. Both free-flow speed and jam density are easily
determined, and the model is easily manipulated to find flow�speed and flow�density relationships. Most recent studies, however, have indicated that speed�density data are not perfectly linear.
Greenberg (1959) hypothesised a logarithmic shape for the speed�density
relationship, but the major flaw in this model is that it collapses at low densities.
For this reason, a maximum free-flow speed must be independently assumed or
observed and superimposed on this model. Underwood (1961) proposed an
exponential model of speed�density. This model is reasonable at low densities, but
is rather unreliable at high densities because speed asymptotically approaches zero
without ever reaching it.
The fitting of data to these simple models is accomplished using multiple linear re-
gression analysis. The speed�density equations developed by Greenshields, Underwood
and Greenberg in relation to their hypothesised basic shapes are summarised in Table 1.
Given a speed�density model, corresponding parabolic equations for flow�speed
and flow�density may be defined algebraically from the general relationship: Volume
� Speed � Density. Once speed�flow�density relationships are established,
capacity can therefore be defined either graphically or mathematically from the
peak of the flow�density curve.
Table 1. Summary of basic speed�density models.
Model Speed�density equation Simple linear equation
Linear (Greenshields) S ¼ Sf �Sf
DfD S ¼ Sf �
Sf
DfD
Exponential (Underwood) S ¼ Sf e�DDc
� �ln Sð Þ ¼ ln Sfð Þ � 1
DcD
Logarithmic (Greenberg) S ¼ Sc lnDj
D
� �S ¼ Sc ln Dj
� �� Sc ln Dð Þ
Note:S�speed; Sf�free-flow speed; Sc�critical speed; D�density; Dc�critical density; Dj�jam density.
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3. Methodology
3.1. Field parameters
As in the general vehicular traffic stream, the understanding of the macroscopic
parameters of a motorcycle traffic stream, such as motorcycle speed, motorcycle flow
and motorcycle density, is essential. Parameters recorded in the field were individual
motorcycle spot speeds, motorcycle volumes and total paved width of the motorcycle
lanes. Time-mean speeds were converted to space-mean speeds according to
established traffic flow theories (Wardrop 1952). Data collection was carried out to
cover the two observable riding behaviour patterns, i.e. the headway pattern (where the
motorcycle lane is 1.7 m wide or less) and also the space pattern (where the motorcycle
lane is more than 1.7 m wide). Motorcycle volumes collected in 1-minute intervals
were converted to an equivalent rate of flow in motorcycles per hour. The motorcycle
flow rate for the headway riding pattern was computed as motorcycles per hour per
lane. For the space riding pattern, motorcycles per hour per unit width was obtained
by dividing the rate of flow by the total width of the motorcycle lane.
3.2. Field and experimental study sites
In an attempt to collect data ranging from stable-flow to unstable-flow conditions,
the study was conducted in three stages. In the initial stage, data were collected at
three sites of the motorcycle lane along Federal Highway Route 2. This is the stretch
of exclusive motorcycle lane noted earlier and shown in Figure 1. The availability of
elevated positions or concealed locations such as pedestrian overhead bridges
ensured that the observed motorcyclists were not inhibited by any external factors
such as the presence of study observers at the vicinity of the study site.
All sites were level and straight basic segments with total widths of 2.4, 3.0 and
3.3 m, respectively, representing the minimum to maximum available lane width.
Figure 1. Motorcyclists riding along exclusive motorcycle lane, Federal Highway Route 2,
Selangor, Malaysia.
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Observations from these three sites exhibited only the initial portion of a stable flow
condition (i.e. low density, high speed) even under peak-hour conditions and
minimum width of 2.4 m. It indicated that the lane width provided using the rule-of-
thumb approach is overdesigned in comparison to the volume of motorcycles ridingalong this stretch. As such, the chances of recording motorcycle flow at capacity and
near-jam density conditions along this exclusive motorcycle lane are rather slim.
Observations of motorcycle flow at capacity could be made possible if the widths
were narrower than 2.4 m and coupled with considerably higher motorcycle flows.
The second stage involved three experimental studies representing three different
widths of less than 2.4 m conducted on the Universiti Putra Malaysia campus. These
studies involved 100 motorcyclists who volunteered to ride along level and straight
basic segments that were narrowed on one side by safety cones. The experimentaltotal lane widths were 1.5, 1.7 and 1.9 m, respectively.
The success of these experimental studies in obtaining data covering capacity and
near-jam density conditions led to similar experimental studies which were
conducted along the motorcycle lane on Federal Highway Route 2. In this third
stage, the experimental studies were conducted during the morning peak hour of
motorcycle traffic riding along the level and straight basic segments of narrowed
experimental total widths 1.4, 1.6 and 2.0 m, respectively.
4. Regression models
A total of 193 data points measured at 1-minute intervals were aggregated from the
study sites, covering total widths ranging from 1.4 to 3.3 m. Adopting earlier findings
pertaining to headway and space riding patterns (Hussain et al. 2005), the model for the
headway pattern covered data points belonging to observations for total widths of 1.4-
1.7 m. For comparison purposes, the space pattern model encompassed all 193 data
points (i.e. total widths from 1.4 to 3.3 m). Scatter plot diagrams for three relationships
� flow (F)-speed (S), flow (F)-density (D) and speed (S)� density (D) � were obtained.The initial calibrations focused on the S�D relationships because S�D curves are
monotonically decreasing and involve simpler mathematical forms than the other
two curves. Linear regression analysis at a 95% confidence interval was employed for
the model fitting and model validation process using the Statistical Package for
Social Sciences (SPSS) software. The three underlying assumptions � that random
errors are independent of one another (Durbin�Watson, du), have constant variance
(scatter diagram) and are distributed normally (P�P plot) � were tested.
The outcome of the model-building process for the S�D relationship suggestedthat the data are best described by Greenberg’s logarithmic model (Greenberg 1959).
Since F � S � D, the calibration of the S�D relationship leads to the derivation of
the F�D and S�D relationships.
4.1. Motorcycle headway riding pattern (total lane width 5 1.7 m)
From the linear regression analysis, the motorcycle speed versus motorcycle density
relationship may be described in a linear form as
S ¼ 84� 13 ln Dð Þ (1)
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where S is the motorcycle speed and D is the motorcycle density.
Using Greenberg’s logarithmic model which is expressed in linear form as
S ¼ Sc ln Dj
� �� Sc ln Dð Þ (2)
the following results were obtained:
Jam motorcycle density; Dj ¼ 640 mc=km=lane
Critical motorcycle speed; Sc ¼ 13 km=hr
Critical motorcycle density; Dc ¼ 235 mc=km=lane
Maximum motorcycle flow; Fmax ¼ 3060 mc=hr=lane
Hence, the motorcycle speed�flow�density relationships may be expressed as
follows:
(a) Motorcycle speed versus motorcycle density (Figure 2):
S ¼ 13 ln 640=Dð Þ (3)
(b) Motorcycle flow versus motorcycle density (Figure 3):
F ¼ 13D ln 640=Dð Þ (4)
Figure 2. Relationship between motorcycle speed and motorcycle density (headway riding
pattern).
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Figure 3. Relationship between motorcycle flow and motorcycle density (headway riding
pattern).
Figure 4. Relationship between motorcycle speed and motorcycle flow (headway riding
pattern).
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(c) Motorcycle speed versus motorcycle flow (Figure 4):
F ¼ 640S e�S=13 (5)
(Note that D ] 11 mc/km/lane.)
4.2. Motorcycle space riding pattern (total lane width � 1.7 m)
Similarly, the linear regression analysis of the motorcycle speed (S) versus motorcycle
density (D) relationship may be described in the following linear form:
S ¼ �10; 759� 13; 330 ln Dð Þ (6)
From Greenberg’s model, the following results were computed:
Jam motorcycle density; Dj ¼ 0:45 mc=m2 ðor space; M j ¼ 1=Dj ¼ 2:2 m2=mcÞCritical motorcycle speed; Sc ¼ 13; 330 m=hr ð13 km=hrÞCritical motorcycle density; Dc ¼ 0:166 mc=m2 ðor space; Mc ¼ 1=Dc ¼ 6:0 m2=mcÞMaximum motorcycle flow; F max ¼ 2207 mc=hr=m
The motorcycle speed�flow�density relationships are described as follows:
(a) Motorcycle speed versus motorcycle density (Figure 5):
S ¼ 13; 330 ln 0:45=Dð Þ (7)
(b) Motorcycle flow versus motorcycle density (Figure 6):
F ¼ 13; 330D ln 0:45=Dð Þ (8)
Figure 5. Relationship between motorcycle speed and motorcycle density (space riding
pattern).
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(c) Motorcycle speed versus motorcycle flow (Figure 7):
F ¼ 0:45Se�S=13;330 (9)
(Note that D ] 0.003 mc/m2.)
Figure 6. Relationship between motorcycle flow and motorcycle density (space riding
pattern).
Figure 7. Relationship between motorcycle speed and motorcycle flow (space riding pattern).
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5. Discussion
In this study, 99% of motorcycles observed along the uninterrupted exclusive
motorcycle lane (one-way) comprised small- and medium-sized motorcycles with
engine capacities of 150 c.c. and below. It therefore described an almost
homogeneous motorcycle traffic stream under ideal conditions. It may also be
hypothesised that under non-ideal conditions where there exists a reasonable mixture
of small- and large-sized motorcycles, together with effects of side frictions and
psychological barriers, riding manners would be rather similar.
5.1. Motorcycle speed�density relationship (headway and space patterns)
The logarithmic function is the best model that describes the data of the motorcycle
speed�density relationships for both headway pattern (Figure 2) and space pattern
(Figure 5). The establishment of the motorcycle speed�density models led to the
derivation of the motorcycle flow�density and motorcycle speed�flow relationships
for the headway pattern (Figures 3 and 4) and the space pattern (Figures 6 and 7).
The three fundamental motorcycle speed�flow�density relationships developed in
this study exhibited trends that are similar to the ones established for pedestrians,
bicycles and automobiles. In fact, all of them obeyed the theory of flow that was
originally established by Greenshields (1934). A noticeable difference between
motorcyclists and other transport modes is that motorcyclist riding behaviour
utilised both headway and space patterns depending on the availability of safe space
within the motorcycle lane. In comparison, cars followed a headway pattern while
bicycles and pedestrians followed a space pattern.
The motorcycle speed�density models for both the headway and space patterns
(Figures 3 and 5) indicated that as the motorcycle density increases, motorcycle
speed would continue to drop. This is because as more motorcycles are present along
the motorcycle lane, motorcyclists have less freedom to select their own desired
speed. The fastest motorcyclists are slowed down first, but eventually even the slow
motorcyclists are affected. As the motorcycle speed drops to about 5 km/hr, the
motorcyclists will have problems to maintain the stability of their vehicles and will be
forced to put their feet on the ground. Eventually, all motorcyclists will practically
come to a stop as the traffic stream approaches the jam density, which occurred at
640 mc/km/lane (in the headway pattern) and 0.46 mc/m2 (in the space pattern) � as
shown in Figures 2 and 5, respectively.
In the headway pattern, the motorcycle speed�density relationship (Figure 2) along
the uninterrupted exclusive motorcycle lanes shared similar trends to that for the speed�density of cars. The car following car movements along a lane is based on headway
(HCM 2000). But unlike motorcycles, cars can travel at speeds lower than 5 km/hr.
As for the space pattern, the motorcycle speed�density relationship (Figure 5)
along the uninterrupted exclusive motorcycle lanes is comparable to cyclists riding
along exclusive bicycle lanes. But due to their low operating speeds (15�25 km/hr),
the bicycle speeds remain relatively insensitive over a wide range of flows (HCM
2000). It is reasonable to expect that the riding manner of both motorcyclists and
cyclists to be equivalent within the riding speed of 25 km/hr and below.
254 H. Hussain et al.
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5.2. Motorcycle flow�density relationship (headway and space riding patterns)
With respect to motorcycle flow�density relationships, both Figure 3 (headway
pattern) and Figure 6 (space pattern) showed that motorcycle flow is zero when
motorcycle density is zero. Theoretically, it is zero when there is no motorcyclist
present in the exclusive motorcycle lane. As motorcyclists begin to join the motorcycle
lane, the flow increases with further increments in density. As density reaches a critical
value of 235 mc/km/lane (headway pattern), the motorcycle flow reaches a maximum
point of the parabolic curve that corresponds to the maximum motorcycle flow of 3060
mc/hr/lane and critical speed of 13 km/hr. This maximum point is the capacity of the
motorcycle lane facility. Similar trends were exhibited for the space pattern. At a
critical density of 0.166 mc/m2 (or critical space of 6 m2/mc), capacity is reached at a
maximum motorcycle flow of 2207 mc/hr/m, corresponding to 13 km/hr.
Note that at capacity (headway and space patterns), motorcyclists are riding very
close to each other but within a stable motorcycle traffic flow. Even though the
maximum motorcycle flows for the headway and space patterns are different in their
units of measurement, the capacities are reached at the same critical speeds of
13 km/hr. The similarity in critical speeds for both the headway and space patterns
may be attributed to the earlier assumptions in the data analysis with regard to the
scatter plots for the space pattern. That is, in order to obtain the range of stable flow
through unstable flow conditions for the space pattern, the data points from
motorcycle lanes of 1.7 m or less (which fall under the headway pattern) were used
with the assumption that the motorcyclists were actually being constrained by the
narrower lane widths. This limitation of space within the motorcycle lane width
forced them to ride in a single file.
On the other hand, it also means that motorcyclists adjust their riding speeds in
reaction to the available space and proximity to other motorcyclists riding along the
exclusive motorcycle lanes. Thus, the same critical speeds of 13 km/hr indicated that
the motorcyclist perception of density or proximity with other motorcyclists under
the headway pattern and the space concept are similar. As the available space
approaches a critical condition, the riding speeds continue to drop but still within the
stable flow conditions. The motorcyclists were still able to maintain the stability of
their motorcycles.
After this point of maximum motorcycle flow, a further increase in the number of
motorcyclists caused the flow to become unstable. Within this region, motorcycle
speeds drop slowly from 13 to 5 km/hr over a wide range of motorcycle densities
because motorcyclists tend to utilise the lesser space more efficiently � by
occasionally putting their feet on the ground in their effort to move forward and
at the same time maintaining the stability of their motorcycles. However, when
motorcycle speeds drop to 5 km/hr due to the large number of motorcyclists along
the motorcycle lane, they are forced to put their feet down � which brings the
motorcycle flow to a halt.
5.3. Motorcycle speed�flow relationship (headway and space patterns)
The motorcycle speed�flow relationships (Figures 4 and 7) exhibited that after the
free-flow speed region, the motorcycle speed gradually dropped with further
increases in the motorcycle flow. This is because the faster motorcyclists had to
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reduce their speeds due to the reduction in available space along the uninterrupted
exclusive motorcycle lanes. As more motorcyclists are present, this trend continues
until the maximum motorcycle flow condition where the motorcyclists are riding at a
minimum speed of 13 km/hr while maintaining a stable flow. Further increases in
motorcycles caused an unstable flow condition. The motorcycle speed continues to
drop as the motorcycle flow gets slower until it comes to a complete stop at 5 km/hr
and below, when motorcyclists were unable to stabilise their vehicles and forced to
put their feet on the ground.
Conclusions
This paper has established that the shape of the motorcycle speed�density relation-
ships for an uninterrupted exclusive motorcycle lane for both types of observable
motorcycle riding behavior (i.e. the headway or platoon pattern and space pattern)
takes the form of a logarithmic curve. Further, based on the fundamental theory that
flow is a product of speed and density, the motorcycle flow�density and motorcycle
speed�flow relationships were derived mathematically. The three fundamental
motorcycle speed�flow�density relationships exhibited trends similar to the ones
established for pedestrians, cyclists and automobiles, which followed the theory of
flow.
From the motorcycle speed�flow�density curves, it was determined that under
the headway riding pattern (lane width of 1.4�1.7 m) capacity is reached at a
maximum motorcycle flow of 3306 mc/hr/lane corresponding to a critical speed of
13 km/hr and critical density of 235 mc/km/lane. While under the space riding
pattern (lane width � 1.7 m), capacity occurs at a maximum motorcycle flow of
2207 mc/hr/m, which corresponds to a critical motorcycle speed of 13 km/hr and
critical motorcycle density of 0.166 mc/m2 (or space of 6.0 m2/mc). Practically, a 1.4�1.7-m-wide motorcycle lane is capable of carrying a maximum motorcycle flow of
3306 mc/hr. By doubling the lane widths would mean that a 2.8�3.4-m-wide
motorcycle lane is capable of carrying 6612 mc/hr as if the motorcyclists are riding in
two single files across the width of a motorcycle lane. In the case of the space riding
pattern, which has a capacity of 2207 mc/hr/m width, a motorcycle lane of 2.0 m
wide is, for instance, capable of carrying 4414 mc/hr.
Overall, this paper is seen as an initiative to fill the knowledge gap pertaining to
motorcycle speed�flow�density relationships and the capacity of exclusive motor-
cycle lanes under ideal conditions as well as contributing new knowledge to the field
of motorcycle traffic engineering. Results should provide useful guidance for traffic
engineers to decide on the appropriate width of motorcycle lanes in relation to the
expected motorcycle demand flows along particular segments so as to minimise
construction costs and maximise the performance of the facility.
Acknowledgements
Data, grants and support for field data collections were provided by the National ScienceCouncil IRPA Malaysia, the Public Works Department, Ministry of Works Malaysia andRoadcare (Malaysia) Sdn. Bhd.
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