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Transportmetrica
Vol. 7, No. 5, September 2011, 321–345
Heterogeneous traffic flow modelling: a complete methodology
Ch. Mallikarjuna
a
*and K. Ramachandra Rao
b
a
Department of Civil Engineering, Indian Institute of Technology Guwahati,
Guwahati 781039, Assam, India;
b
Department of Civil Engineering, Indian Institute of
Technology Delhi, Hauz Khas, New Delhi 110016, India
(Received 31 March 2009; final version received 11 February 2010)
A comprehensive methodology for modelling the heterogeneous traffic is
presented in this article. Considering the no-lane discipline and the presence of
various sizes of vehicles, several microscopic and macroscopic traffic variables are
analysed for their suitability in describing the heterogeneous traffic. Applicability
in the modelling process and the feasibility in collecting field data are the
important criteria used in deciding the suitable traffic variables. In place of
occupancy, its variant termed as area occupancy was found to be suitable in
describing the heterogeneous traffic. Vehicle size, mechanical characteristics,
lateral distribution of vehicles and the lateral gaps maintained by them are found
to be more suitable microscopic traffic variables. Data on these variables have
been used in modifying the cell structure and the updating procedures of the
cellular automata (CA)-based traffic flow model. A customised video image
processing-based data collection technique has been used in collecting the field
data on these variables. The modified CA model with the relevant parameter
values has been used in simulating the flow. Model results are validated using the
field data and the results expressed in terms of cells are found to be better in
capacity analyses under heterogeneous traffic conditions as well as fit into the
established traffic flow theory.
Keywords: heterogeneous traffic; traffic flow modelling; cellular automata; video
image processing; data collection
1. Introduction
Traffic composed of identical vehicles and following the lane discipline is termed as
homogeneous. Traffic comprising of motorised and non-motorised two-wheelers (TWs)
and three-wheelers along with several other vehicles with no-lane discipline is termed as
heterogeneous. This heterogeneous traffic is clearly different from the one with the
presence of trucks which has also been termed as heterogeneous traffic. The absence of
lane discipline results in vehicular movement that is influenced by the presence of vehicles
in the front as well as on the sides. This led to a complex traffic behaviour and it cannot be
analysed by using conventional microscopic and macroscopic traffic variables. Using
conventional measurement techniques, it is also difficult to collect the data. Modelling
methodology to be adopted in these conditions would also be considerably different
compared to the existing traffic modelling methodologies. Traffic flow variables,
*Corresponding author. Email: c.mallikarjuna@iitg.ernet.in
ISSN 1812–8602 print/ISSN 1944–0987 online
ß2011 Hong Kong Society for Transportation Studies Limited
DOI: 10.1080/18128601003706078
http://www.informaworld.com
relationships among the variables and the observed data on these variables are the crucial
inputs for the traffic flow modelling purposes. Any efforts in the area of traffic flow
modelling should consider the above aspects and it is even more crucial when dealing with
the heterogeneous traffic. In this scenario, formulating new theoretical and modelling
concepts or adopting the conventional microscopic and macroscopic traffic flow concepts
are the available alternatives for the researchers.
Several researchers (Chari and Badarinath 1983, Palaniswamy et al. 1985, Ramanayya
1988, Kumar 1994, Singh 1999, Oketch 2000) have attempted to model the heterogeneous
traffic and most of these models are microscopic in nature. Some researchers (Chari and
Badarinath 1983, Singh 1999) have proposed alternative measures for density, but where
exactly they fit into the overall modelling process and the relationship with the other traffic
variables were not clearly discussed. Explicit vehicular interactions under varying traffic
conditions are modelled in these studies. Vehicle composition and the gap maintaining
behaviour were the important input data to these models. In most of these studies, video
recording techniques were utilised in collecting the data on vehicular interactions. Video
recording technique requires extensive manpower to collect the data on vehicular
interactions and is prone to error. Some other data collection techniques, such as dual-
loop detectors, image processing-based traffic data collection techniques, can be used to
estimate vehicle lengths which in turn can be used in estimating vehicle width (Lan and
Kuo 2002). Using these techniques, vehicle lengths under free-flow conditions can be
found with a fair amount of accuracy. To overcome the errors observed in forced-flow
conditions in measuring vehicle lengths, Zhang et al. (2005) proposed a new dual-loop
algorithm which can handle erroneous raw loop actuation signals. Lateral gap data that
are equally important to model the vehicular interactions can be collected using a recently
developed image processing software called TRAZER (Mallikarjuna et al. 2009).
Implementing the cellular automata (CA) concept for modelling the heterogeneous
traffic has been suggested by some researchers (Lan and Chang 2005, Hsu et al. 2007,
Mallikarjuna and Ramachandra Rao 2009). Lan and Hsu (2006) have proposed new
variants for density and flow using the modified CA structure developed for modelling the
heterogeneous traffic. These variants have been derived based on generalised definitions
for speed, flow and the density (Edie 1965, Maerivoet 2006). Mallikarjuna and
Ramachandra Rao (2006) have proposed a new variant for occupancy termed as area
occupancy and this variable was found to be suitable for CA-based modelling
methodology. Mallikarjuna and Ramachandra Rao (2009) have proposed a detailed
methodology in formulating the CA structure for modelling the heterogeneous traffic.
Field traffic data collected using the video image processing-based software, TRAZER
(Mallikarjuna et al. 2009), has been utilised in formulating this CA structure.
In this article, an effort is made to develop a comprehensive methodology to model the
heterogeneous traffic. While choosing the appropriate traffic variables, factors such as the
usefulness in describing the traffic, data measurability and usefulness in modelling are
taken into consideration. Important microscopic variables, such as lateral gaps,
longitudinal gaps and lateral distribution of vehicles have been utilised in formulating
the CA structure. Data collected on these variables using video image processing software,
TRAZER, have been analysed. Relationship between area occupancy and a variant of
flow measured in terms of cells has been utilised in calibrating and validating the proposed
CA model. Model validation was done using the field data collected on different road
sections. Data collected from the simulation model in terms of cells, which are the basic
322 Ch. Mallikarjuna and K.R. Rao
units of vehicles in the modified CA structure, are found to be conforming to the
fundamental traffic flow theory.
The organisation of the remainder of this article is presented below. Section 2 deals
with the traffic variables that are used in modelling the heterogeneous traffic.
Methodology used in developing the CA structure is presented in Section 3. Field data
collected on various traffic variables is briefly discussed in Section 4. Section 5 deals with
the calibration and validation of the CA model. Detailed description of various results
obtained in the process of validation is also presented in this section. Summary of the
overall methodology and the important conclusions are presented in Section 6.
2. Traffic variables
2.1. Macroscopic traffic characteristics
Flow, speed and density are the commonly used macroscopic traffic characteristics.
Measurability of each of these depends on the kind of equipment used and length of time
and space periods over which the measurements are taken. Definitions and the feasibility
of data collection on flow, speed and density are not discussed here. Definitions for
occupancy and the variant of occupancy called area occupancy are discussed in the
following sections.
2.1.1. Occupancy
Occupancy is defined as the percentage time the road section is occupied by a vehicle over
a given period of time. Occupancy is equivalent to density under equilibrium conditions
but only somewhat related to density under non-equilibrium conditions (Revised
Monograph on Traffic Flow Theory: A State-of-the-Art Report 1997).
¼PN
i¼1Oi
T,ð1Þ
Oi¼liþd
vi
,ð2Þ
where is the occupancy, O
i
is the time the i-th vehicle occupied the detector, l
i
is the
length of the i-th vehicle, v
i
is the speed of i-th vehicle and dis the detector’s length.
When both density and occupancy are measured over a general measurement region,
A, (Figure 1) they can be related in the following manner (Daganzo 1997):
ðAÞ¼kðAÞlðAÞð3Þ
where occupancy, density and average vehicle length are measured over time and space.
Occupancy measured over time is related to the density and average vehicle length
measured over space as follows:
k
l,ð4Þ
where is measured over time, density (k) and average vehicle length ð
lÞare measured over
space. In the case of traffic with different vehicle lengths, it is apparent that occupancy is
more meaningful than density. Even this improved traffic measure is not suitable when the
Transportmetrica 323
traffic is heterogeneous. In the heterogeneous traffic, most of the time vehicles travel on
the central portion of the road for different reasons. Since occupancy is a function of
length and speed of the vehicle, in the case of homogeneous traffic it could consider the
effect of large slow-vehicle’s impedance by means of its length (generally long vehicles are
wide-bodied vehicles). In the case of heterogeneous traffic (observed on Indian roads),
traffic is composed of some short vehicles whose weight to horsepower ratio is more.
Effects of these vehicles are more pronounced when these vehicles are obstructing the
vehicles behind while travelling on the middle of the road. Lengths and widths of the
vehicles that are sharing the road space are also found to be not correlated. In order to
represent heterogeneous traffic, we propose to modify the formula for occupancy. This
formula would incorporate vehicle area and total road width, and is discussed in detail in
the following section.
2.1.2. Area occupancy
Occupancy may not exactly depict the collective traffic behaviour moving in a 3-D region,
including 2-D for the roadway (longitudinal and transverse) and 1-D for the time (Lan and
Hsu 2006). To overcome these difficulties, in estimating this new metric, absolute width of
the road is considered irrespective of number of lanes. If this is the case, at any time
instance there can be more than one vehicle, depending on the vehicle size, moving across
the road width. This term is also considering the size of the vehicle, which has a significant
bearing on the traffic behaviour in heterogeneous traffic conditions. When considering a
small section (e.g. detector) of the road, area occupancy expresses for how long a
particular size of the vehicle is moving on that section of the road. Like occupancy, area
occupancy is also measured over time (temporal area occupancy, the term area occupancy
is used throughout this report to refer to this quantity) and is formulated as follows;
A¼PN
i¼1Oiwid
TWd,ð5Þ
where Ais the area occupancy, O
i
is the occupancy time of the i-th vehicle in seconds, w
i
is
the width of the i-th vehicle, Wis the road width, dis the length of the road section under
consideration and Tis the observed time period in seconds.
Time
ds
General measurement region (A)
L
dt
TSpatial region
Temporal region
Space
Figure 1. Time–space diagram showing the temporal, spatial and the general data measurement
regions.
324 Ch. Mallikarjuna and K.R. Rao
In the above formula, the numerator value takes care of the occupancy time (similar to
occupancy); the amount of time a vehicle with a given area is spending on the road section
under consideration. Its value will depend on the composition of traffic and speeds of the
vehicles.
Figure 2 gives the graphical representation of the area occupancy measurements over a
short section (e.g. induction loop) of the two-lane road. It is assumed that there are two
vehicles on the road at a time instance T
1
and both vehicles are travelling at the same
speed. Figure 2(a) shows the top view of a two-lane road on which two vehicles (vehicles
shown with solid lines) are just entering into the detection area at the time instance T
1
and
their respective positions at the time instance T
2
(vehicles shown with dotted lines). From
the definition of occupancy, the difference between T
1
and T
2
gives the occupancy time of
the large-sized vehicle. Occupancy time for small vehicle is different from large vehicle. As
discussed earlier in these kinds of situations (RHE traffic), representing time–space
evolution of vehicles in a 2-D time–space diagram may not help in identifying the real
traffic conditions. Figure 2(b) shows the 3-D time space evolution of the vehicles is. In
addition to the time and space, road width is represented in the third dimension.
Figure 2. Graphical representation of factors considered in area occupancy measurements.
Transportmetrica 325
The volume (time road width detector length) in between the two horizontal planes
shown in Figure 2(b) represents the total control volume. Two vertical planes which are
shown in the figure represent the time instances at which the large-sized vehicle enters and
leaves the detection zone. The volume which is common to the vertical and horizontal
planes ((T
1
T
2
)vehicle width d) represents the time spent by the large-sized vehicle –
area in the detection zone. Extending this to the total vehicles which may have crossed the
detection zone during the observed period, the formulation of area occupancy is obtained
as shown below:
A¼PiðT2T1Þiwid
TWd)Pi
ðliþdÞ
viwid
TWd)PiOiwid
TWd:ð6Þ
This formulation has been found to be a better explanatory variable in studying the
heterogeneous traffic. This variable is useful in correlating the gap maintaining behaviour
of vehicles with the varying traffic conditions as discussed in Section 4.1.2.
2.2. Microscopic characteristics
Analysis of microscopic characteristics, such as individual vehicle characteristics, lateral
gap, longitudinal gap and lateral position of the vehicles, which are useful in describing the
heterogeneous traffic as well as in developing the CA-based models, are presented below.
2.2.1. Vehicle characteristics
Traffic composition is one of the major factors influencing the lane discipline observed in
heterogeneous traffic. In car following, when the leading vehicle is TW, there will be a
considerable gap on the side of this vehicle. The following vehicle travelling may utilise this
gap as well as some portion of the adjacent lane. Hence when modelling the heterogeneous
traffic, it is necessary to incorporate this behaviour in the model. In addition to the
physical characteristics, widely varying mechanical characteristics are also very important
when dealing with heterogeneous traffic. To replicate this behaviour, the basic cell
structure in the CA model has been modified accordingly (Figure 4). The parameters, such
as p
0
,p
dec
,a
n
and d
n
that are used in the longitudinal updating procedure (Section 3.2) take
different values (Tables 2 and 3) corresponding to the mechanical characteristics of various
vehicle types.
2.2.2. Lateral gap
In the heterogeneous traffic, in addition to the driver’s discomfort, the presence of
small vehicles influence the lateral gaps (g
lat
in Figure 3) maintained by different
vehicles. Since lane discipline is not enforced under heterogeneous traffic conditions,
even in the absence of small vehicles many vehicles tend to travel in the middle of the
road. Lateral gaps maintained by different vehicles may influence speeds as well as
longitudinal gaps. This gap maintaining behaviour may vary from vehicle type to
vehicle type. Utility of this variable in formulating the CA structure is discussed in
Section 3.
326 Ch. Mallikarjuna and K.R. Rao
2.2.3. Longitudinal gap
Under heterogeneous traffic conditions, there may be more than one leading vehicle for
the corresponding following vehicle. Measuring or estimating the longitudinal gaps in
these conditions requires trajectory data. From the filed data, it has been observed that the
separation in the centrelines (g
cl
in Figure 3), and lateral and longitudinal gaps maintained
by the vehicles are interdependent on one another. While developing the vehicle updating
procedure, it is necessary to consider this behaviour. In the present CA model, this
behaviour is not incorporated due to lack of understanding on the interaction of these
three variables. It has been assumed that longitudinal gap is a function of vehicle type and
the speeds of the leading and following vehicle types.
2.2.4. Lateral position of the vehicle
Under heterogeneous traffic conditions where significant number of TWs and three-
wheelers are present, lateral positions maintained by different vehicles under different
traffic conditions are not the same. In left side driving environment which is prevalent in
India, it is assumed that fast moving vehicles stick to rightmost portion of the road space.
This is not true when significant numbers of fast moving TWs are present in the traffic
stream. The vehicle distribution in the lateral direction under different traffic conditions is
very crucial while modelling the traffic flow. The cell structure adopted in the present CA
model allows the vehicles to take a finite number of lateral positions, but the segregation of
vehicles under different traffic conditions is not considered in this study.
3. Developing the CA model
3.1. Cell structure
The presence of vehicles with different physical and mechanical characteristics makes it
necessary to alter the conventional cell structure and along with it the updating procedures
used in the CA models. This nature of heterogeneous traffic is also necessitating the study
of lateral movements in addition to the longitudinal movements. Vehicle’s mechanical
characteristics, specifically the acceleration behaviour, constrain the cell length that can be
adopted for heterogeneous traffic flow modelling. In this study, the cell length is taken as
0.5 m considering the slow/heavy vehicles present in the heterogeneous traffic. The lateral
gap information is important in deciding the effective vehicle width under varying
glat
glong
gcl
Figure 3. Lateral and longitudinal gaps maintained by vehicles with staggered car following
behaviour.
Transportmetrica 327
traffic conditions. Effective vehicle width is the summation of actual width and the gaps
maintained on both sides. This effective width is the basis in deciding the cell width used in
the CA model. Cell width may vary depending on the effective vehicle width that is varying
with the gap maintaining behaviour. This behaviour is represented in Figure 4 and gap-
related data at different traffic conditions should be the basis in adopting this cell
structure. The number of vehicles that can travel side-by-side vary depending on the
occupancy/density and the same is shown in Figure 4. This results due to the fact that at
higher occupancy levels vehicles maintain less lateral gaps and more vehicles can travel
side-by-side. The effective widths of various types of vehicles have been found from
the field data collected (Section 4) and the same are presented in terms of cells in Tables 2
and 3.
3.2. Longitudinal updating procedure
Longitudinal updating procedure in this study is adopted from Knospe et al. (2000) with
the modifications discussed in this section. One of the important features of Knospe’s
model is that the acceleration is delayed for standing vehicles and directly after braking
events. The delay in acceleration is modelled using the slow-to-start (p
0
) parameter and,
the delay after braking has been modelled using the brake light probability ( p
bl
)
parameter. For homogeneous traffic, these values are the same for all the vehicles present
in the traffic stream. This is not true for heterogeneous traffic and these parameters are
modified accordingly. The delay in acceleration for stationary vehicles and immediately
after braking is considered to be different for various types of vehicles observed in the
heterogeneous traffic. Another parameter called the slow down probability ( p
dec
) is also
considered to be different for various vehicle types. In addition to these changes, maximum
allowable speeds, accelerations and decelerations are considered to be different and these
values are chosen in accordance with the field data. Data related to these modifications of
the model are given in Tables 2 and 3. Effects of these modifications along with the
modified cell structure have been evaluated through various parametric studies. The effect
of the reduced cell length on various model parameters has been analysed through
parametric studies (Mallikarjuna and Ramachandra Rao 2009).
Figure 4. Modified cell structure in the CA-based heterogeneous traffic flow model at two different
occupancy levels.
328 Ch. Mallikarjuna and K.R. Rao
Updating procedure used in the present model, represented mathematically is given
below;
(1) Determination of the randomisation parameter:
p¼p(v
n
(t), b
nþ1
(t), th
n,t
s
)¼p
bl
if b
nþ1
(t)¼1 and th
n5t
s,
¼p
0
if v
n
(t)¼0,
¼p
dec
in all other cases.
(2) Acceleration:
If (b
nþ1
(t)¼0) and (b
n
(t)¼0) or ðth
ntsÞthen:
v
n
(tþ1/3) ¼min(v
n
(t)þa
n
(v
n
,l
n
), v
max
)
th
n¼(g
n
(t)þmaximum(0,v
nþ1,anticipated
(t)security distance))/v
n
(t)
(3) Braking rule:
v
n
(tþ2/3) ¼min(v
n
(tþ1/3), geff
n)
if (v
n
(tþ2/3) 5v
n
(t)) then:
b
n
(tþ1) ¼1.
(4) Randomisation, brake:
If (rand( ) 5p) then:
If ( p¼p
bl
or p
0
)
v
n
(tþ1) ¼max(v
n
(tþ2/3) d
n
(l
n
), 0)
If ( p¼p
dec
)
v
n
(tþ1) ¼max(v
n
(tþ2/3) 1, 0)
If ( p¼p
bl
) then: b
n
(tþ1) ¼1.
(5) Car motion:
x
n
(tþ1) ¼x
n
(t)þv
n
(tþ1).
where th
nis the available time headway for n-th vehicle, t
s
is the interaction headway, b
n
(t)is
the binary variable denoting brake light’s status of the n-th vehicle (if equal to 1, brake
light is on, if equal to 0 brake light is off), security distance is the parameter used to offset
the anticipated movement of leading vehicle, geff
nis the effective gap available after
considering anticipated movement of leading vehicle, l
n
is the length of the n-th vehicle,
a
n
is the acceleration of the n-th vehicle and d
n
is the deceleration of the n-th vehicle. (tþ1/
3) and (tþ2/3) denotes various stages at which speed values are updated within each
updating step.
3.3. Lateral updating procedure
When vehicles are following lane discipline like in homogeneous traffic, lane changes are
classified into two types, namely discretionary and mandatory. Under heterogeneous
traffic conditions where vehicles are not following lane discipline, the term lane change has
no relevance. Under these conditions, vehicles adjust their lateral positions in a way that
optimises the usage of the road space. In this study, emphasis is given on how the vehicle
moves laterally under different traffic conditions. Lateral movements carried out by car
and TW with the modified CA structure is shown in Figure 5. Each lateral division of the
Transportmetrica 329
road is called a sub-lane. With the given CA structure, different types of lateral movements
are possible and some of the possible lateral movements are shown in Figure 5. There can
be many other lateral movements, but in this work it is restricted to five.
In all of the lane changes, the subject vehicle can shift laterally both in left and right
directions depending on the gap availability in the corresponding directions. Any vehicle
may perform lane changing manoeuvre based on two criteria, namely incentive criterion
and safety criterion. Any vehicle changes lanes if the gap available in the front is less than
its anticipated speed in the next time step. This suggests the intention of the vehicle to shift
lanes. At the same time, the other lane must be more attractive and safe. The target lane is
more attractive if the gap available in the target lane is more than the gap available in the
current lane. Target lane is safe if no vehicle is expected to be on the target lane near the
intended location of lane changing. With certain probability, a vehicle will change lanes
when the following conditions are satisfied. Lane changing rules used in the present model
are as follows.
Incentive criterion
(1) (v
n
þa
n
(v
n
,l
n
)) 4g
n
(2) (v
n
þa
n
(v
n
,l
n
)) 4v
nþ1.
Safety criteria
(3) g
n,o,f
4v
n
(4) g
n,o,b
4v
max
of the corresponding back vehicle þD,
where a
n
is the acceleration of the vehicle which is a function of speed, is the non-zero
parameter, value of which is greater than one, g
n
is the gap in the front on the same lane,
g
n,o,f
is the gap in the front on the other or target lane and g
n,o,b
is the gap in the back on
the other or target lane.
One more incentive criterion is added through which a driver would decide whether to
change lanes or not. This incentive criterion is added to consider the effect of front
vehicle’s speed on the following vehicle in lane changing. The parameter is significant in
the sense that the vehicle which is changing lanes may look for a sufficiently large gap
compared to its anticipated speed in the next time step. Because the gap in the same lane is
slightly less than what is required for the anticipated speed and the gap in the target lane is
slightly more, the vehicle may not always change lanes. The overall procedure adopted in
the CA model is shown in Figure 6.
TW
TW
CAR
CAR
CAR
CAR
CAR
(1)
(2)
(3)
(4)
(5)
Figure 5. Some of the possible lateral movements under heterogeneous traffic conditions.
330 Ch. Mallikarjuna and K.R. Rao
4. Data collection
Video image processing software, TRAZER, has been utilised in collecting the trajectory
data over a road length of 50 m. This software has the capability to classify the vehicles
and to capture the lateral movement of vehicles. A detailed methodology adopted in
TRAZER can be found in the work of Mallikarjuna et al. (2009). Various data collected
from the trajectory data are presented in the following sections.
4.1. Microscopic data from the trajectories
Acceleration/deceleration data corresponding to different vehicles has been extracted from
the trajectory data (Mallikarjuna et al. 2009). Acceleration data of the stationary vehicles
have been utilised in arriving at the appropriate values for the parameter p
0
corresponding
to various vehicle types. Lateral distribution of vehicles and the gaps maintained by
vehicles under different traffic conditions are the other key data extracted from the
trajectories. Lateral gaps are measured with respect to the closest side vehicles if more than
one vehicle is present on the sides. Longitudinal gaps are obtained for those vehicles which
can be seen in one frame of the video, i.e. if the front vehicle is not visible in the same
frame, no gap is calculated for the subject vehicle. Dependency of lateral gap maintaining
Allocating vehicles
based on composition
and global occupancy
Assigning vehicle
characteristics
Finding gaps in the
same sub-lane and on
adjacent sub-lanes
Updating vehicle’s
longitudinal position
Repositioning the
vehicles
with updated speeds
Extracting global
measurements
in cells and vehicles
Extracting local
measurements in cells
and vehicles
Updating vehicle’s
lateral position
Figure 6. Outline of CA model for simulating heterogeneous traffic.
Transportmetrica 331
behaviour on various traffic characteristics has been analysed. Various combinations of
macroscopic and microscopic variables are tested to know whether there exists any
consistent relationship among them. The relations obtained with different combinations
are presented in the following sections.
4.1.1. Lateral distribution of the vehicles
From the analysis of the data on lateral distribution of vehicles, it has been observed that
the traffic volume and composition are the important factors influencing the lateral
distribution of vehicles (Mallikarjuna 2007). A common feature observed was that the
three-lane road on which data was collected was being utilised as a two-lane road
irrespective of the traffic volume. When traffic volumes are relatively high, segregation of
TWs and light multirole vehicles (LMVs) has been observed. At low traffic volumes, this
kind of segregation has not been observed. Under free-flow conditions (relatively low
traffic volumes), road space utilisation is uniform, i.e. lateral distribution of vehicles is not
influenced by the type and the size of the vehicle.
4.1.2. Lateral gaps
Corrected trajectories and vehicle dimensions (length and width) are the inputs in
extracting the lateral gap data. Influence of flow, speed, occupancy, area occupancy and
fraction of major vehicle type present in the traffic stream on the gap maintaining
behaviour has been analysed. LMV–LMV, LMV–Auto, LMV–TW and TW–TW are the
vehicle combinations that are utilised for this purpose. Influence of flow, fraction of
LMVs, occupancy, speed and area occupancy, on the lateral gap maintaining behaviour of
LMV–LMV vehicle combination is presented in Figure 7. Average lateral gap for this
vehicle combination decreases with increasing flow, occupancy and area occupancy. The
gap increases with increasing speed and fraction of LMVs present in the traffic stream.
Among the macroscopic characteristics, area occupancy has been found to be consistently
correlated with the lateral gap maintaining behaviour for different vehicle combinations
(Table 1).
Area occupancy showing negative correlation with the average lateral gap consistently
for all the vehicle combinations is as shown in Table 1. The area occupancy values
obtained in this study falls in the range 2–6.5%. Corresponding to these area occupancy
values there is no significant variation in the gaps maintained by vehicles. The effective
vehicle widths resulting from this data have been used in deciding the cell widths presented
in Tables 2 and 3. The following linear relationships are formulated from the observed
data for lateral gap and area occupancy.
Average lateral gap for LMV–LMV, (m) ¼0.013 area occupancy þ1.58,
Average lateral gap for LMV–three-wheeler, (m) ¼0.039 area occupancy þ1.44,
Average lateral gap for LMV–TW, (m) ¼0.025 area occupancy þ1.63,
Average lateral gap for TW–TW, (m) ¼0.059 area occupancy þ1.74.
These equations are useful in dynamically updating the gaps maintained by various
vehicles under different traffic conditions. The variation in the gap maintaining behaviour
has significant influence on the cell structure to be used when modelling various traffic
conditions.
332 Ch. Mallikarjuna and K.R. Rao
4.1.3. Longitudinal gaps
Difference in centrelines of vehicles following one another is found to be influencing the
longitudinal gaps when staggered following is observed in the traffic. When vehicles are
following one another and lateral difference in the centrelines is high, the following vehicle
tends to follow the leading vehicle more closely (Mallikarjuna 2007). Under similar traffic
conditions when the lateral difference is less, following vehicles maintain more longitudinal
gap. Under heterogeneous traffic conditions if TWs are either leading or following the
other vehicles, staggered following is more visible. From the data it has been observed that
0.48 0.5 0.52 0.54 0.56
1
1.25
1.5
1.75
2
Fraction of LMVs
Avg. gap (m)
(b)
20 30 40 50
1
1.25
1.5
1.75
2
Occupancy (%)
Avg. gap (m)
(c)
3 4 5 6 7
1
1.25
1.5
1.75
2
Area occupancy (%)
Avg. gap (m)
(d)
44 45 46 47 48
1
1.25
1.5
1.75
2
S
p
eed (Km h–1)
Avg. gap (m)
(e)
2000 3000 4000 5000
1
1.25
1.5
1.75
2
Flow (Veh h–1)
Avg. gap (m)
(a)
Figure 7. Influence of various traffic characteristics on average lateral gap observed for LMV–LMV
vehicle combination.
Table 1. Correlation between average lateral gap and various traffic characteristics.
Flow Speed Fraction
a
Occupancy Area occupancy
LMV–LMV 0.30714 0.17011 0.592048 0.2487729 0.1547052
LMV–three-wheeler 0.238252 0.09482 0.41826 0.2214324 0.3309846
LMV–TW 0.45232 0.22723 0.47271 0.3635307 0.2973601
TW–TW 0.49643 0.18171 0.53751 0.5528511 0.4964641
Notes:
a
For LMV–LMV, LMV–three-wheeler combination, fraction denotes the fraction of LMVs
and in remaining two cases it is fraction of TWs.
TW, two-wheeler.
Transportmetrica 333
Table 2. Different parameters used in validating simulation model for urban traffic.
Vehicle
type Percentage
Length
(cells)
Width
(cells)
Mean, V
max
(cells s
1
)
SD of V
max
(cells s
1
)
Acceleration
(cells s
2
)
Deceleration
(cells s
2
)
Security
distance
(cells)
Interaction
headway (s) p
0
p
dec
p
lc
Car 52 12 2 40 4 4 3 2 4 21 6 0.5 0.3 1.5 0.5
TW 43 5 1 30 4 5 4 3 2 2 6 0.3 0.1 1.5 0.5
HMV 4 20 3 25 3 2 1 1 3 21 6 0.6 0.1 1.5 0.5
Auto 1 8 2 22 3 2 2 1 3 21 6 0.4 0.3 2 0.5
Note: TW, motorised two-wheeler; HMV, heavy motor vehicle; and auto, motorised three-wheeler.
334 Ch. Mallikarjuna and K.R. Rao
Table 3. Different parameters used in validating simulation model for rural traffic.
Vehicle
type Percentage
Length
(cells)
Width
(cells)
Mean,
V
max
(cells s
1
)
SD of
V
max
(cells s
1
)
Acceleration
(cells s
2
)
Deceleration
(cells s
2
)
Security
distance
(cells)
Interaction
headway
(s) p
0
p
dec
p
lc
Car 60 12 2 45 1 4 3 2 4 21 6 0.5 0.3 1.5 0.5
TW 23 5 1 30 2 5 4 3 2 2 6 0.3 0.1 1.5 0.5
Bus 5 25 2 25 3 3 2 1 3 21 6 0.6 0.1 2 0.5
Truck 5 20 2 25 3 2 1 1 3 21 6 0.6 0.1 1.5 0.5
LCV 5 16 2 20 2 2 2 1 3 21 6 0.45 0.1 2 0.5
Auto 2 8 2 22 3 2 2 1 3 21 6 0.4 0.3 2 0.5
Note: TW, motorised two-wheeler; LCV, light commercial vehicle; and auto, motorised three-wheeler.
Transportmetrica 335
with the increase in the difference between centrelines of the vehicles, longitudinal gap
maintained by the following vehicles decreases.
5. Calibration and validation of the CA model
5.1. Data collection in the CA model
In this study the macroscopic traffic variables, such as flow, speed and density are defined
differently to incorporate the heterogeneous nature of the traffic (Lan and Hsu 2006,
Mallikarjuna and Ramachandra Rao 2006). The basis for these modifications follows
conventional traffic measurements over a general measurement region (Figure 1). Since
lane discipline is absent under heterogeneous traffic conditions, measurements taken over
a single lane have no relevance under these conditions. To overcome these problems, each
cell (which is a part of the vehicle) is considered as one vehicle and each sub-lane is
considered as one lane while taking measurements over the general measurement region
(Figure 4). On account of the above assumptions, the cells (unit vehicle size) inevitably
follow the lane discipline. A measurement region of width W, length Land at time Tis
considered while taking the measurements. The traffic variables, such as flow, speed and
density are defined over this measurement region by
qðsÞ¼dðsÞ
jsj,ð7Þ
kðsÞ¼tðsÞ
jsj,ð8Þ
vðsÞ¼qðsÞ
kðsÞ¼dðsÞ
tðsÞ,ð9Þ
where d(s) and t(s) are the total distance travelled and the total time spent by all the cells
over the considered general measurement region, respectively, whereas |s| denotes the
volume of the general measurement region. The units for flow, density and speed are cells
per second, cells per unit cell length and cell length per second, respectively, for one cell
width of the road. Since the density represents the cell occupancy, it is expressed as the
percentage occupancy in this study. Multiplying these values with the number of lateral
divisions of the road, one gets the values for the total road width.
Measurements taken on a car that passes the measurement region is described here.
The size of the car is taken as 2 9 cells and it is assumed that the car is travelling with
constant speed of 2 m s
1
(4 cells s
1
) such that it takes 5 s to traverse a stretch of 10 m (20
cells) road length. It is also assumed that all the 18 cells (vehicle area) enter as well as leave
the measurement region within the stipulated measurement period. About 18 cells of the
cars in the region are considered as separate vehicles and the time taken by these 18 cells to
traverse the measurement region is 180 s and the distance traversed by these 18 cells is 360
cells. The volume of the measurement region is 10 s 20 cells 5 cells. If only one car
passes through the measurement region, from Equations (7) and (8), the flow value
becomes 0.36 cells per second per unit road width (cell width), whereas the density value
becomes 0.09 cells per unit road length (cell length) per unit road width (cell width).
336 Ch. Mallikarjuna and K.R. Rao
5.2. Calibration results
Main emphasis has been given to understand the heterogeneous traffic behaviour in the
free-flow regime. As discussed earlier, all the measurements are taken over a general
measurement region. A homogeneous traffic stream is simulated and the results are used to
validate the new CA structure and the new data collection methodology. The flow–
occupancy relationships obtained for different homogeneous vehicle groups over a two-
lane road are shown in Figure 8(a), and it can be seen that the results obtained conform to
the established results available in the literature. The slope of the free-flow branch is equal
to the free-flow velocity of the respective vehicle group. In this figure, the flow value
represents the number of cells per second per sub-lane that pass the considered road
section. Maximum flows achieved in the case of only cars and only buses are
3000 vehicles h
1
and 1800 vehicles h
1
, respectively.
In another simulation run, about 95% cars and 5% buses (89.1% car cells and 10.9%
bus cells) are simulated and the resulting maximum flow achieved over the two-lane road is
12 cells s
1
(Figure 8(b)). In absolute number of vehicles, the maximum flow consists of
111 buses and 2140 cars. To simulate the real heterogeneous traffic behaviour, different
types of vehicles are incorporated into the model and the resulting flow–occupancy
Figure 8. Flow–occupancy relationships from the CA model. (a) For cars and buses only (b) for
95% car and 5% buses.
Transportmetrica 337
relationship is shown in Figure 9. The simulated traffic stream consists of 50% cars, 5%
buses, 20% three-wheelers and 25% TWs. In this case also, the maximum flow equals 12
cells s
1
and under maximum flow conditions, about 1482 cars, 150 buses, 594 three-
wheelers and 1500 TWs are found to flow in a 1 h period.
5.3. Validation of the simulation model
Macroscopic data, such as flow, speed and occupancy measured at a road section
(equivalent to the detector of unit length in the simulation model) is available for two road
sections. In the case of urban traffic, data has been collected from Dabri road in Noida,
Delhi. Video data has been collected and processed using image processing software,
TRAZER. Macroscopic data utilised in the model validation has been obtained from the
trajectory data. In the case of rural traffic, data has been collected from National
Highway-1 (NH-1), connecting Delhi and Amritsar. In this case, video film has been
collected and macroscopic data has been obtained manually. Similar data has been
collected from the simulation model using a detector of unit cell length. Using these data
sets, validation of the simulation model for urban and rural traffic conditions is presented
in the following sections.
5.3.1. Urban traffic
From the data collected on Dabri road, it has been observed that the composition of
motorised TWs and cars is about 43% and 52%, respectively. Near this location, road is of
10 m wide. From the lateral distribution of vehicles, it has been observed that about 8 m
road width was being utilised by the vehicles. Reasons for this behaviour can be attributed
to the occasional slow vehicles (non-motorised TWs and three-wheelers) moving on curb
side of the road and discomfort to the drivers travelling near the curb. Since it is difficult to
consider all these in the simulation model, road width is taken as 8 m. Road stretch is
represented in the simulation model as shown in Figure 5 with a cell width of 1.6 m. This
cell width has been arrived at based on the actual vehicle width and the lateral gaps
maintained by the vehicles. Other important traffic characteristics and CA parameters
Figure 9. Flow–occupancy relationships for heterogeneous traffic.
338 Ch. Mallikarjuna and K.R. Rao
used in the simulation model are shown in Table 2. The values attached to the parameters
p
0
, and p
bl
are partly based on the field observations and partly based on intuition. The
value attached to p
dec
(stochastic deceleration) is completely based on intuition and on the
basis of the assumption that drivers of heavy vehicles may not decelerate unless there is an
interaction with the other vehicle. In the case of TWs, since they are small in size, they
always have freedom for the movement. Mean and standard deviations (SDs) of free-flow
speeds (or maximum speed) and acceleration behaviour observed in the field are also
presented in this table.
Flow, speed and occupancy obtained for each 1 min interval, collected over a period of
3 h has been utilised in validating the simulation model. Simulated and observed flow–
occupancy relationships are shown in Figure 10. From these relationships, it can be found
that the observed and the simulated data are fairly matching. From these relationships it
can also be said that, since observed data on gap maintaining behaviour is limited to
certain occupancy range the validity of this model is limited to only these occupancy
values. More data is needed to enhance the model’s capability to simulate various other
traffic conditions. Correlation coefficient between the observed and simulated flow is
0.742. This seemingly low correlation may be attributed to the grouping of buses, trucks
and light commercial vehicles (LCVs) under a single vehicle type called heavy motor
vehicles (HMVs) and other.
5.3.2. Rural traffic
An important characteristic of rural traffic is the composition of heavy vehicles, such as
trucks and LCV in the traffic stream. In this context, as discussed earlier data collected on
NH-1 has been utilised in validating the simulation model. Near the study location,
around 15% of heavy vehicles have been observed in the traffic stream. The road width in
this case is 7.5 m and in the simulation model it has been considered as 7.4 m. Further, the
road is divided into 4 sub-lanes. In this case, sub-lane width is slightly high (1.85 m)
compared to the sub-lane width used in the previous case (1.6 m). Higher cell width is
taken to replicate the gap maintaining behaviour of vehicles at higher speeds. From Tables
2 and 3, it can be seen that maximum speed of cars is relatively high in this case compared
0
1000
2000
3000
4000
5000
6000
7000
8000
0 1020304050607080
Occ upancy (%)
Flow (v ehic les /hour)
Observed
Simulated
Figure 10. Observed and simulated flow, occupancy relationships for urban traffic.
Transportmetrica 339
to urban traffic. Important traffic characteristics and CA parameters used in simulation
are shown in Table 3.
Flow, speed and occupancy obtained for each 1 min interval collected over a period of
1 h has been utilised in validating the simulation model. In this case, entire data has been
collected manually. Observed and simulated flow–occupancy relationships are shown in
Figure 11. Simulated data points for the occupancy levels that are not corresponding to
observed data points are also present in this figure. Range of occupancy values is still less
in this case compared to the urban traffic scenario. In this case, observed and simulated
flow values are correlated in a better way. Correlation coefficient between observed and
simulated flow values is 0.9 in this case.
5.4. Analysis of global measurements
When flows and densities are expressed in terms of vehicles, analysing their relationships
is difficult and the approach presented here overcame that difficulty. When each sub-
lane is considered as a lane and each cell is considered as a vehicle, it can be assumed
that cells are following lane discipline. This can be seen in Figure 5, where individual
cell of any vehicle adhere to lane discipline. In this scenario, heterogeneous traffic can
be considered as equivalent homogeneous traffic stream composed of cells of identical
size. Edie’s (1965) generalised definitions for flow, speed and occupancy have been
utilised in collecting the data. Macroscopic measurements made in terms of cells adhere
to the fundamental relationships among the macroscopic traffic variables (Figures 12
and 13). Since all vehicles are composed of cells and number of cells composing each
vehicle type is clearly known (assuming the gap related data is known), it is easy to
convert all the variables in terms of vehicles. This information has been utilised in
finding the capacities of rural and urban road sections in terms of cells. The analysis of
global measurements obtained for urban and rural traffic conditions is presented in the
following sections.
0
1000
2000
3000
4000
5000
6000
0 20406080100
Occupancy (%)
Flow (Vehicles/hour)
Simulated
Observed
Figure 11. Observed and simulated flow, occupancy relationships for rural traffic.
340 Ch. Mallikarjuna and K.R. Rao
5.4.1. Urban traffic
In this analysis, global flow is collected in terms of cells and global occupancy is the
percentage of cells filled with vehicles in the CA lattice. Flow–occupancy relationship
obtained from the simulation model is shown in Figure 12. It can be seen that a maximum
flow of 3.5 cells per sub-lane per second is observed at a global occupancy of 20%.
Converting flow values from cells per second per sub-lane to vehicles per hour is described
in Table 4. Total flow in cells per hour comes out to be 63,000 and for individual vehicle
types values are given in column 7 of Table 4. From this information and the
corresponding vehicle area in cells (column 5), it is possible to get flow value for each
vehicle type. When this flow is converted into vehicles per hour, it comes out to be 3861
and it consists of 2049 cars, 79 HMVs, 39 motorised three-wheelers and 1694 TWs. This
maximum flow of 3861 vehicles h
1
is far below the maximum flow observed in Figure 10,
which is also in terms of vehicles per hour. The main reason for this difference could be the
representation of flow–occupancy relationship in terms of absolute number of vehicles.
One other reason could be the data points corresponding to the maximum flow (in Figure
3) might be consisting of more small vehicles and less number of heavy vehicles.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Global occupancy
Flow (cells/sub-lane/s)
Figure 12. Simulated global flow and global occupancy relationship for urban traffic.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.05 0.1 0.15 0.2 0.25 0.3
Global occupancy (%)
Flow (cells/sublane/s)
Figure 13. Simulated global flow and global occupancy relationship for rural traffic.
Transportmetrica 341
This methodology of collecting flow data in cells is useful when flow is composed of
different vehicles, which is the case with heterogeneous traffic. It can be seen from Table 4
that vehicle composition, number of sub-lanes and vehicle area in cells are crucial in
converting the flow from cell per second per sub-lane to vehicles per hour. Number of sub-
lanes and vehicle area is dependent on the gap maintaining behaviour of vehicles under
different conditions. Hence, the data related to gap maintaining behaviour is crucial in
developing a realistic flow model.
5.4.2. Rural traffic
The methodology explained in the previous section holds for this case also. When global
measurements are taken the maximum flow comes out to be 3.5 cells sub-lane s
1
(Figure 13), which is the same in the case of urban traffic. But the corresponding
occupancy value is slightly higher (global occupancy 22.5%) compared to the urban
traffic. In this case, the maximum flow in terms of vehicles comes out to be
2295 vehicles h
1
. It is composed of 1376 cars, 528 TWs, 115 buses, 115 trucks, 115
LCVs and 46 autos. This maximum flow is true only for the traffic characteristics and CA
parameters given in Table 5. Though maximum flow in terms of cells is the same for both
urban and rural traffic, flow in absolute number of vehicles is different in these two cases.
This concept can also be used in converting the traffic stream into equivalent number of
passenger cars. When maximum flows are converted into equivalent passenger cars it
Table 5. Converting global flows obtained in cells per second per sub-lane to vehicles per hour, in
the case of rural traffic.
Vehicle
type
Percentage
of
vehicles
Length
(cells)
Width
(cells)
Vehicle
area
(cells)
Composition
(cells)
Percentage
of cells
Flow
(cells h
1
)
Flow
(vehicle h
1
)
Car 60 12 2 24 1440 65.5 33,034 1376
TW 23 5 1 5 115 5.2 2638 528
Bus 5 25 2 50 250 11.4 5735 115
Truck 5 20 2 40 200 9.1 4588 115
LCV 5 16 2 32 160 7.3 3670 115
Auto 2 8 2 16 32 1.5 734 46
Table 4. Converting global flows obtained in cells per second per sub-lane to vehicles per hour, in
the case of urban traffic.
Vehicle
type
Percentage
of vehicles
Length
(cells)
Width
(cells)
Vehicle
area
(cells)
Composition
(cells)
Percentage
of cells
Flow
(cells h
1
)
Flow
(vehicle h
1
)
Car 52 12 2 24 1248 78.0 49,171 2049
TW 43 5 1 5 215 13.4 8471 1694
Truck 2 20 3 60 120 7.5 4728 79
Auto 1 8 2 16 16 1.0 630 39
342 Ch. Mallikarjuna and K.R. Rao
comes out to be 2625 passenger cars per hour in the case of urban traffic and 2100
passenger cars per hour in the case of rural traffic. These values are reasonable given the
low free-flow speeds and the geometric conditions observed on these road sections.
6. Summary and conclusions
This study is aimed at understanding and modelling the heterogeneous traffic behaviour
on mid-block sections of urban and rural roads. A systematic methodology was followed
in developing the traffic flow model starting from finding the useful traffic variables which
can describe the heterogeneous traffic behaviour. Several microscopic variables, such as
lateral and longitudinal gaps are analysed to know their usefulness in developing a
CA-based traffic flow model. This basic CA model has been modified in such a way that it
accommodates the observed heterogeneous traffic features. Emphasis was put on data
collection under heterogeneous traffic conditions which is important in developing and
validating the model. An image processing-based data collection system, specifically
developed for data collection under heterogeneous traffic conditions, has been utilised in
collecting important microscopic and macroscopic traffic data. Interdependency between
lateral gap maintaining behaviour and various macroscopic characteristics have been
tested. A simulation model has been developed based on the modified CA concept and the
field observations. This model has been validated for both rural and urban traffic at
macroscopic level. Important conclusions drawn out of this study are categorised into four
sections and are presented below;
6.1. Traffic characteristics
(1) It is found that vehicle size, its mechanical characteristics and lateral and
longitudinal gap data are more useful microscopic characteristics to describe the
heterogeneous traffic. These variables are found to be crucial in developing the cell
structure of the CA-based traffic flow models.
(2) Area occupancy, a variant of occupancy and function of vehicle area, is found to
be useful in explaining the lateral gap maintaining behaviour of vehicles under
varying traffic conditions. This variable would be useful in varying the cell
structure of the CA model depending on the traffic conditions.
6.2. CA model
(1) Basic structure of the CA model has been arrived at based on road geometry and
microscopic traffic characteristics, such as vehicle size, lateral gap and acceleration/
deceleration behaviour.
(2) Modified Knospe’s BL model is found to be suitable in updating the
vehicles in longitudinal direction. In concurrence with the modified CA cell
structure, a suitable lateral movement procedure has been developed for
heterogeneous traffic.
Transportmetrica 343
6.3. Data collection
(1) An effective and customised image processing-based data collection methodology
has been utilised for data collection under heterogeneous traffic conditions.
(2) Since traffic moving on certain road area can be studied using this technique,
obtaining actual lateral and longitudinal spacing data is relatively easy and more
accurate compared to the manual data collection method.
(3) This technique is also useful in collecting occupancy and area occupancy data at a
given road section which is difficult otherwise.
6.4. Calibration and validation of the model
(1) A simulation model has been developed based on the modified CA methodology.
From the extensive sensitivity analyses carried out on the model parameters, it was
found that vehicle specific parameters, such as length, width, gaps maintained and
acceleration/deceleration behaviour are crucial in modelling the heterogeneous
traffic.
(2) The new CA model for heterogeneous traffic has been validated on rural and urban
traffic using macroscopic observable traffic characteristics. In both the cases,
simulation model could regenerate the observed flow–occupancy relationships.
(3) Obtaining traffic measurements in common units called cells is found to be a useful
alternative in analysing the heterogeneous traffic.
(4) From the comparison of Figures 10 and 12, it is evident that the flow–occupancy
relationships are more meaningful when the measurements are made in terms of
cells as they adhere to the established traffic flow theory.
(5) The maximum flow observed in the flow–occupancy relation, expressed in terms of
vehicles per hour (in Figures 10 and 11), may not be the true maximum flow
corresponding to the given traffic composition.
(6) For a given composition of the traffic, maximum flows observed in Figures 12
and 13 seem to be reasonable and the same is evident from the equivalent
maximum flows in terms of passenger cars. The maximum flows in terms of cars
are coming out to be 2625 and 2100 passenger cars per hour.
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Transportmetrica 345
