TRB-09-1738

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DEVELOPING AND VALIDATING A SIMULATION MODEL FOR

HETEROGENEOUS TRAFFIC

Authors

Mallikarjuna C.

Assistant Professor

Civil Engineering Department

Indian Institute of Technology Guwahati

Guwahati 781039

Email: [email protected]

and

Ramachandra Rao K.

Assistant Professor

Civil Engineering Department

Indian Institute of Technology Delhi

New Delhi 110016

Email: [email protected]

Total length of the paper 7638 words, including 8 Figures and 4 Tables

Dr. Mallikarjuna C. is the corresponding author.

TRB 2009 Annual Meeting CD-ROM Paper revised from original submittal.
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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Mallikarjuna and Ramachandra Rao 1

ABSTRACT

This paper presents an approach used in developing and validating a cellular automaton basedsimulation model for studying the heterogeneous traffic. As a part of the model development,

longitudinal and lateral updating procedures for the vehicular movement have been discussed in

detail. Vehicle movement patterns on mid-block sections are studied and utilized this

information as input for developing the vehicle updating procedures. This model is validated atmacroscopic level for both urban and rural heterogeneous traffic conditions. The methodology

adopted for collecting the macroscopic data from the simulation model uses cell as a unit ofthe vehicle. Using flow-occupancy relationships in terms of cells, utility of this methodology in

analyzing the heterogeneous traffic is also presented. Traffic observed on urban and rural mid-

block road sections has been studied using this model.


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INTRODUCTIONTraffic composed of identical vehicles and following lane discipline is termed as homogeneous

traffic. Traffic with the presence of motorized and non-motorized two-wheelers 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 and hasalso been termed as heterogeneous traffic. Undivided two-lane two-way roads, divided two-lane

two-way roads, and divided four-lane two-way roads, are predominantly present in both ruraland urban areas of India. Modeling undivided two-way roads with non-motorized traffic requires

extensive data for understanding the numerous interactions between traffic elements. Some

major roads in urban areas and some rural highways are exceptions to this where non-motorized

traffic is minimum or close to zero.Many attempts were made in 80s (1, 2) to develop a modeling approach for

heterogeneous traffic observed on rural and urban roads. Palaniswamy et al (3) developed a

discrete-event-based simulation model based on Swedish Road Traffic Simulation model(SWERTS) with modifications to include heterogeneous traffic. Likewise, Kumar (4) developed

a simulation model for highway traffic which was continuous in space but discrete in time. Singh(5) developed a simulation model for heterogeneous urban traffic which was discrete in bothtime as well as space. Similarly, Oketch (6) introduced a modeling approach suitable for a

heterogeneous traffic stream with non-standard vehicles. Using this model, Oketch (7) later

suggested theoretical performance characteristics for heterogeneous traffic and observed that thetraffic stream behavior in heterogeneous flow might not be consistent with the fundamental

relationships on which the macroscopic analysis is based on. Arasan and Koshy (8) proposed a

methodology to model a highly heterogeneous traffic stream wherein the entire road was

considered as a single unit and the vehicles were assigned some coordinates.Furthermore, implementing the Cellular Automata (CA) based models for the

heterogeneous traffic has been suggested by some researchers (9, 10). Lan and Chang (10)

modeled heterogeneous traffic comprising of cars and motorized two-wheelers with the help of arefined CA structure wherein the basic CA updating rules were applied to simulate the

heterogeneous traffic. Modified CA structure used in the above models further helped in

obtaining slightly modified traffic variables that were suitable for heterogeneous traffic (11, 12).From the literature it can be observed that developing microscopic models for heterogeneous

traffic requires huge data and a thorough understanding of the vehicular movements. Both lateral

and longitudinal movements of vehicles have to be studied in detail. CA based models have

been tried for modeling heterogeneous traffic streams and found to be performing well. Limiteddata requirement in developing the models and the data extractability from the model are the

advantages in using CA based models.

In this paper a simulation model is developed and validated for unidirectional trafficstreams observed on rural and urban roads. Modified cellular automata model has been utilized

to develop the simulation model. Lateral and longitudinal movement procedures have been

presented for heterogeneous traffic conditions. This model has been validated at macroscopiclevel for both urban and rural traffic conditions. An alternate approach is proposed to analyze

macroscopic flow-density relationships observed under heterogeneous traffic conditions.


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MODELING METHODOLOGY

Heterogeneous traffic consists of several vehicle types and the absence of lane discipline makesit difficult to model. Poor lane discipline is the major concern when collecting the traffic data as

well as in developing vehicle movement procedures. Presence of vehicles with different physical

and mechanical characteristics makes it necessary to alter available longitudinal updating

procedures. This characteristic of heterogeneous traffic is necessitating the study of lateralmovements in addition to longitudinal movements. From the data collected it has been observed

that vehicle type is significantly influencing the space headways maintained by the followingvehicles. Besides this, scattering of vehicles while following one another is also significantly

influencing the space headways. This data is crucial in developing the longitudinal updating

procedures. Unlike the homogeneous traffic in heterogeneous traffic, analysis of lateral gap

maintaining behavior of vehicles is crucial. This information is important in deciding theeffective vehicle width occupied by vehicles. Effective width of a vehicle is the summation of

actual width and the gaps maintained on both sides. This effective width is the basis in deciding

the cell width that is to be used in the CA model. In the following subsections longitudinal andlateral updating procedures adopted in this study are discussed.

Longitudinal Updating ProcedureKnospe et al. (13) proposed Brake Light model to implement a dynamic interaction of the

vehicles, in various traffic states. Longitudinal updating procedure in the present study is adopted

from knospe et al. (13) with the modifications discussed in this section. In the original BL modelcell length is considered as 1.5 m. This cell length is considered to accommodate the observed

acceleration values of about 1 m/sec2 (13). In the present study cell length is taken as 0.5 m

keeping in view the vehicle characteristics observed in heterogeneous traffic. Effect of the

reduced cell length on various model parameters has been analyzed through parametric studies(14).

When following vehicles are having time headways that are greater than the perceived

safe time headways, their movement is not depending on the leading vehicles speed. Underthese conditions, following vehicles always try to achieve their maximum speed, only limited by

their acceleration capabilities. At intermediate headways, drivers react to the speed changes of

the leading vehicle or in a way to the brake lights of the leading vehicle. When vehicles arehaving headways less than the perceived safe headways, and if the leading vehicles break lights

are on, vehicles try to adjust their speeds depending on the leading vehicles speed. At small

headways, the drivers adjust their speed such that safe driving is possible. The acceleration is

delayed for standing vehicles and directly after braking events. In this step, in addition to theslow-to-start (p0) and slow down (pdec) probabilities, one more parameter called break light

probability (pbl) is used. When the vehicles break light is on and if its headway is falling within

the safe headway then with certainty (pbl is close to 1) the vehicle will have certain delay inacceleration.

Updating procedure used in the present model, represented mathematically is given below;

0 Determination of the randomization parameter:

p = p(vn(t), bn+1(t), tnh, t

s) =pbl ifbn+1(t) = 1 and tn

h< t

s

=p0 ifvn(t) = 0


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=pdec in all other cases

1. Acceleration:

If(bn+1(t) =0) and (bn(t)=0) or (tnh

>=ts) then:

vn(t+1/3) = min(vn(t) + an(vn,ln), vmax)

tnh=(gn(t)+maximum(0,vn+1,anticipated(t)-Security distance))/vn(t)

2. braking rule:

vn(t+2/3) = min(vn(t+ 1/3), gneff

)

if (vn(t+2/3) < vn(t)) then:

bn(t+1) = 1

3. Randomization, brake:

If(rand()

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TW

TW

CAR

CAR

CAR

CAR

CAR(1)

(2)

(3)

(4)

(5)

Figure 1 Some of the possible lateral movements under heterogeneous traffic conditions

Lateral Updating ProcedureWhen vehicles are following lane discipline like in homogeneous traffic, lane changes areclassified 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. It is assumed that vehicles under these conditions adjust their lateral positions in a

way that optimizes the usage of the road space. In this study emphasis is given on how thevehicle moves laterally under different traffic conditions. Lateral movements carried out by car

and two-wheeler with the modified CA structure is shown in Figure 1. Each lateral division of

the road is called as a sub-lane. With the given CA structure different types of lateral movementsare possible and some of the possible lateral movements are shown in Figure 1. 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 on the corresponding sub-lanes. Any vehicle mayperform lane changing maneuver based on two criteria namely incentive criterion and safety

criterion. Normally vehicle changes lanes if the gap available in the front is less than its

anticipated velocity in the next time step. This suggests the intention of the vehicle to shift lanes.At the same time, other lane must be more attractive and safe. The target lane is more attractive

if the gap available in front 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 oflane 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

0. (vn + an (vn, ln)) > gn1. (vn + an (vn, ln)) > vn+1

Safety criteria

2. gn,,o,f> * vn3. gn,,o,b > vmax of the corresponding back vehicle +

Where, anis the acceleration of the vehicle which is a function of speed; is the non-zeroparameter, value of which is greater than one; gn is the gap in the front on the same lane; gn,o,f is


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the gap in the front on the other or target lane; gn,o,b is the gap in the back on the other or target

lane.

Figure 2 Outline of CA model for simulating heterogeneous traffic

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 vehicles

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 sufficiently large gap compared to itsanticipated speed in the next time step. Because the gap in the same lane is slightly less than the

anticipated speed and the gap in the target lane is slightly more than the anticipated speed, the

vehicle may not change lanes.

SIMULATION MODEL

Outline of the simulation model developed in the present study is shown in Figure 2. Some of theimportant parameters of the simulation model are run time, length of the road stretch, boundary

conditions used etc. Flow-occupancy relationship has been utilized in studying the influence of

each of these parameters. No significant difference is found in the output with the change insimulation runtime. Effect of lattice length has also been studied and found no significant

Allocating vehicles

based on compositionand global occupancy

Assigning vehicle

characteristics

Finding gaps in thesame sub-lane and on

adjacent sub-lanes

Updating vehicles

longitudinal position

Repositioning the

vehicleswith updated speeds

Extracting global

measurements

in cells and vehicles

Extracting local

measurements in cells

and vehicles

Updating vehicles

lateral position


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difference in the result obtained for 1 km and 3 km lattice lengths. Since periodic boundary

conditions are used in the present CA model, it is easy to simulate different traffic scenarios suchas free flow and congested flow by controlling occupancy. Different methodologies such as local

measurements, global measurements are used to extract data from the CA model. Local

measurements are taken from the simulation model to compare with the observed data. Under the

same conditions, global measurements are also obtained in terms of number of cells. This datahas been collected considering each cell as a vehicle and Edies generalized measurement region

(15).

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 case ofurban traffic, data has been collected from Dabri road in Noida, Delhi. Video data has been

collected and processed using image processing software called TRAZER. Macroscopic data

utilized in the model validation has been obtained from the trajectory data. In case of ruraltraffic, 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 obtainedmanually. Similar data has been collected from the simulation model using a detector of unit celllength. Using these data sets, validation of the simulation model for urban and rural traffic

conditions is presented in the following subsections.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 10 20 30 40 50 60 70 80

Occupancy (%)

Flow

(Vehicles/Hr)

Observed

Simulated

Figure 3 Observed and simulated Flow, Occupancy relationship for urban traffic


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0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80

Occupancy (%)

Speed(Km

/Hr)

Observed

simulated

Figure 4 Observed and simulated relationship between speed and occupancy for urban traffic

Urban TrafficFrom the data collected on Dabri road it has been observed that the composition of motorized

two-wheelers (TW) 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 widthwas being utilized by the vehicles. Reasons for this behavior can be attributed to the occasional

slow vehicles (non-motorized two wheelers and three wheelers) moving on Curb side of the road

and discomfort to the drivers traveling near 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 modelas shown in Figure 1 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 used in the simulation model are presented in Table 1. Meanand standard deviations of free flow speeds (or maximum speed) observed in the field are also

presented in this table.

Flow, speed, and occupancy obtained for each one minute interval, collected over aperiod of three hours has been utilized in validating the simulation model. Simulated and

observed flow-occupancy relationships are shown in Figure 3. Similarly, observed and simulated

speed-occupancy relationships are shown in Figure 4. From these relationships it can be found

that observed and simulated data is fairly matching. From these relationships it can also be saidthat, observed data is limited to certain occupancy range and validity of this model is limited to

these occupancy values. More data is needed to enhance the models capability to simulate

various observed traffic conditions and it depends on the availability of suitable equipment tocollect the data under heterogeneous traffic conditions. This is also true since gaps maintained by

different vehicles with respect to side vehicles are only valid for certain range of occupancy

values. Correlation coefficient between observed and simulated flow is 0.742. This seeminglylow correlation may be attributed to the grouping of buses, trucks and light commercial vehicles

under a single vehicle type called heavy motor vehicles.


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Rural Traffic

Important characteristic of rural traffic is the composition of heavy vehicles such as trucks and

light commercial vehicles (LCV) in the traffic stream. In this context, as discussed earlier datacollected on NH-1 has been utilized in validating the simulation model. Near the study location

around 15% of heavy vehicles have been observed in the traffic stream. Road width in this case

is 7.5 m and in the simulation model it has been considered as 7.4 m. Further, road is dividedinto 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 behavior of vehicles at higher speeds. From Tables 1 and 2, it can be seen thatmaximum speed of cars is relatively high in this case compared to urban traffic. Important traffic

characteristics and CA parameters used in simulation are shown in Table 2.

Flow, speed, and occupancy obtained for each one minute interval collected over a periodof one hour has been utilized in validating the simulation model. In this case, entire data has been

collected manually. Observed and simulated flow-occupancy and speed-occupancy relationshipsare shown in Figures 5 and 6 respectively. Simulated data points for the occupancy levels thatare not corresponding to observed data points are also present in these Figures. 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.

0

1000

2000

3000

4000

5000

6000

0 20 40 60 80 100

Occupancy (%)

Flow

(Veh/Hr)

Simulated

Observed

Figure 5 Observed and simulated flow, occupancy relationship for rural traffic


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Mallikarjuna and Ramachandra Rao

Table 1 Different parameters used in validating simulation model for urban traffic

Vehicle

type %

Length

(cells)

Width

(cells)

MeanVmax(cells/sec)

Standard

deviationof Vmax(cells/sec)

Acceleration

(cells/sec2)

Deceleration

(cells/sec2)

Securitydistance

(cells)

Interactheadwa

(sec)

Car 52 12 2 40 4 4 3 2 4 21

TW 43 5 1 30 4 5 4 3 2 2

HMV 4 20 3 25 3 2 1 1 3 21

Auto 1 8 2 22 3 2 2 1 3 21

TW Motorized two-wheeler, HMV Heavy Motor Vehicle, Auto Motorized Three-wheeler

Table 2 Different parameters used in validating simulation model for rural traffic

Vehicle

type %

Length

(cells)

Width

(cells)

Mean

Vmax(cells/sec)

Standard

deviation

of Vmax(cells/sec)

Acceleration

(cells/sec2)

Deceleration

(cells/sec2)

Security

distance

(cells)

Interact

headwa

(sec)

Car 60 12 2 45 1 4 3 2 4 21

TW 23 5 1 30 2 5 4 3 2 2

Bus 5 25 2 25 3 3 2 1 3 21

Truck 5 20 2 25 3 2 1 1 3 21

LCV 5 16 2 20 2 2 2 1 3 21

Auto 2 8 2 22 3 2 2 1 3 21

TW Motorized two-wheeler, LCV Light Commercial Vehicle, Auto Motorized Three-wheeler

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0

10

20

30

40

50

60

70

80

0 20 40 60 80 100

Occupancy (%)

Speed(Km/Hr)

Simulated

Observed

Figure 6 Observed and simulated speed, occupancy relationship for rural traffic

ANALYSIS OF GLOBAL MEASUREMENTSFrom the simulation model it is possible to collect data over the entire CA lattice and

these are called global measurements (16). When each sub lane is considered as a laneand each cell is considered as a vehicle, it can be assumed that cells are following lane

discipline. In this scenario, heterogeneous traffic is converted into equivalent

homogeneous traffic where traffic is composed of cells of identical size. Ediesgeneralized definitions for flow, speed and occupancy have been utilized in collecting the

data. Macroscopic measurements made in terms of cells, adhere to the fundamentalrelationships among the macroscopic traffic variables. Since all vehicles are composed ofcells and number of cells composing each vehicle type is clearly known, it is easy to

convert all the variables in terms of vehicles. This information has been utilized in

finding the capacities of rural and urban road sections in terms of cells. Analysis of global

measurements obtained for urban and rural traffic conditions is presented in the followingsubsections.

Urban TrafficIn this analysis global flow is collected in terms of cells and global occupancy is the

percentage of cells in the CA lattice filled with vehicles. Flow-occupancy relationship

obtained from the simulation model is shown in Figure 7. It can be observed that amaximum flow of 3.5 cells/sub-lane/sec is observed at a global occupancy of 20%.

Converting flow values from cells/sec/sub-lane to vehicles/hr is described in Table 3.

Total flow in cells/hr is comes out to be 63,000 and for individual vehicle types valuesare given in column 7 of this table. 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/hr, it comes out to be 3,861 and it consists of 2,049 cars,

79 heavy motor vehicles, 39 motorized three-wheelers and 1,694 TWs. This maximum


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flow of 3,861 vehicles/hr is far below than the maximum flow observed in Figure 3

which is also in terms of vehicles/hr. Main reason for this difference could be therepresentation of flow-occupancy relationship in terms of absolute number of vehicles.

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 3 that vehicle composition, number of sub-lanes, and vehicle area incells are crucial in converting the flow from cell/sec/sub-lane to vehicles/hr. Number of

sub-lanes and vehicle area is dependent on the gap maintaining behavior of vehiclesunder different conditions. Hence the data related to gap maintaining behavior is crucial

in developing a realistic flow model.

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/sec)

Figure 7 Simulated global flow and global occupancy relationship for urban traffic

Table 3 Converting global flows obtained in cells/sec/sub-lane to vehicles/hr, in case of urban traffic

Vehicle

type

%

vehicles

Length

(cells)

Width

(cells)

Vehicle

Area

(cells)

Composition

(cells)

%

cells

Flow

(cells/hr)

Flow

(Veh/Hr)

Car 52 12 2 24 1248 78.0 49171 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

Rural Traffic

The methodology explained in the previous subsection holds for this case also. Whenglobal measurements are taken the maximum flow comes out to be 3.5cells/sub-lane/sec

(Figure 8) which is the same in case of urban traffic. But the corresponding occupancy

value is slightly higher (global occupancy 22.5%) compared to the urban traffic. In thiscase the maximum flow in terms of vehicles is comes out to be 2295 vehicles/hr. It is

composed of 1,376 cars, 528 TWs, 115 buses, 115 trucks, 115 LCVs and 46 autos. This


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maximum flow is true only for the traffic characteristics and CA parameters given in

Table 2. Though maximum flow in terms of cells is 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 comes out to be 2625

passenger cars/hr in case of urban traffic and 2,100 passenger cars/hr in case of ruraltraffic.

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/sec)

Figure 8 Simulated global flow and global occupancy relationship for rural traffic

Table 4 Converting global flows obtained in cells/sec/sub-lane to vehicles/hr, in case of rural traffic

Vehicle

type

%

Vehicles

Length

(cells)

Width

(cells)

VehicleArea

(cells)

Composition

(cells)

%

cells

Flow

(cells/Hr)

Flow

(Veh/Hr)

Car 60 12 2 24 1440 65.5 33034 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 115Auto 2 8 2 16 32 1.5 734 46


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CONCLUSIONS

In this paper, the methodology adopted in developing and calibrating a simulation modelis presented. Longitudinal and lateral updating procedures used for heterogeneous traffic

conditions are discussed. Modifications made to the cellular automata model structure are

discussed. Validation of the model is carried out for both urban and rural traffic

scenarios. It is found that in the both the cases, observed and simulated relationshipsbetween macroscopic traffic variables are matching closely with each other. Utilization of

global measurements made in terms of cells in analyzing the heterogeneous traffic flowsis explained in detail. These measurements are useful in finding the capacities of different

road sections under heterogeneous traffic conditions. It is found that capacities are

function of traffic composition and the amount of road space a vehicle occupies under

different traffic conditions including the gaps maintained it on both sides.

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