evaluating the time headway distributions in congested ... · evaluating the time headway...

Evaluating the Time Headway Distributions in

Congested Highways

Sara Moridpour School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, 3001, Australia

Email: [email protected]

Abstract—Time headway is a significant traffic flow

parameter that affects the capacity and safety of highways

and freeways. Time headways are broadly used in different

areas of traffic and transport engineering such as capacity

analysis, safety studies, car following and lane changing

behavior modeling, and level of service evaluation. In this

paper, the time headway distribution is investigated for an

urban highway at different traffic flow rates during

congestion. To analyze the headway characteristics, the time

headways to the preceding and following vehicles are

analyzed for heavy vehicles and passenger cars. The

trajectory data used in this study was provided for a highway

section in California: Berkeley Highway, I-80. Appropriate

models of headway distribution are selected for heavy vehicles

and passenger cars using Chi-Square test. Using the selected

models, headway distributions are predicted for each vehicle

type at different traffic flow rates. The results confirm

existence of different time headway distributions in vicinity of

heavy vehicles and passenger cars which is due to the

difference in the behavior of drivers in vicinity of heavy

vehicles and passenger cars under congestion.

Index Terms—headway distribution, highways, heavy

vehicles, passenger cars

I. INTRODUCTION

Time headway or headway is defined as the time

between two consecutive vehicles (in seconds) when they

pass a single point on a roadway [1]. Headway is measured

as the time between the same common features of two

consecutive vehicles (e.g. front bumper). Time headway is

one of the important microscopic traffic flow parameters

which is extensively applied in planning, analysis, design

and operation of roadway systems [2]-[7]. Therefore, it is

essential to accurately evaluate this parameter based on

real behavior of drivers [8]-[10]. Understanding drivers’

behavior in selecting their desired headway is important in

order to have better traffic planning and policy making in

different traffic conditions. This is due to the fact that time

headways and their distributions would influence different

traffic flow parameters such as capacity, level of service

and safety [11], [5]. Precise modeling and analysis of

vehicle headway distributions is required to maximize

roadway capacity and minimize the delays that vehicles

experience [12], [5]. Furthermore, headway analysis is

used in understanding the reasons of accidents as well as

evaluating policies to enhance road safety. In general,

Manuscript received January 5, 2014; revised April 9, 2014.

existing studies mainly ignore the safe headway

requirements in capacity analysis and safety studies. This

may cause inaccurate estimation of traffic flow

characteristics specifically on roadways with traffic flows

less than the perceived capacity [13].

II. LITERATURE REVIEW

Many factors influence the headway distribution of

vehicles including traffic volume, proportion of heavy

vehicles, lane position, road structure, time of the day and

weather condition [14]. Mei and Bullen [15] investigated

different statistical distributions for time headways

measured on a four-lane highway during the morning

peak traffic. According to their results, lognormal

distribution with a shift of 0.3 or 0.4 seconds was the best

fit for the time headways in high traffic volumes.

Sadeghhosseini [16] analyzed time headways at flow

rates varying from 140 to 1704 vehicles per hour per lane

on interstate highways of Illinois, U.S. In his study, using

a lognormal distribution with a shift of 0.36 seconds was

recommended to generate the time headways. In another

study by Arasan in 2003, the headway distribution was

investigated for a four-lane divided urban arterial in

Chennai City in India [11]. In this study, negative

exponential distribution was found to be suitable for

modeling headways at different lanes and over the entire

range of traffic flows. In 2006, Bham and Ancha

analyzed the time headway of drivers in a basic freeway

section as well as a ramp merge, a lane drop and a ramp

weaving section [17]. According to their study, shifted

lognormal distribution provided an accurate fit for all

studied areas. Zwahlen et al. [18] evaluated the

cumulative headway distributions at different traffic

flows and traffic lanes in Ohio freeways in the U.S. Their

results showed that the headway distributions at different

lanes are almost the same for similar hourly traffic flows.

Previous studies are mainly based on the entire time

headway data collected from a highway/freeway section

regardless of considering the vehicle types. Furthermore,

previous studies were mainly undertaken under light to

medium traffic flow conditions. In this paper, headway

distributions are analyzed and compared for heavy vehicles

and passenger cars under heavy traffic conditions. To

evaluate the headway characteristic, the time headways to

the preceding (front) and following (rear) vehicles are

separately evaluated for each vehicle type. To better analyze

the headway distribution in the vicinity of heavy vehicles

Journal of Traffic and Logistics Engineering Vol. 2, No. 3, September 2014

©2014 Engineering and Technology Publishing 224doi: 10.12720/jtle.2.3.224-229

mailto:[email protected]

and passenger cars, the headways are evaluated at different

traffic flows. Then, simple mathematical models are

suggested to estimate the parameters of the front and rear

headway distributions at different traffic flow rates. This

paper is structured as follows. The following section

explains the dataset used in this study. The methodology as

well as the appropriate models of headway distributions

which are selected for each vehicle type (heavy vehicles and

passenger cars) is explained after. The relationship between

the parameters of the front and rear headway distributions

for heavy vehicles/passenger cars and traffic flows is also

analyzed. The final section summarizes the results of this

paper and provides directions for future research.

III. DATASET

Trajectory data used in this study was provided for a

highway section in California: Berkeley Highway (I-80).

The schematic illustration of this highway section is shown

in Fig. 1. The section of I-80 is 503 meters long and

comprises five main lanes with one auxiliary lane. There is

one on-ramp in this section and one exit off-ramp

downstream of the section [19]. There are no lane

restrictions for heavy vehicles in this section. The data

were collected from 4:00 to 4:15 PM and 5:00 to 5:30 PM

using a video capture rate of 10 frames per second. The

data was collected using seven video cameras mounted on

a 30-story building. The dataset was provided in clear

weather, good visibility, and dry pavement conditions. The

dataset has classified vehicles as automobiles, heavy

vehicles and motorcycles. Table I shows the traffic flow

parameters for the section of I-80. For the time period that

the data was collected, the proportion of heavy vehicles is

4.7%, 3.8% and 2.7% of the total traffic at 4:00 to 4:15 PM,

5:00 to 5:15 PM and 5:15 to 5:30 PM, respectively.

Figure 1. Schematic illustration of lane configuration for section of I-80.

The trajectory dataset used in this study makes it

possible to determine the time and space headways

between the heavy vehicles or passenger cars and their

surrounding vehicles at discrete time points. The vehicles

(front and rear vehicles) which are considered for

headway distribution analysis are presented in Fig. 2. In

this figure, the subject vehicle can be either a heavy

vehicle or a passenger car. In this study, the headways are

measured as the time between the front bumper of the

subject vehicle (heavy vehicle or passenger car) and the

front bumper of the front/rear vehicles which are called

front/rear time headways. Due to the noise in the NGSIM

dataset, the dataset was aggregated at each 0.5 second

time interval. Then, the aggregated trajectory data at each

0.5 second time interval (2 observations per second) was

used in this study.

Rear Vehicle Subject Vehicle Front vehicle

Figure 2. The subject vehicle and the preceding and following vehicles.

To analyze the time headway in the vicinity of each

vehicle type, a sample size of 50 heavy vehicles and 50

passenger cars were randomly selected. The main

statistical characteristics of time headways for the selected

heavy vehicles and passenger cars are presented in Table II.

TABLE I. TRAFFIC FLOW PARAMETERS IN THE SECTION OF I-80.

Time Interval Traffic Flow

(veh/hr)

Speed

(km/hr)

Density

(veh/km)*

Level Of

Service (LOS)

4:00 to 4:05 PM 8436 32.3 261 E

4:05 to 4:10 PM 7968 28.7 278 E

4:10 to 4:15 PM 8028 25.2 319 E

5:00 to 5:05 PM 8124 27.5 295 E

5:05 to 5:10 PM 7752 23.2 334 E

5:10 to 5:15 PM 5988 15.1 397 E

5:15 to 5:20 PM 7836 21.9 358 E

5:20 to 5:25 PM 7284 21.2 344 E

5:25 to 5:30 PM 6024 15.9 279 E

Total 7493 23.1 324 E

* Density is calculated as the number of vehicles per kilometer length of

all lanes.

TABLE II. STATISTICAL CHARACTERISTICS OF HEADWAYS FOR

SELECTED HEAVY VEHICLES AND PASSENGER CARS.

Time Headway

Characteristics

(sec)

Heavy Vehicles Passenger Cars

Front Headway

Rear Headway

Front Headway

Rear Headway

Mean 3.23 2.96 1.48 1.05

Median 2.91 2.42 1.17 0.87

Minimum 0.25 0.11 0.09 0.07

Maximum 12.78 9.36 4.91 4.58

IV. METHODOLOGY

To identify the appropriate model for headway

distribution, the statistical models should be applied to fit

the data. To be consistent with the results from majority

of the previous studies, shifted lognormal distribution is


©2014 Engineering and Technology Publishing 225

applied in this paper to present the time headways.

Lognormal is a well-known distribution model which is

frequently used to represent time headways in many

studies. Lognormal distribution is also proposed to model

time headways under car-following situations [20]. The

mathematical equation of the shifted lognormal

distribution is as follows:

t;

2

))(ln(exp

2)(

1) , ,|(

2

2t

ttf (1)

where, t is the time headway, is the shift value in

seconds, and μ and σ are parameters of lognormal

distribution known as location and scale parameters,

respectively. The two parameters are estimated from the

observed data (sample size = n) using Equations 2 and 3.

n

tn

i

i

1

)ln(

(2)

2

1

1

2

1

))(ln(

n

tn

i

i

(3)

To identify the shift value of the front and rear

headway distributions for each vehicle type, the

lognormal distribution model with shifts ranging from 0.0

to 1.0 seconds (with steps of 0.02 second) are examined.

The goodness of fit of the models is checked using Chi-

Square test with 95% confidence level. The null

hypothesis for each test is presented as follows:

The compatibility hypothesis of time headway

distribution with fitted model is rejected (h = 1) or not

rejected (h = 0). (4)

In this study, the most appropriate front and rear

headway distributions for each vehicle type are

determined using two steps. At the first step, the

goodness of fit on the distribution of front and rear

headways is examined for each vehicle type (heavy

vehicles and passenger cars). For that, the p-value

parameter is used. In a Chi-Square test with 95%

confidence level, larger p-values (p-values should be

larger than 0.05) represent a more compatible model. At

the second step, the headway distributions are obtained

for the selected front and rear headway distribution

models for heavy vehicles and passenger cars at different

levels of traffic flow. For each vehicle type, the goodness

of fit of headway distributions is examined at traffic

flows at each 5 minute time interval (Table I).

V. RESULTS AND DISCUSSIONS

As explained in the previous section, the goodness of

fit models on the headway distributions is examined to

model the time headway distributions for each vehicle

type. At the first step, 204 Chi-Square tests are conducted

for models with different shifts using SPSS software. For

each test, the parameters of the model are estimated from

the time headway data. The results of each step are

presented in Table III which shows the values of ‘h’ for

Chi-Square tests on all headways collected for each

vehicle type. The values of h equal to 1 represent

rejection of hypothesis test and its values with zero

represents approval of the hypothesis test.

TABLE III. RESULTS OF CHAI-SQUARE TEST FOR FRONT/REAR

HEADWAY DISTRIBUTIONS FOR EACH VEHICLE TYPE.

Shift

Heavy Vehicles Passenger Cars

Front

Headway

Rear

Headway

Front

Headway

Rear

Headway

0.00 1 1 1 1

0.02 1 1 1 1

0.04 1 1 1 1

0.06 1 1 1 0

0.08 1 1 0 0

0.10 1 1 0 0

0.12 1 0 0 1

0.14 1 0 0 1

0.16 1 0 0 1

0.18 1 0 1 1

0.20 1 0 1 1

0.22 1 0 1 1

0.24 1 0 1 1

0.26 0 1 1 1

0.28 0 1 1 1

0.30 0 1 1 1

0.32 0 1 1 1

0.34 0 1 1 1

0.36 0 1 1 1

0.38 0 1 1 1

0.40 0 1 1 1

0.42 1 1 1 1

0.44 1 1 1 1

0.46 1 1 1 1

0.48 1 1 1 1

0.50 1 1 1 1

0.52 1 1 1 1

0.54 1 1 1 1

0.56 1 1 1 1

0.58 1 1 1 1

0.60 1 1 1 1

0.62 1 1 1 1

0.64 1 1 1 1

0.66 1 1 1 1

0.68 1 1 1 1

0.70 1 1 1 1

0.72 1 1 1 1

0.74 1 1 1 1

0.76 1 1 1 1

0.78 1 1 1 1

0.80 1 1 1 1

0.82 1 1 1 1

0.84 1 1 1 1

0.86 1 1 1 1

0.88 1 1 1 1

0.90 1 1 1 1

0.92 1 1 1 1

0.94 1 1 1 1

0.96 1 1 1 1

0.98 1 1 1 1

1.00 1 1 1 1



a) Front time headway distribution

b) Rear time headway distribution

Figure 3. Selected models fitted on distribution of front and rear headways of heavy vehicles.

a) Front time headway distribution

b) Rear time headway distribution

Figure 4. Selected models fitted on distribution of front and rear

headways of passenger cars.

As it is shown in Table III, the lognormal distribution

models are generally well-fitted to headways. For heavy

vehicles, the lognormal distribution models with shifts

ranging from 0.26 to 0.40 seconds are well-fitted to front

headways. Meanwhile, lognormal distribution models with

shifts ranging from 0.12 to 0.24 are fitted to rear headways

of heavy vehicles. For passenger cars, the lognormal

distributions with shifts ranging from 0.08 to 0.16 and

shifts from 0.06 and 0.10 are well-fitted to front and rear

time headways, respectively. This shows the larger front

and rear time headways in the vicinity of heavy vehicles

compared to the corresponding values in passenger cars.

The larger values of the front time headways in heavy

vehicles may be due to the operational limitations

(acceleration, deceleration, maneuverability) of heavy

vehicles compared to passenger cars. The larger values of

the rear time headways for heavy vehicles may be due to

the safety concerns of the drivers following a large heavy

vehicle. Selected models fitted on distribution of front and

rear headways of heavy vehicles and passenger cars are

presented in Fig. 3 and Fig. 4, respectively.

TABLE IV. ESTIMATION RESULTS OF FRONT/REAR HEADWAY DISTRIBUTIONS OF EACH VEHICLE TYPE.

Traffic Flow

(veh/hr) Heavy Vehicles Passenger Cars

Front Headway Rear Headway Front Headway Rear Headway

μ σ μ σ μ σ μ σ

5988 4.26 1.13 3.50 1.04 1.97 0.90 1.47 0.89

6024 4.23 1.14 3.46 1.07 1.94 0.94 1.43 0.91

7284 3.54 1.09 3.21 1.03 1.69 0.96 1.21 0.87

7752 3.28 1.12 3.08 0.97 1.55 0.87 1.02 0.89

7836 3.17 1.03 2.96 1.00 1.47 0.92 0.94 0.86

7968 3.11 1.01 2.89 0.89 1.39 0.76 0.86 0.77

8028 3.02 1.07 2.73 0.90 1.34 0.81 0.81 0.81

8124 2.84 1.04 2.68 0.86 1.26 0.79 0.75 0.83

8436 2.76 0.96 2.43 0.82 1.15 0.75 0.66 0.79



To further analyze the headway distributions in the

vicinity of heavy vehicles and passenger cars, the

headways are evaluated at different traffic flows. Therefore,

at the second step, the goodness of fit of headway

distribution models is examined at traffic flows at each 5

minute time intervals (Table I). The shifted lognormal

models are fitted on front and rear headway data for heavy

vehicles and passenger cars from traffic flows at each 5

minute time intervals. Estimation results of the parameters

of headway distributions are presented in Table IV. In

general, lognormal distribution is identified by two

parameters including location (μ) and scale (σ). The results

of Table IV show the influence of changes in traffic flows

on the parameters of the lognormal distribution. In other

words, the influence of changes on traffic flows on the

time headway patterns are presented in this table.

To better understand the relationship between traffic

flows and time headway patterns, the parameters of the

headway distributions (μ, σ) can be calculated as a

function of traffic flows. Therefore, linear regression

models are used to simply estimate the parameters of the

front and rear headway distributions for each vehicle type

(Equations 5 and 6).

qba

(5)

qdc

(6)

where, μ is the location of the distribution, σ is the scale

of the distribution, q is the traffic flow, and a, b, c and d

are parameters. The estimation results from the regression

modeling are presented in Table V. By having the

parameters of each headway distribution model, the front

and rear headway distributions can be obtained for heavy

vehicles and passenger cars at different traffic flow rates.

According to the results from Table V, the location of

the front and rear headway distribution models (μ) which

represents the mean value of the headways can be

accurately estimated (R2 values of more than 0.87) for

each vehicle type. However, the scale parameter (σ)

which shows the standard deviation of the time headways

can be estimated with lower accuracy (R2 values of more

than 0.56).

TABLE V. ESTIMATION RESULTS OF HEADWAY DISTRIBUTIONS’ LOCATION (Μ) AND SCALE (Σ) PARAMETERS.

Vehicle

Type

Headway

distribution

μ σ

a b R2 c d R2

Heavy

Vehicles

Front

Headway 7.946 -0.006 0.988 1.160 -0.019 0.724

Rear

Headway 5.783 -0.004 0.872 1.580 -0.008 0.749

Passenger

Cars

Front

Headway 3.864 -0.003 0.943 1.429 -0.009 0.689

Rear

Headway 3.392 -0.003 0.946 1.151 -0.000 0.561

VI. CONCLUSIONS

In this paper, headway distributions were analysed for

heavy vehicles and passenger cars under heavy traffic

conditions. To comprehensively evaluate the headway

characteristic, the time headways to the preceding (front)

and following (rear) vehicles were separately evaluated

for each vehicle type. To better analyse the headway

distribution in the vicinity of heavy vehicles and

passenger cars, the time headways were evaluated at

different traffic flow rates. Then, simple mathematical

models were suggested to estimate the parameters of the

front and rear headway distributions at different traffic

flow rates for heavy vehicles and passenger cars.

According to the results from this study, lognormal

distribution models were generally well-fitted to time

headways. For heavy vehicles, the lognormal distribution

models with shifts ranging from 0.26 to 0.40 seconds were

well-fitted to front headways and lognormal distribution

models with shifts ranging from 0.12 to 0.24 were fitted to

rear headways of heavy vehicles. Meanwhile, the

lognormal distributions with shifts ranging from 0.08 to

0.16 and shifts from 0.06 and 0.10 were well-fitted to the

front and rear time headways of passenger cars,

respectively. This shows the larger front and rear time

headways in the vicinity of heavy vehicles compared to the

corresponding values in passenger cars. The larger values

of the front time headways in heavy vehicles may be due to

the operational limitations (acceleration, deceleration,

manoeuvrability) of heavy vehicles compared to passenger

cars. The larger values of the rear time headways for heavy

vehicles may be due to the safety concerns of the drivers

following a large heavy vehicle. The results from this

paper show the existence of difference in the behaviour of

drivers in the vicinity of heavy vehicles and passenger cars

under heavy traffic conditions.

To better understand the relationship between traffic

flows and time headway patterns, the parameters of the

headway distributions (μ, σ) were calculated as a function

of traffic flows. Therefore, linear regression models were

used to simply estimate the parameters of the front and

rear headway distributions for each vehicle type and

different traffic flow rates under heavy traffic conditions.

By having the parameters of each headway distribution

model, the front and rear headway distributions can be

obtained for heavy vehicles and passenger cars at

different traffic flow rates.

In this study, the headway distributions were evaluated

based on entire headway data collected from a highway

section without separating data of each lane. However,

each lane has different traffic flow characteristics which



may influence the time headway distributions. Exclusive

analysis of the headway distributions for each lane can be

a direction for future research. This may assist in more

accurate traffic planning and policy making at different

traffic conditions.

REFERENCES

[1] Transportation Research Board, Highway Capacity Manual,

Washington: National Research Council, 2010. [2] P. G. Michael, F. C. Leeming, and W. O. Dwyer, “Headway on

urban streets: Observational data and an intervention to decrease

tailgating,” Transportation Research Part F: Traffic Psychology and Behavior, vol. 3, no. 2, pp. 55-64, June 2000.

[3] M. Brackstone, B. Waterson, and M. McDonald, “Determinants of following headway in congested traffic,” Transportation Research

Part F: Psychology and Behavior, vol. 12, no. 2, pp. 131-142,

March 2009. [4] Y. S. Ci, W. Lina, Y. L. Pei, and X. Z. Ling, “Gap acceptance

capacity model for on-ramp junction of urban freeway,” Journal of Transportation Systems Engineering and Information

Technology, vol. 9, no. 4, pp. 116-119, August 2009.

[5] S. M. Abtahi, M. Tamannaei, and H. Haghshenash, “Analysis and modeling time headway distributions under heavy traffic flow

conditions in the urban highways: case of Isfahan,” Transport, vol. 26, no. 4, pp. 375-382, 2011.

[6] S. K. Dubey, B. Ponnu, and S. S. Arkatkar, “Time gap modeling

under mixed traffic condition: a statistical analysis,” Journal of Transportation Systems Engineering and Information Technology,

vol. 2, no. 6, pp. 72-84, Dec 2012. [7] W. K. M. Alhajyaseen, M. Asano, and H. Nakamura, “Left-turn

gap acceptance models considering pedestrian movement

characteristics,” Accident Analysis and Prevention, vol. 5, pp. 175-185, 2013.

[8] M. Jakimavicius and M. Burinskiene, “A GIS and multi-criteria-based analysis and ranking of transportation zones of Vilnius

city,” Technological and Economic Development of Economy, vol.

15, no. 1, pp. 39-48, 2009. [9] B. S. Kerner, Introduction to Modern Traffic Flow Theory and

Control: the Long Road to Three-Phase Traffic Theory, Springer, 2009.

[10] B. Mesarec and M. Lep, “Combining the grid-based spatial

planning and network-based transport planning,” Technological and Economic Development of Economy, vol. 15, no. 1, pp. 60-77,

2009.

[11] T. V. Arasan and R. Z. Koshy, “Headway distribution of heterogeneous traffic on urban arterials,” Journal of the Institution

of Engineers, vol. 84, pp. 210-215, 2003.

[12] G. Zhang, Y. Wang, H. Wei, and Y. Chen, “Examining headway distribution models with urban freeway loop event data,”

Transportation Research Record, vol. 1999, pp. 141-149, 2007. [13] P. Yi, Y. Zhang, J. Lu, and H. Lu, “Safety-based capacity analysis

for Chinese highways – a preliminary study,” IATSS Research, vol.

28, no. 1, pp. 47-55, 2004. [14] S. Daisuke, O. Izumi, and N. Fumihiko, “On estimation of

vehicular time headway distribution parameters,” Traffic Engineering, vol. 34, no. 6, pp. 18-27, 1999.

[15] M. Mei and A. G. R. Bullen, “Lognormal distribution for high

traffic flows,” Transportation Research Record, vol. 1398, pp. 125-128, 1993.

[16] S. Sadeghhosseini, “Time headway and platooning characteristics of vehicles on interstate highways,” PhD. Dissertation, University

of Illinois, 2002.

[17] G. H. Bham and S. R. P. Ancha, “Statistical models for preferred time headway and time headway of drivers in steady state car-

following,” in Proc. Ninth International Conf. Applications of Advanced Technology in Transportation, Chicago, 2006, pp. 344-

349.

[18] H. T. Zwahlen, E. Oner, and K. Suravaram, “Approximated headway distributions of free-flowing traffic on Ohio freeways for

work zone traffic simulations,” Transportation Research Record, vol. 1999, pp. 131-140, 2007.

[19] Cambridge Systematics. (2005). NGSIM I-80 Data Analysis,

Summary Reports. Federal High Way Administration (FHWA), [Online]. Available: https://camsys.com

[20] I. Greenberg, “The log-normal distribution of headways,” Australian Road Research, vol. 2, no. 7, pp. 14-18, 1966.

Sara Moridpour holds a Bachelor of Civil Engineering and Masters degree in

Transportation Planning and Engineering from Sharif University of Technology, Iran. She also

received her PhD degree from Monash

University. She has 9 years of work and research experience in the field of traffic and

transport. Her main research interests include on driving

behavior modeling and analysis, micro

simulation, transport network modeling and optimization. She has been lecturer in the School of Civil,

Environmental and Chemical Engineering, RMIT University, from 2010.



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