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This paper aims to analyze the impact of trucks on traffic flow and propose an improved cellular automaton model, which considers both the performance difference between passenger cars and trucks and the behaviour change of passenger cars under the impact of trucks. A questionnaire survey has been conducted to find out whether the impact of trucks exists and how the behaviour of passenger car drivers changes under the impact of trucks. The survey results confirm that the impact of trucks exists and indicate that passenger car drivers will enlarge the space gap, decelerate, and change lanes in advance when they are affected. Simulation results show that traffic volume is still affected by percentages of trucks in the congestion phase in the proposed model compared with traditional heterogeneous cellular automaton models. Traffic volume and speed decrease with the impact of trucks in the congestion phase. The impact of trucks can increase traffic congestion as it increases. However, it has different influences on the speed variance of passenger cars in different occupancies. In the proposed model, the relative relationship of the space gap between car-following-truck and car-following-car is changeable at a certain value of occupancy, which is related to the impact of trucks.

With the development of truck transportation, the number of trucks and their proportion in freeway traffic have been increasing significantly in the world. The average percentage of trucks in most freeways in China is around 25% and some can even reach as much as 60% [

The study of traffic flow has attracted many researchers from different fields because of its complexity and comprehensiveness and many theoretical approaches have been presented, such as hydrodynamic models, gas kinetic models, car-following models, and cellular automaton (CA) models [

Heterogeneous traffic flow composed of passenger cars and trucks is a common phenomenon in road traffic. However, few CA models are built for heterogeneous traffic flow. Most of them are built for homogenous traffic flow currently, which means only cars in the system. Meng and Weng have constructed a heterogeneous CA model for freeway work zones. There were two vehicle types in the system and each had different characteristics [

The primary objective of this study is to analyze the impact of trucks on traffic flow using an improved heterogeneous CA model. More specifically, this study includes the following two tasks:

In order to understand the impact of trucks on the behaviour of passenger car drivers, a questionnaire survey has been conducted in Nanjing, Jiangsu Province, China. The respondents were passenger car drivers. The survey was conducted in three places. The first survey was conducted in a service area of Shanghai-Nanjing freeway on December 1, 2015. A total of 165 responses from passenger car drivers were collected. The second survey was conducted in the parking lot of Nanjing Railway Station on December 6, 2015. A total of 200 responses were collected. The third survey was conducted in the parking lot of a supermarket on December 12, 2015. A total of 185 responses were collected. After removing the invalid questionnaires, 520 samples were obtained. Among the samples, in regard to the gender, 31.73% were females and 68.27% were males. Concerning their age, 54.81% were under 30 years of age; 15.38% were between 30 and 40 years of age; 27.88% were between 40 and 50 years of age; and only 1.92% were above 50 years of age. For their driving experience, 38.46% had less than 1 year of driving experience, 29.81% had from 1 to 5 years, and 31.73% had more than 5 years.

There are 5 questions in this survey and the results are presented in Figure

The results of the questionnaire survey.

The results of question one

The results of question two

The results of questions three and four

The results of question five

From the survey, the impact of trucks on the following passenger car exists, including sight distance obstruction, speed reduction, and psychological pressure. The behaviour of passenger car drivers will change under the impact, like to enlarge the space gap, decelerate, and change lanes in advance. Therefore, if the update rules in the CA model are still the same for passenger cars under the impact of trucks, it would cause some problems and reduce the accuracy of the model.

In this section, the parameters used in the CA model are first presented. Then the improved CA model is proposed to consider the impact of trucks.

The simulated road consists of two lanes: lane 0 and lane 1. Each lane is divided into

When simulating vehicle movements on the road, the update rules for the passenger car following a truck are different. We call it the truck impact rule. In other cases, (e.g., the passenger car following a car) the basic rule is used, which is based on the NaSch model.

In the basic rule, vehicles will change lanes with probability

Interval criterion:

Incentive criterion:

Security criterion:

Based on the survey, when a passenger car follows a truck, the passenger car driver will change lanes in advance even though the condition of the current lane can still satisfy his/her speed. Therefore, the incentive criterion in the basic rule is improved to be used in the truck impact rule. Other criterions in the basic rule and the truck impact rule are the same. The incentive criterion in the truck impact rule is as follows.

Incentive criterion:

In the car-following rules, vehicles will update their speed and longitudinal position. The four steps of car-following in the basic rule are as follows.

Acceleration:

Collision avoidance:

Randomization:

Movement:

Based on the survey, when a passenger car follows a truck, the passenger car driver will enlarge the space gap and decelerate. Hence, the steps of collision avoidance and randomization are modified to be used in the truck impact rule. Other steps in the truck impact rule are the same as those in the basic rule. The modified steps of collision avoidance and randomization in the truck impact rule are as follows.

Collision avoidance:

Randomization:

Most previous CA models set the cell size with 7.5 m, which is too coarse, leading to unrealistic acceleration and deceleration rates. In the improved CA model, according to the actual sizes of vehicles, acceleration and deceleration rates, and so forth, in the used data set and the computational speed, the cell size is set as 1.5 m. A numerical simulation was performed with periodic boundary conditions and the road length ^{2} (3 m/s^{2}), while ^{2} (1.5 m/s^{2}), while

Note that the effect and magnitude are two factors in the study of the impact of trucks. In this study, however, the magnitude of the impact of trucks was not determined in detail through the survey. The emphasis of our study is to introduce the impact of trucks to the CA model and analyze the feature of traffic flow by changing it. For example, the fundamental diagram is determined by different imp and the effect is studied. Hence, it is not necessary to determine the absolute magnitude of the impact of trucks in this study. In some places of this study, the magnitude of the impact of trucks (i.e., imp) needs to be fixed to study the effect of the percentage of trucks. In this case, the value of imp will be set as 6 based on the result of question one in the survey (

Let the total number of vehicles on the road be

At the initial time, passenger cars and trucks were randomly distributed on the road according to the percentage of trucks, and the initial speed of each vehicle was a random value. Each time step

The relationship between speed and occupancy with different percentages of trucks when

The fundamental diagram under different

Speed versus occupancy

Volume versus occupancy

The fundamental diagram under different

Speed versus occupancy

Volume versus occupancy

The fundamental diagram with different truck impacts at

The fundamental diagram under different imp when

Speed versus occupancy

Volume versus occupancy

For a deeper understanding of traffic flow dynamics under different conditions, the spatial-temporal diagrams were obtained by simulations as shown in Figure

Spatial-temporal diagrams.

imp = 0,

imp = 10,

imp = 0,

imp = 10,

imp = 6,

imp = 6,

imp = 6,

imp = 6,

From the above analysis, the impact of trucks does not have a significant influence on traffic volume and speed when the critical occupancy has not yet been fetched. However, this does not mean absolutely no impact of trucks at that time. The speed variance of passenger cars with different truck impacts when

Speed variances of passenger cars when

Speed variances of passenger cars

Lane-changing rate of passenger cars with different imp when

A space gap is an important parameter in CA models, which determines the choice of deceleration and lane change in the update rules. This section studied the feature of the space gap of car-following-truck (C-T). The relationship between the space gap of C-T and occupancy under different impacts of trucks when

The relationship between the space gap of C-T and occupancy under different imp when

This paper studied the impact of trucks on traffic flow based on the improved CA model. A questionnaire survey was conducted. From the survey, the impact of trucks exists when passenger cars drive behind a truck and it is significant. The behaviour of passenger car drivers changes under the impact of trucks, including enlarging the space, increasing the probability of deceleration, and changing lanes in advance. Grounded upon the existing heterogeneous CA models, the imp was introduced to reflect the degree to which trucks affect passenger cars quantitatively and the lane-change and car-following rules were modified to build the improved CA model. The simulation results show that

The proposed CA model has considered not only the performance differences between passenger cars and trucks, but also the impact of trucks on the behaviour of passenger cars. It can reflect the impact of trucks on traffic flow more comprehensively and improve the accuracy of the simulation of traffic flow. The simulation results can help to understand the impact of trucks on traffic flow further and provide a theoretical basis for improving road traffic efficiency and safety.

With limited resources and time, there are still some aspects this study could improve. Firstly, this study does not determine the magnitude of the impact of trucks specifically and uses the identical value. It is important to understand how the magnitude of the impact of trucks changes in different conditions by different factors. This could help to improve the accuracy of simulation in the further study and we will collect more field data to study this aspect. For the convenience of analysis, this paper only used the linear and quadratic functions to fit the space gap of C-T. The accuracy will be further improved if more function forms are used. Also, the impacts of trucks on trucks exist but are not as obvious as on passenger cars. This part is not explored in this study and can be considered further. Meanwhile, the responses of different kinds of vehicle drivers to the impact of trucks will be a focus in the next study to further improve the correctness and applicability of the proposed model.

The authors declare that they have no competing interests.

This research is funded by the Young Scientists Fund of the National Natural Science Foundation of China (no. 51408253) and the Jiangsu Traffic Scientific Research Project (no. 2011-Y-30).