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A three-lane traffic flow model is proposed to investigate the effect of car accidents on the traffic flow. The model is an extension of the full velocity difference (FVD) model by taking into account the lane changing. The extended lane-changing rules are presented to model the lane-changing behaviour. The cases that the car accidents occupy the exterior or interior lane, the medium lane, and two lanes are studied by numerical simulations. The time-space diagrams and the current diagrams are presented, and the traffic jams are investigated. The results show that the car accident has a different effect on the traffic flow when it occupies different lanes. The car accidents have a more serious effect on the whole road when they occupy two lanes. The larger the density is, the greater the influence on the traffic flow becomes.

Traffic jam is a complicated traffic phenomenon and has been investigated by various traffic models [

Recently, the studies of the influence of the car accident on traffic flow have attracted considerable attention. Nagatani [

Kurata and Nagatani [

As for the study of the macroscopic model, Tang et al. [

The abovementioned models concentrate on modeling the effects of car accidents on traffic flow at a single-lane or two-lane roadway. However, there exist a large number of three-lane roads in real traffic. In comparison with two-lane roads, the greater traffic flow and more frequent lane changing in three-lane roads make the accident easier to happen. It is thus necessary to further investigate the effect of the car accidents on traffic flow in three-lane roads.

In this paper, we extend the FVD model to the three-lane traffic by taking into account the lane changing. We investigate the traffic jams caused by the car accidents which occupy the exterior or interior lane, the medium lane, and two lanes. We derive the time-space diagrams and the current diagrams to study the effect of the car accidents on traffic flow (Figure

Schematic illustration of (a) a car accident occupying one lane, (b) two car accidents occupying lane 1 and lane 2, and (c) two car accidents occupying lane 1 and lane 3.

We consider traffic flow on a highway which consists of three lanes: the exterior lane (lane 1), the medium lane (lane 2), and the interior lane (lane 3). We discuss the cases where a car accident is located at lane 1 or lane 2, two car accidents occupy lane 1 and lane 2, and two car accidents occupy lane 1 and lane 3, as shown in Figure

A schematic illustration of lane changing for cars on lane 2.

The car motion is divided into two parts: the forward motion and the sideways motion. We employ the FVD model [

The optimal velocity function

In general, a driver has an incentive to change lane if the adjacent lane can provide better driving conditions. Lane-changing decision of a driver needs to satisfy two criteria:

Based on the lane-changing rules [

cars on lane 1 change to lane 2.

We adopt the rules of Kurata and Nagatani [

Change from lane 3 to lane 2, if

Change from lane 2 to lane 1, if

Cars on lane 2 change to lane 3.

The rules are similar to those of cars on lane 2 changing to lane 1 (consult (

Change from lane 2 to lane 1 and lane 3 with equal probability, if

In (

The explanation of lane-changing rules is as follows. The rule described by (

In this section, we use the above model to explore the effects of car accidents on traffic flow. There are a certain number of cars in each lane at the beginning of simulation. The cars’ motion is split into two parts: one is the forward motion and the other is the lane changing. The forward motion is described by (

The simulation is performed by varying the initial density

We first investigate the case that the accident happens on the exterior lane (i.e., lane 1). The situation that the car accident is in the interior lane (i.e., lane 3) can be discussed similarly. Assume that a car accident is located at

The time-space diagrams of three lanes for the case that a car accident is in lane 1 at density

The time-space diagrams of three lanes for the case that a car accident is in lane 1 at density

Figure

Plots of traffic currents against density for the case that a car accident is in lane 1.

For a comparison with the case that the car accident is in lane 1, we next study the case that a car accident occupies the middle lane. The car accident is located at

The time-space diagrams of three lanes for the case that a car accident is in lane 2 at density

The time-space diagrams of three lanes for the case that a car accident is in lane 2 at density

Figure

Plots of traffic currents against density for the case that a car accident is in lane 2.

In real traffic, many traffic accidents happen when cars are changing lanes. Under this situation, the car accidents usually occupy two lanes at the same time. Thus, we finally explore the cases that there are two car accidents.

The first situation is that two car accidents are, respectively, located at

The time-space diagrams of three lanes for the case that two car accidents occupy lane 1 and lane 2 at density

The time-space diagrams of three lanes for the case that two car accidents occupy lane 1 and lane 2 at density

Figure

Plots of traffic currents against density for the case that two car accidents occupy lane 1 and lane 2.

The second situation is that two car accidents are located at

The time-space diagrams of three lanes for the case that two car accidents occupy lane 1 and lane 3 at density

The time-space diagrams of three lanes for the case that two car accidents occupy lane 1 and lane 3 at density

Figure

Plots of traffic currents against density for the case that two car accidents occupy lane 1 and lane 3.

The car accidents have an important influence on traffic flow. To address this problem, we have presented an extended three-lane traffic model to investigate the traffic jam caused by the car accidents. We obtain the time-space diagrams and the current diagrams for the cases that the car accidents occupy lane 1, lane 2, lanes 1 and 2, or lane 1 and lane 3. Results indicate that the effect of the car accident located at lane 1 on the traffic flow is greater than the case of the car accident located at lane 2, while the car accidents have a more serious effect on the whole road when they occupy two lanes. These results are in coincidence with our daily experiences in real traffic. In this paper, the proposed model is used to explore the effect of the car accidents upon the traffic flow on a highway. In our future work, this model will be extended to city traffic and to study the traffic behaviors discussed in the works of Toledo et al. [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This paper is supported by the National Natural Science Foundation of China (Grant no. 11102165), the Natural Science Basis Research Plan in Shaanxi Province of China (Grant nos. 2012JM1001 and 2013JQ7014), and NPU Foundation for Fundamental Research (Grant no. NPU-FFR-JC201254). The authors would like to thank two anonymous referees for their valuable suggestions on improving the paper.