Multi-lane Changing Model with Coupling Driving Intention and Inclination

Considering the impact of drivers’ psychology and behaviour, a multi-lane changing model coupling driving intention and inclination is proposed by introducing two quantitative indices of intention: strength of lane changing and risk factor. According to the psychological and behavioural characteristics of aggressive drivers and conservative drivers, the safety conditions for lane changing are designed respectively. The numerical simulations show that the proposed model is suitable for describing the traffic flow with frequent lane changing, which is more consistent with the driving behaviour of drivers in China. Compared with symmetric two-lane cellular automata (STCA) model, the proposed model can improve the average speed of vehicles by 1.04% under different traffic demands when aggressive drivers are in a higher proportion (the threshold of risk factor is 0.4). When the risk factor increases, the average speed shows the polarization phenomenon with the average speed slowing down in big traffic demand. The proposed model can reflect the relationship among density, flow, and speed, and the risk factor has a significant impact on density and flow.


INTRODUCTION
Vehicle lane changing can bring vital influence to the efficiency and safety of the entire traffic flow. It also leads to speed variance and flow instability that will directly cause traffic accidents. Vehicle lane changing contributes to about 4% to 10% of traffic accidents, of which about 75% are caused by human factors. In addition, about 10% of traffic delays are caused by lane changing, bringing about huge economic losses to the society, and irreparable negative effect to the ecological environment [1].
Drivers' psychological activities and behaviours are strongly stochastic in lane changing process and result in the randomness and complexity of traffic flow [2]. To reveal the influence mechanism of lane changing behaviour on the efficiency and safety of the entire traffic flow, scholars at home and abroad have been attempting to study the effect of the law of drivers' psychology and behaviour in lane changing process, and have proposed many improved models which are suitable for weaving sections impact analysis [3], access control strategy [4], lane changing trajectory [5] and crash risk reduction [6]. The contributions of these studies focus on the analysis and modelling of lane changing behaviours in specific areas using traffic flow theory. In terms of research means, Hoseini uses probability theory, and Cellular Automaton (CA) to analyse the impact of lane changing behaviour on the traffic flow [7]. The results indicate that the model based on driving regulations is not valid, but that three probabilistic models appear useful for predicting the driver's behaviour on freeway segments during non-congested conditions. CA has some advantages such as non-linear simulation, flexible calculation and reproduction of a variety of real traffic conditions, etc. It is a classic method for studying lane changing behaviour [8,9,10,11,12]. The first use of stochastic cellular automata for traffic flow was introduced by Nagel and Schreckenberg, referred as the NaSch model [13]. Most Intention and Inclination   control and urban lane changing model are presented  based on the CA model according to the actual traffic  flow and corresponding lane changing rules [14,15]. The STCA model is proposed to descript the flow in two lanes, and can simulate the lane changing behaviour [16][17][18][19]. However, the drivers' lane changing intention and inclination are neglected in these models.
Different drivers have obviously different behaviours, thus rendering randomness and complexity to the traffic flow. However, the existing studies cannot reflect the implicit difference in driving behaviour in the real traffic flow [20]. Due to the importance of driver's lane changing intention and behaviour, many scholars conduct studies about recognizing lane changing intention [21], and apply the drivers' behavioural preferences [22], cooperation intention [23,24] and sensitivity factor [25,26] to design the lane changing model. In these studies, the driver characteristics are introduced into the lane changing model. Besides, common simulation software, such as VISSIM, also provide several parameters, such as expected speed to reflect qualitatively the impact of drivers' characteristics; however, it lacks quantitative parameters. Based on the analysis of lane changing requirements, two quantitative characteristic variables are introduced in this paper; namely, the intention strength of lane changing and the risk factor, which describe the driver's psychology and behaviour. A multi-lane changing model is also proposed, known as the Coupling Driving Intentions and Inclination (C-DIaI) model. C-DIaI model is used to simulate traffic flow under different traffic demands and to analyse the differences and reasons of traffic flow under various risk factors.

Analysis of lane changing behaviour
Driving behaviour can be classified as car following model and lane changing model. Lane changing model is an integrated process based on the driver's judgment and adjustment of the information of the surrounding environment, which is affected by the driver's spatial-temporal perception characteristics. The lane changing intention will be produced when the leading vehicle status does not meet the driver's expectations.
To have a comfortable driving environment, a driver will undertake the lane changing behaviour coupling their driving inclination.
Generally, the driver type (D T ) can be divided into conservative type (D T =0) and aggressive type (D T =1). Conservative drivers tend to slow down and follow the leading vehicle when traffic is congested, and choose to change lanes only when changing conditions are good enough, while aggressive drivers tend to change lanes to keep the expected speed once the conditions are satisfied.
Lane changing does not depend only on the vehicle status of the current lane and the adjacent lane, but it also depends on the driving inclination and the perception of the space resources around, and other factors. The lane changing intention and implementation are affected by the driver's perception of the road traffic, lane change constraints and risk acceptance. The decision-making process and the influencing factors of lane changing are shown in Figure 1.

Model design
Before introducing the C-DIaI model, the classical NaSch model is briefly recalled [13]. The NaSch model is a discrete model for the traffic flow. The road is divided into cells, which can be either empty or occupied by a vehicle with a velocity v=0, 1,…, v max . The vehicles which are numbered 1, 2, …, i move from the left to the right on a lane with periodic boundary conditions. At each discrete time step t→t+1 the system update is performed in parallel according to the following four rules: Step 1: Step 4: position update, x(i)→x(i)+v(i).
Here v(i) and x(i) denote the velocity and position of vehicle i, respectively; v max is the maximum velocity and  The value is set as b∈(0,1). In the simulation process, b is determined by random numbers, and the driver type of each vehicle can be calculated by Formula 2.
where b T is the threshold of driver type, b∈(0,1 where int() is integral function; d(i,lv), d(i,fv) are the distance between the i-th vehicle and the leading vehicle of adjacent lane, the distance between the i-th vehicle and the followings vehicle of adjacent lane, m. The aggressive drivers, who have a stronger intention of lane changing, and are more likely to undertake frequent lane changing to satisfy their intention in a higher risk factor b. Hence, the constraints of lane changing of aggressive drivers are relatively stricter than those of conservative drivers. According to reference [27], the lane changing conditions can be indicated by Formula 4. , , , Therefore, C-DIaI model is proposed as follows, considering lane changing intention and the characteristic of driving inclination of different types of drivers.
where C is the lane changing decision variable, C=1 means changing lane according to lane changing logic priority rule; C=0 means continue following the leading vehicle by using NS model.
A logical flow chart of the model simulation is provided in Figure 2, and the C-DIaI model is validated.
Lane changing logic priority rule should be considered in multi-lane (n>2, n=3 in this paper) traffic flow. It involves the position of vehicles and the lane changing order between different vehicles with lane changing intention. Several typical lane-changing scenarios are shown in Figure 3. In

NUMERICAL SIMULATION
To verify the efficiency of the model, an experimental scheme for three lanes has been designed. Lane changing intention strength a and risk factor b are used as independent variables to analyse the effect of the C-DIaI model on the traffic flow. With classical STCA model as reference, a comparative analysis was made of the effect on traffic flow under different traffic demands.
The settings of parameters in the simulation experiment are shown in Table 1.

Lane changing frequency under different traffic demands
Given a certain proportion of driver type (b T =0.4), the cumulative lane changing frequency under different traffic demands of two models is shown in Figure 4.  In order to explore the impact of different types of drivers on the lane changing manoeuvre, the interaction between risk factor b and lane changing frequency is analysed. Figure 5 shows the impact of risk factor b on lane changing frequency corresponding to input volume of 400 veh/h/ln and 600 veh/h/ ln. The result shows that the lane changing frequency of C-DIaI model is bigger compared with STCA model. Lane changing frequency of two models shows a rapid growth when the input volume is 400 veh/h/ln, and C-DIaI model has a more obvious increasing trend. The lane changing frequency of two models has a slow growth when the input volume is 600 veh/h/ln because of the limit of changing space.

Variety of traffic flow parameters in different traffic demands
Given b T =0.4, the average speed distribution of two models in different input flows is shown in Figure 6.  As shown in Figure 6, with the increase of the input flow, the average speed of the traffic flow showed a decreasing trend. C-DIaI model considers driving intention and inclination, so that more vehicles can change lane to increase vehicle speed when b T =0.4; therefore, the higher speed can be reached under C-DIaI model with the same input volume. The comparison of the average speed of two models under different traffic demands is shown in Table 2. It can be seen from Table 2 that the average speed of the C-DIaI model has savings according to that of the STCA model when the input volume is relatively small (≤400 veh/h/ln). This can be explained by the reasons that more aggressive drivers would change lane to achieve a higher speed; therefore, a significant improvement in the average speed is present under the C-DIaI model. When the input volume exceeds a certain value (>400 veh/h/ln), though lane changing space  available is limited, a majority of aggressive drivers would still change lane when the changing conditions are satisfied. Therefore, a decline tendency of average speed is present under the C-DIaI model. According to the above analysis, the average speed of the C-DIaI model will be lower than that of the STCA model when the input volume is at a certain value between 400 veh/h/ln and 500 veh/h/ln. In general, the efficiency of the entire traffic flow is improved as the average speed of the C-DIaI model features an increase of 1.04% compared with the STCA model.
The impact of the proportion of different types of drivers on the traffic flow is analysed further in the text. Figure 7 shows the impact of b T on the average speed under different traffic demands. In order to explore the impact of risk factor on the traffic flow, the relationship between density and volume in different risk factors b T is analysed, as shown in Figure 8. As shown in Figure 8, the relationship between density and volume could be reflected correctly by the C-DIaI model, and different risk factors would also affect their relationships. For low density, the impact of risk factor on the relationship between density and volume is not obvious. However, the impact is obvious for the case of high density. With the same density, a higher proportion of aggressive drivers means lower average volume of the C-DIaI model. It is reasonable that less lane changing space available in high density results in higher proportion of aggressive drivers changing lane. It would lead to serious interference on the traffic flow and reduce the average volume by the traffic congestion.
The relationship between density and speed of the C-DIaI model at different b T values is shown in Figure 9. The relationship between density and speed could be reflected correctly by the C-DIaI model, and the impact of different risk factors on the relationship between density and speed is not obvious.

CONCLUSIONS AND DISCUSSION
By coupling the driving intention and inclination, the C-DIaI model is presented considering the impact of the driver's character on lane changing. Numerical analysis results show that frequency of lane changing is related to the proportion of different types of drivers. Generally, there is a positive correlation between risk factor and traffic flow efficiency in lower traffic demand. Lane changing behaviour is helpful to improve the traffic efficiency. However, frequent lane changing will have a negative impact on the traffic efficiency under higher traffic demand, because it will decrease the vehicle average speed. Compared with the STCA model, the C-DIaI model is suitable for representing the traffic flow with high lane changing proportion, which is more consistent with the driver's frequent lane changing behaviour in China. This study will provide a reference for the design of multi-lane changing CA model from the driver's character perspectives.
Vehicles in simulation are considered as the standard passenger cars. However, there are different types of vehicles with different sizes in actual conditions, and vehicle speeds are more random sometimes with overspeeding behaviour. Meanwhile, there may be special road conditions, traffic accidents and traffic controls that will affect the traffic flow. This study only considers the driver's character of each vehicle that depends on the intention strength of lane changing in perfect road conditions. In our future work, the model will be improved based on the actual road conditions, and other relevant factors will be further investigated.