Modeling And Simulation Of Traffic Flows Based On Detailed Analysis Of Driving Behavior

The aim of the fundamental research for traffic science is to find the basic regulations governing traffic systems through modeling, simulating and analyzing real traffic. In this dissertation, based on an overview of the existing models for traffic flows, several modified mathematical models of traffic flow in accordance with empirical observations are proposed. The theoretical analysis and numerical simulation are performed in order to explore the nonlinear phenomena in traffic systems.This dissertation consists of the following four main parts:Ⅰ. Based on the NaSch model of traffic flow, two novel cellular automaton traffic models are presented. One takes into account the effects of local density and the driver response delay on the randomization, and the other includes the effects of road density and drivers' individual behavior on the randomization.It is claimed that the randomization probability in the cellular automaton model is affected not only by the vehicle velocity, but also by the local density and drivers' delay in response. The randomization increases as the local density increases. Besides, a driver can usually sense the local density at previous time step and adjust the vehicle velocity at the present time step. So a modified NaSch model, i.e., the density dependent randomization model (abbreviated as the DDR model), is proposed, in which the randomization probability is assumed to depend on the local density at the preceding time step. The simulation results indicate that this model can reproduce the complicated behavior of real traffic, such as the stop and go traffic, metastable state and hysteresis. The fundamental diagram obtained by numerical simulation shows that the resulted road capacity is close to the empirical data compared with that by the NaSch model. And it is of greater importance that the DDR model can reproduce the free flow, the homogeneous flow and the traffic jam. Furthermore, another modified NaSch model, i.e., the individual behavior dependent randomization model (abbreviated as the IBDR model), is established by considering the effects of road density and the drivers' individual behavior on the randomization. The model can also reproduce the stop and go traffic, metastable state, the hysteresis and the larger value of maximum flow which is close to the observed data compared with that obtained from the NaSch model. Besides, it is found that the driving feature of the individual driver has more appreciable influence on the maximum traffic flow than density does. When there are some vehicles owned by the conservative drivers in traffic flow, the random deceleration probability is larger and the road capacity is reduced apparently. For practical use, this fact indicates that it is meaningful and essential to distinguish clearly fast lanes from slow traffic lanes. In summary, the two modified NaSch model proposed herein can capture some respects of the real traffic, even though not the entire. And they can be contributed to the development of the traffic flow theory.Ⅱ. Based on the two-lane CA model proposed by Chowdhury et al, the nonlinear dynamics of the mixed traffic flow with a bottleneck caused by a traffic accident is studied via numerical simulation.The property of the mixed traffic flow with a bottleneck caused by an accident vehicle is studied by using the two-lane cellular automaton model proposed by Chowdhury et al. The results of the numerical study, i.e., the fundamental diagrams and the macroscopic features of spatial-temporal traffic patterns at the blockage, are given by applying both symmetric and asymmetric lane changing rules. It is shown that when there is no accident on the road, the presence of slow vehicles has a strong influence on the dynamics of traffic flow. And the fundamental diagrams for the different lanes exhibit different properties when the different lane changing rules are adopted and the accident car appears on the different lanes. In the low and moderate density regions, if the prection of slower cars is 10%, the asymmetric lane changing rule is more advantageous in reducing jam than the symmetric lane changing rule when there is a blockage on the right lane (the slow lane); and in the contrary, the symmetric lane changing rule is superior provided that there is a blockage on the left lane (the fast lane). The spatial-temporal diagrams show that the accident not only causes the local jam in the lane with the accident, but also causes vehicle cluster in the bypass lane. The results also indicate that when traffic is inhomogeneous with different types of vehicles and even with an accident or other defeats, the vehicles will change lane more frequently. In addition, the maximum lane changing rate using the asymmetric rule is lager than that using the symmetric rule. And as there is no slow vehicle and no accident, the corresponding lane changing rate is the lowest.Ⅲ. An extended car following model is proposed by taking into account the delay of the driver response in sensing headway and the delay of car motion respectively, and the nonlinear properties of the density waves are studied in the metastable and unstable regions.The soliton and kink-antikink density waves in the traffic flows are simulated with periodic boundaries, by adding a small disturbance in the initial condition on a single-lane road based on the car-following model proposed by Nagatani et al and the optimal velocity function proposed by Bando et al. The waves are reproduced in the form of the spatial-temporal evolution of headway, and both of the density waves propagate backwards. It is found that the solitons appear only near the neutral stability line regardless of the open boundary conditions or periodic boundary conditions, and they exhibit upward form when the initial headway is smaller than the safety distance, otherwise they exhibit downward form. Comparison is made between the numerical and analytical results about the amplitude of kink-antikink wave, and the result shows that the varying tendency of the amplitude is the same, i.e., the amplitude decreases with the increase of the sensitivityα. However, asαis smaller (α<2.3), the numerical results of amplitude are greater than the analytical ones, and then they exhibit a good agreement asα> 2.3. The underlying mechanism is analyzed and this difference is related to the neglected higher-order terms in the nonlinear analysis. Besides, it is shown that the maximal flow increases with the decrease of the safety distance. The numerical simulation shows a good agreement with the analytical results.Based on the above model, an extended car-following model is proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability line and the critical point are obtained by using the linear stability theory. Furthermore, the KdV equation and mKdV equation are derived to describe traffic behavior near the neutral stability line and the critical point respectively by applying the reductive perturbation method. The phase diagrams for the headway and sensitivity with neutral stability lines and coexisting curves are given for different values of n, which denotes the proportion of drivers' delay in response to the total delay. It can be found that the stability regions decrease with the increase of n. This means that the traffic jams will appear easily when the delay of drivers' response in sensing headway increases. The numerical results reproduce the soliton-type density waves and kink-antikink density waves in the form of the spatial-temporal evolution of headway, and both of them propagate backwards. Furthermore, the wave number of kink-antikinks increases with the increase of n. Meanwhile the results show that the delay of drivers' response in sensing headway plays an important role in phase transition, i.e., the longer the delay of driver response is, the easier the formation of the traffic jam is. This model elucidates the mechanism of the traffic jam to some extent from a microscopic viewpoint.Ⅳ. Two lattice hydrodynamic models for the traffic flow are constructed and the linear and nonlinear analyses are conducted.Based on the lattice hydrodynamic models proposed by Nagatani et al and incorporated with the results obtained with the car-following model in this dissertation, two lattice hydrodynamic models (model I and model II) for the traffic flow are proposed by taking into account the delay of drivers' response in sensing headway and the delay of car motion respectively. The neutral stability lines and the critical points for the two models are obtained by using the linear stability theory. The mKdV equations near the critical point are derived to describe the traffic jam by using the reductive perturbation method, and the kink-antikink soliton solutions related to the traffic density waves are given. The phase diagrams in the headway-sensitivity plane with neutral stability lines and coexisting curves are given for different values of n . The corresponding critical points, neutral stability lines and coexisting curves in model I are lower than those in model II. And this coincides with the result of Nagatani et al. It can be found that the stability regions decrease with increasing n in both the models and the propagation velocity in model II also decreases with increasing n. It indicates that the traffic jams will be easy to appear and difficult to disperse as the drivers' delay in response increases, and this coincides with the result of study with the car-following model. Then the study indicates the fact that the delay of drivers' response in sensing headway plays an important role in jamming formation from the macroscopic viewpoint. Meanwhile it indicates that the lattice hydrodynamic models can capture the intrinsic properties in traffic flows, and are effective in traffic analysis.The final chapter of this dissertation is devoted to an analysis and prospect of further study for the traffic flow in our country.