From the macroscopic viewpoint for describing the acceleration behaviour of drivers, a weighted probabilistic cellular automaton model （the WP model, for short） is proposed by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatiotemporal patterns, are analysed in detail. It is shown that the presented model leads to the results consistent with the empiricaZ data rather well, nonlinear flow-density relationship existing in lower density regions, and a new kind of traific phenomenon called neo-synchronized flow. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomenon. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and the randomicity of drivers and vehicles have indeed a remarkable effect on traffic dynamics.
＜正＞Based on the Nagel-Schreckenberg（NaSch）model of traffic flow,a modified cellular automaton（CA）traffic model...
Hui-bing Zhu~(1,2),Shi-qiang Dai~1 (1.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072,Zhejiang Province,China
In this paper, the speed gradient （SG） model is extended to describe the traffic flow on two-lane freeways. Terms related to lane change are added into the continuity equations and velocity dynamic equations. The empirically observed two-lane phenomena, such as lane usage inversion and lane change rate versus density, are reproduced by extended SG model. The local cluster effect is also investigated by numerical simulations.
In this paper, the velocity anticipation in the optimal velocity model （OVM） is investigated. The driver adjusts the velocity of his vehicle by the desired headway, which depends on both instantaneous headway and relative velocity. The effect of relative velocity is measured by a sensitivity function. A specific form of the sensitivity function is supposed and the involved parameters are determined by the both numerical simulation and empirical data. It is shown that inclusion of velocity anticipation enhances the stability of traffic flow. Numerical simulations show a good agreement with empirical data. This model provides a better description of real traffic, including the acceleration process from standing states and the deceleration process approaching a stopped car.
In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.
Based on the pioneer work of Konishi et al, a new control method is presented to suppress the traffic congestion in the coupled map （CM） car-following model under an open boundary. A control signal concluding the velocity differences of the two vehicles in front is put forward. The condition under which the traffic jam can be contained is analyzed. The results axe compared with that presented by Konishi et al [Phys. Rev. 1999 E 60 4000-4007]. The simulation results show that the temporal behavior obtained by our method is better than that by the Konishi＇s et al. method, although both the methods could suppress the traffic jam. The simulation results are consistent with the theoretical analysis.
Recently, a number of efforts are underway to investigate inter-vehicle communications （IVC）. This paper studies the instantaneous information propagation behaviours based on IVC in three different tragic situations （free flow, synchronized flow and stop-and-go waves） in a cellular automaton model. It is shown that different behaviours appear in stop-and-go waves from those in free flow and synchronized flow. While the distribution of Multi-hop Communication Distance （MhCD） is either exponential or uniform in free flow and synchronized flow, the distribution of MhCD is either exponential or with a single peak in stop-and-go waves.
Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries （KdV） equation and the modified Korteweg-de-Vries （mKdV） equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.
Through introducing a generalized optimal speed function to consider spatial position, slope grade and variable safe headway, the effect of slope in a single-lane highway on the traffic flow is investigated with the extended optimal speed model. The theoretical analysis and simulation results show that the flux of the whole road with the upgrade （or downgrade） increases linearly with density, saturates at a critical density, then maintains this saturated value in a certain density range and finally decreases with density. The value of saturated flux is equal to the maximum flux of the upgrade （or downgrade） without considering the slight influence of the driver＇s sensitivity. And the fundamental diagrams also depend on sensitivity, slope grade and slope length. The spatiotemporal pattern gives the segregation of different traffic phases caused by the rarefaction wave and the shock wave under a certain initial vehicle number. A comparison between the upgrade and the downgrade indicates that the value of saturated flux of the downgrade is larger than that of the upgrade under the same condition. This result is in accordance with the real traffic.
