Two Way Selection Traffic Flow: Mean Field Theory

Bing-Hong Wang, P.M. Hui, , Chin-Kun Hu 3 1Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei 230026, China Email: [email protected] 2 Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong Email:[email protected] 3 Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan Email: [email protected] Using a simple route choice traffic scenario, Ref. [1] studied the influence of dynamical information on the stability of traffic patterns. In order to understand home possible effect of information for traffic controlling, in this paper, we propose and study the mean field theory of route choice decision traffic flow. Suppose that there are two routes A and B with the same number of cells L. Every time step a road user enters the system and has to chose one route. Two different types of vehicles are considered: “normal” ones and the so-called floating cars (FCs). When leaving the system, FCs can transmit their travel times to a board visible to every vehicle. Hence FCs generate dynamic traffic information which is the basis for the route decisions of new car entering the system. The number of FCs is represented by the variable sFC . The road users are divided as static and dynamic types. Static drivers ignore the dynamic information and select route at random. Dynamic drivers receive the information displayed on the board and always choose the route with the shortest travel time, i.e. they behave “rational”. If the travel time on both routes is the same, the route is chosen randomly. The number of dynamic drivers is represented by the variable sdyn. After the route choice both kinds of vehicles behave in the same way. All the cars move ahead along the chosen lane according to Fukui-Ishibashi (FI) traffic flow cellular automaton model [2]. To adopt FI model instead Nagel-Schreckenberg (NS) model is due to the convenience of presenting analytical approach