Keywords: vehicular traffic flow, macroscopic and microscopic models, multilane traffic.

The paper deals with the simulation of vehicular traffic flows. There are two basic types of the traffic flow models [1]. In the so-called "microscopic" models vehicles are treated as separate particles, which interact according to certain laws. The other model type is called "macroscopic" or hydrodynamical. This treats traffic flows as slightly compressible fluids, without taking into account separate vehicles.

Most of the present models are one-dimensional and do not account for parameter distribution across the road. The paper is dedicated to the development of original two-dimensional macro- and microscopic models of multi-lane traffic to predict flows for the real road geometry [2].

The macroscopic model describes synchronized traffic: distances between vehicles are comparable with vehicle sizes. With this condition it is possible to use the continuum approach and derive equations similar to the gas dynamics equations namely the quasi-gas-dynamic (QGD) system of equations [3]. Additional mass fluxes guarantee solution smoothness on the reference distances. Contrary to the earlier traffic flow models, the variable transverse velocity is introduced. The traffic flow equations differ from the gas dynamic equations, since the former include the terms accounting for the human will. Numerical implementation is based on approximations with second order conservative explicit finite-difference schemes.

The proposed microscopic model is based on the cellular automata theory. This type of model is the most promising for more detailed description of local road situations for short distances. In this case the computational domain is a two-dimensional grid. Each cell may or may not contain one particle, representing a car. The particle movement is performed under special laws incorporating stochastic observations. The particles are equivalent and comply with the same laws.

Both macroscopic and microscopic models have been improved to simulate multiphase traffic flows, while a phase is a group of vehicles with identical features.

A large number of test predictions have been performed: traffic jam evolution on the road, the traffic flow on multilane roads with entries and exits, the flow on the road with a local widening, multiphase flows. The results obtained demonstrated good agreement of the models in both qualitative and quantitative senses.

1

A. Klar, R. Wegener, "A hierarchy of models for multilane vehicular traffic I: Modeling", SIAM J. Appl. Math., 59, 983-1001, 1999. doi:10.1137/S0036139997326946

2

A.B. Sukhinova, M.A. Trapeznikova, B.N. Chetverushkin, N.G. Churbanova, "Two-Dimensional Macroscopic Model of Traffic Flows", Mathematical Models and Computer Simulations, 1(6), 669-676, 2009. doi:10.1134/S2070048209060027

3

B.N. Chetverushkin, "Kinetic schemes and Quasi-Gas Dynamic system of equations", CIMNE, Barcelona, 2008.

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