The paper deals with mathematical modeling of traffic flows on urban road networks. The original model is based on the cellular automata theory and presents a generalization of Nagel-Schreckenberg model to a multilane case.Numerical realization of the model is represented in a form of the program package that consists of two modules: User Interface and Visualization module (for setting initial conditions and modelling parameters and visual representation of calculations) and Computation module (for calculations).Computations are carried out for each element of the road (i.e. T or X type intersection, straight road fragment) separately and in parallel, that allows performing calculations on various complex road networks. Different kinds of average characteristics (e.g. the capacity of the crossroad) can be also obtained using the program package.

The paper deals with mathematical modelling of traffic flows on urban road networks using cellular automata theory. Two versions of the model based on Nagel-Schreckenberg traffic flow model were created. They both are multilane, include complex driver behaviour algorithms and allow simulating traffic on various road elements and on road networks. One of the models is using "slow-to-start" concept that represents the fact that it takes drivers more time to accelerate when they just start moving in comparison with the situation when their speed is already above zero. The goal of the work was to reproduce experimental spatio-temporal patterns on traffic velocity diagrams with the created models and to research the difference between them and to determine the range of the applicability for each. Parallel algorithms of realisation for the models are created. Computations are carried out for each element of the road (T or X type intersection, on-ramp, road fragment with widening or bottleneck, straight road fragment, etc.) separately and in parallel, that allows performing calculations on various complex road networks. Different kinds of average characteristics (such as, for instance, the capacity of the crossroad) can be also obtained using the created program package. Computations show that the results obtained are in an agreement with experimental data and therefore can be used for practical traffic flow modelling in cities.

The research deals with the creation of mathematical tools for the simulation of vehicular traffic flows on complex urban transport networks using modern supercomputers. The goal of the present paper is further development of micro-and macroscopic models created by the authors earlier. The proposed 2D microscopic model is based on the cellular automata theory. In this work algorithms taking into account various driving strategies have been incorporated into the model. The model is implemented as a program package that includes User interface and Visualization module. The macroscopic model uses the continuous medium approximation: it is constructed by analogy with the quasigasdynamic system of equations. The one dimensional version is proposed in the paper, nevertheless, it allows reproducing changes in the number of lanes as well as possible road entrances and exits. Parallel algorithms adapted to high-performance computing systems have been created for both models, ensuring rapid computations on city road networks.

Abstract. The paper deals with the mathematical modeling of traffic flows on urban road networks using microscopic approach. The model is based on the cellular automata theory and presents a generalization of the Nagel-Schreckenberg model to a multilane case. The created program package allows to simulate traffic on various types of road fragments (T or X type intersection, strait road elements, etc.) and on road networks that consist of these elements. Besides that, it allows to predict the consequences of various decisions regarding road infrastructure changes, such as: number of lanes increasing/decreasing, putting new traffic lights into operation, building new roads, entrances/exits, road junctions.

The work is devoted to the development of new algorithms describing the complex interaction of drivers for the parallel numerical implementation of the traffic flow model developed by the authors based on the cellular automata theory. As is known from observations, the behaviour of drivers largely determines how difficult it will be to pass a section with a bottleneck (a narrowing, a motionless obstacle, etc.) or even without it at the same flow values. In such conditions, cars can move in a synchronized flow at a more or less constant speed or go into “stop-and-go” mode. The authors have developed a set of algorithms for a large number of different road situations, which is featured in this article.