SUPERCOMPUTER SIMULATION OF VEHICULAR TRAFFIC BASED ON QGD SYSTEM OF EQUATIONS
Abstract
The paper is devoted to the problem of modeling traffic flows under the macroscopic ap-proach. In this approach the continuous medium approximation is used, i.e. traffic is represented as compressible fluid flow; the main studied flow characteristics are density and average velocity of cars. The model based on the quasigasdynamic (QGD) system of equations is proposed in the work. The one-dimensional QGD model of vehicular flow is governed by the system of two equations: the continuity equation for density and the momentum conservation equation for average flow velocity. The equations include terms responsible for the “human factor” – the ability of drivers to accelerate and decelerate depending on traffic conditions, in particular, on the flow density in front of them. In the right-hand sides of the equations there are terms describing possible sources in the case of entry or exit or in case of changing the number of lanes. The equations also contain diffusion terms in the right-hand sides to provide the solution smoothing at distances of the order of the medium reference scales. A small parameter is introduced having the sense of the reference time that is the time interval for which several cars are crossing a given point on the road. Despite the one-dimensionality the model allows describing traffic on multi-lane roads and complex junctions qualitatively correctly, while the computation process is simplified greatly, saving computing resources. To approximate differential equations explicit two-level difference schemes of the second order on space were used. The algorithm for parallel computing is proposed on the basis of geometrical parallelism; high speed-up values are obtained. To verify the model a number of test predictions were performed; the results agreed with data obtained by other researchers. In the one-dimensional statement the next problems have been solved: the problem of rush hour traffic on a road with a side entry, the problem of traffic on the clover junction as well as the problem of the effect of the traffic light phases’ dura-tion on the appearance and dynamics of density jumps in a vicinity of the traffic light. Traffic model-ing on a real section of the Moscow city road network has been also fulfilled.
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