Stochastic Models of Traffic Management

Anton S. Aleshkin


This article discusses the problem of blocking nodes in road networks and percolation thresholds for the transport infrastructure of a modern metropolis. For metropolitan networks, the values of percolation thresholds are calculated and displayed, considering the different density of connections between network nodes. Further, it is shown that the dependence of the values of the percolation thresholds on the network’s density can be described by functional dependencies with a high degree of correlation.

The obtained results can be used to assess the reliability of transport infrastructure and to check the increase in the capacity of selected sections of the road network.

Further, the article discusses obtaining a description of road infrastructure from open sources (obtaining data from OpenStreetMap using the SUMO - Simulation of Urban MObility package), after which it is possible to build a graph of the road network and determine its percolation properties. For the constructed nodes of the graph described a model of the stochastic dynamics of blocking a single road lane in the transport network.

The threshold value L of number of cars that can be placed in the lane (based on the length of the road lane) is used as constraints and the incoming and outgoing flows of cars are also determined as income parameters of a model. The constructed model allows us to obtain the predicted blocking time of a road network line, for a given probability of such blocking, where the probability of blocking a single road network line is taken from the percolation properties of this network discussed earlier.

The resulting blocking times of road network nodes make it possible to build an algorithm for controlling traffic light regulation.

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