Approximation of the road segments travel time using Levy distributions in the reliable shortest path problem

Abstract

The current trend towards an increase in the number of vehicles, especially in large cities, as well as the unavailability of the existing road infrastructure to distribute modern traffic flows leads to a higher congestion level in transportation networks. This problem emphasized the relevance of navigation problems. Despite the popularity of these problems, many existing commercial systems consider only deterministic networks, not taking into account the time-dependent and stochastic properties of traffic flows. In this paper, we consider the reliable shortest path problem in a time-dependent stochastic transportation network. The considered criterion is maximizing the probability of arriving at the destination point on time. We consider the base algorithm for the stochastic on-time arrival problem, which has a computationally complex convolution operation for calculating the arrival probability. We propose to use parametrically defined Levy stable probability distributions to describe the travel time of road segments. We show, that the use of stable distributions allows us to replace the convolution operation with the distribution value, and significantly reduces the execution time of the algorithm. Experimental analysis has shown that the use of stable distributions allows approximating the exact value of the arrival probability at a destination with a low approximation error.