PROBABILISTIC MODEL OF A SINGLE VEHICLE AND ONE DESTINATION ROUTING PROBLEM AND ITS MONTE CARLO SOLUTIONS

The paper is devoted to a shortest-time routing problem. A decision-maker has to choose one from several possible routes for a vehicle which should reach its destination as soon as possible. The time required to reach the destination depends on the chosen route and the state of traffic flow in the region and is considered as a random variable. Under an assumption that the probability distribution function of the random traffic flow depends on states of the nature which can be reasonably categorized into finite number of classes a game-theoretic approach is proposed and discussed. Then to solve the problem some global optimization procedure combined with Monte Carlo simulations is adopted. Under some additional assumptions about the route time distributions several examples are solved.