Stochastic Path Finding under Congestion

Abstract

Most of the path planning algorithms use the edge weights in order to select the best path for navigation from an origin point to a specific target. This research focuses on the case where the edge weights are not fixed. Depending on the time of day/week, edge weights may change due to the congestion through the network. The best path is the path with minimum expected cost. The cost is typically travel time which is highly dependent on the level of congestion in the network. Minimizing the costs helps in reducing traffic in the city, alleviates air pollution, and reduces fuel consumption. For modelling cost functions, we consider three possible cost functions (linear, exponential, and step cost functions) in order to model realistic goals. The interpretation of best path depends on the point of view of car drivers. We model two different goals: 1) drivers who desire the path with the highest probability of reaching the destination before the deadline while minimizing waiting time at the destination and 2) the drivers who desire the best time slot to leave in order to meet the deadline and have a shortest travel time. Our findings show that using a realistic path planning algorithm which satisfies users' goals and picks the least congested path is a cost efficient option.