Maximizing the probability of arriving on time

Abstract

We study the problem of maximizing the probability of arriving on time in a stochastic network. Nodes and links in the network may be congested or uncongested, and their states change over time and are based on states of adjacent nodes. Given a source, destination, and time limit, the goal is to adaptively choose the next node to visit to maximize the probability of arriving to the destination on time. We present a dynamic programming solution to solve this problem. We also consider a variation of this problem where the traveler is allowed the option to wait at a node rather than visit the next node. For this setting, we identify properties of networks for which the optimal solution does not require revisiting nodes. © 2013 Springer-Verlag.