Distributed algorithm for traffic dissemination in manhattan networks with optimal routing-time

We consider the problem of traffic routing in a road network in the event of a disaster, when there is a surge in vehicle movement from dense residential areas to designated safe-shelters. We address the problem with multiple sources and a fixed sink in a k × k Manhattan grid road network to find a traffic distribution over the network such that the average time of travel from sources to sink is minimized. We consider queuing delay at each grid point of the Manhattan network when multiple grid points can become potential sources of new traffic generation, and then propose an optimal traffic distribution algorithm to minimize the total queuing delay of all vehicles to reach the given destination point. We then extend our technique to consider variable link delay (as a function of the volume of traffic flow through a link) along the links of the network.