Optimal Distribution of Traffic in Manhattan Road Networks for Minimizing Routing-Time

In a natural disaster, when there is a sudden rush in vehicle movement from dense residential areas of a city towards some designated evacuation centers, traffic needs to be distributed along the road network in an optimal way so as to minimize the travel time for reaching those evacuation centers. We address this traffic distribution problem in a
$k \times k$
Manhattan road network with multiple traffic generating sources and a single fixed destination (sink) at a corner point. We first consider queuing delay at each grid point along with a fixed link delay. We then extend our idea to consider a rectangular grid and also real-life road networks where some of the links may be absent. We present a traffic distribution algorithm that would minimize the average time of all vehicles to reach the given destination point. Simulation of our algorithm using SUMO on the grid-structured road map of Manhattan borough in New York city and also on a part of non-grid road map of city of Carbondale, IL USA shows a much shorter average travel time compared to the existing popular algorithms based on dynamic traffic assignments (DTA). The proposed technique is also robust in the sense that even with 20% deviation from optimal assignment of traffic distribution at cross-points, we get significantly better results compared to the existing traffic distribution policies. We then propose a congestion control technique based on detouring of vehicles and show how variable link delay as a function of the volume of traffic flow through a link can be incorporated in our traffic distribution policy. Finally, we show how to extend our technique to consider a scenario with the destination point being anywhere on the grid, instead of being at the corner point.