Minmax latency flow on the general network

Abstract

In minmax latency problem, one tries to assign link flows to minimize the maximum route travel time. In this paper, we formulate minmax latency problem from a single origin to multiple destinations on a general transportation network as a convex optimization problem and suggest a solution algorithm based on the deflected subgradient method. We derive its first-order optimality condition and show that there are marginal route cost fairness between route with positive flow. We test the proposed algorithm for small scale network having 24 nodes and 76 arcs and compare its solution with the user-optimal traffic assignment solution. We found that loading flows on every route does not improve maximum latency, so that when one applies the proposed model to evacuation planning, the computation of the minmax latency route is critical to reduce the maximum latency.