On optimal routing with multiple traffic matrices

Routing optimization is used to find a set of routes that minimizes cost (delay, utilization). Previous work has addressed this problem for the case of a known, static end-to-end traffic matrix. In the Internet, it is difficult to accurately estimate a traffic matrix, and the constantly changing nature of Internet traffic makes it costly to maintain optimal routing by responding to traffic changes. Thus, it is of interest to maintain a set of routes that are "good" for a number of different possible traffic scenarios. In this paper, we explore ways to find an optimal set of routes with multiple traffic matrices to minimize expected cost. We focus on two general approaches, source-destination routing and destination routing. In the case of source-destination routing, we extend existing methods with a single traffic matrix to solve the optimization problem with multiple traffic matrices: we extend the convex optimization solution methods for a single traffic matrix to the multiple traffic matrix case; we also extend the gradient-based solution methods for a single traffic matrix to the multiple traffic matrix case. However, the multiple traffic matrix case requires many more control variables. In the case of destination routing, we encounter many more differences from the single traffic matrix case. The loop-free property, which is valid for the single traffic matrix case, is no longer valid for the multiple traffic matrix case, and it is difficult to extend existing methods for a single traffic matrix to solve the optimization problem with multiple traffic matrices. We show that it is NP-complete even to determine the feasibility of multiple traffic matrices. We thus propose and evaluate a heuristic algorithm for this case.