Minimax end-to-end delay routing and capacity assignment for virtual circuit networks

We consider the routing and capacity assignment problem for virtual circuit networks where the objective is to minimize the maximum end-to-end packet delay. Compared with traditional aggregate type of performance measures, such as the average packet delay, this performance measure is consistent with those of many new services and achieves better fairness among users. Two cases are considered. In the first case, the capacity assignment is assumed to be given and the routing strategy is to be determined. The problem is formulated as a nonlinear nonconvex multicommodity network flow problem with integer routing decision variables. A dual approach is proposed to calculate primal feasible solutions. The proposed algorithm is computationally shown to uniformly outperform a greedy heuristic and a linear programming relaxation approach in conjunction with a rounding scheme. The algorithm also calculates legitimate lower bounds on the optimal objective function value, which are not easily attainable using the linear programming relaxation approach due to the nonconvex nature of the problem. In the second case, we consider the joint routing and capacity assignment problem. The problem is formulated as a nonlinear nonconvex mixed integer programming problem. We develop a two-phase algorithm where the routing and the capacity assignment decision variables are optimized, respectively. A minimum-hop heuristic is used to calculate the routing assignment, and then a convex programming procedure is devised to solve the capacity assignment problem. Experimental results of this heuristic and comparison with the results of the first case are presented.