A New Multiplier Adjustment Procedure for the Distributed Computation of Routing Assignments in Virtual Circuit Data Networks

Abstract

In this paper, the routine problem in virtual circuit networks is considered. In virtual circuit networks, all of the packets in a session are transmitted over exactly one path established between the origin and the destination. We consider the problem of choosing a path for each origin-destination pair so as to minimize the average number of packets in the network. We consider the formulation of this problem as a nonlinear multicommodity flow problem with integer decision variables. The emphasis of this work is to develop a distributed algorithm to solve this optimization problem. The basic approach is Lagrangean Relaxation. We introduce a new multiplier update rule which facilitates the solution of the nonlinear integer programming problem using distributed computation. In computational experiments, our proposed distributed algorithm determines solutions that are within 1% of an optimal solution in less than 2 minutes of CPU time for networks with 26 to 61 nodes. In addition, the proposed multiplier adjustment procedure provides better bounds and is less sensitive to the algorithm parameters than the subgradient method. An analysis of the communication delays of the control messages needed to support a distributed implementation is given. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.