On computing Markov decision theory-based cost for routing in circuit-switched broadband networks

Abstract

In this paper, we study the problem of dynamic routing in multi-service circuitswitched networks. In a previous work, we have proposed a distributed, state dependent, dynamic routing method, called Least Cost Routing in Multi-Service Networks (LCRM), for multirate circuit-switched networks. Broadband Integrated Services Digital Networks (BISDN) should be capable of supporting a variety of traffic classes (e. g. data, voice, video, facsimile), each of which has its own traffic requirement (bandwidth requirement, call arrival rate, and call holding time) and reward parameter. The LCRM method is obtained through the policy iteration routine of Markov decision theory. It represents a one-step policy improvement on a base policy π0, with direct link routing only. The policy π0 also requires that each call class has a portion of link bandwidth dedicated to it. In this paper, we look for an efficient computational way to obtain the corresponding relative cost values, which represent the cost of routing a call over one link. We consider the one-linke model with two types of traffic. We show that the system of linear equations associated with the two-dimensional Markov chain can be decomposed into a system of linear equation associated with the one-dimensional Markov chain. Examples with two classes of service are presented.