Least cost routing in multi-service networks. II

In Part I, we proposed a distributed, state dependent, dynamic routing method, called least cost routing in multi-service networks (LCRM), for multirate circuit-switched broadband ISDN networks, which support a variety of traffic classes with different characteristics. This method represents the one-step policy improvement on a chosen base policy. As a base policy π₀, we use the policy which allows direct link routing only. The policy π₀ also requires that each call class has a portion of link bandwidth dedicated to it. The task is to find an efficient computational way to obtain the corresponding relative cost values, which represent costs of routing a call over one link. We consider the one-link model with two types of traffic. Our main result is that the system of linear equations associated with the two-dimensional Markov chain can be decomposed into several systems of linear equations, each one associated with the one-dimensional Markov chain