Finding the Best QoS Path in a Gilbert Channel Network

Many different types of modern wired and wireless communication links can be mathematically described as discrete- time Gilbert channels. In this extended abstract, we present an exact method of calculating the best path in a network of discrete- time Gilbert channels, each of which is defined as a Markov chain with two states. In the "Good" state of the chain, the channel produces no erasure, and in the "Bad" state of the chain, the channel produces an erasure. Our method relies on a modified version of the Dijkstra\´s algorithm, which we customize to operate on sets of Gilbert channel parameters, instead of real numbers. We prove that the Gilbert channels obeys a certain set of algebraic properties which makes it compatible with our algorithm.