On Zero avoiding Transition Probabilities of an r-node Tandem Queue - a Combinatorial Approach

In this paper we present a simple combinatorial approach for the derivation of zero avoiding transition probabilities in a Markovian r- node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero avoiding transition probabilities.