Path-additive Functions in Stochastic Flow Networks with Markovian Routing

1.1. Rationale The Jackson network [1] is a basic model favored as a useful beginning approach to many queueing network problems. Its appeal stems from not only its product-form solution for the joint distribution of the number of customers in each queue but also from the simplicity of the structures of the model. Markovian routing is one such structure. The purpose of this paper is to study some ramifications of Markovian routing in a flow network that need not be a Jackson network, principally so that a method can be devised to compute crossnetwork values of phenomena whose values on single links are known. The main result is a simple equation for path-additive functions in a flow network in equilibrium (not necessarily a Jackson network) that has Markovian routing. We use this equation to compute latency and jitter in telecommunications packet networks. The class of flow networks we consider includes open queueing networks as well as generalizations of flow networks of the type introduced by Ford and Fulkerson [2].