Response time calculations in stochastic networks - e.g. queueing networks - are usually developed in terms of sample path analyses beginning in an equilibrium state. We consider the joint probability distribution of the so journ times of a tagged task at each node in a network and observe that this is the same in both the forward and reversed processes. Therefore if the reversed process is known, each node-so journ time can be taken from either process. In particular, the reversed process can be used for the first node in a path and the forward process for the other nodes in a recursive analysis. This approach derives, quickly and systematically, existing results for response time probability densities in tandem, open and closed tree-like, and overtake-free Markovian networks of queues. We also show how to apply the method in stochastic networks that are more general than queueing systems. An example is constructed to illustrate this, which has separable equilibrium state probabilities, a new product-form result in its own right.
Information from pubs.doc.ic.ac.uk/UKEPEW2008.