Turning Back Time—What Impact on Performance?

Consistent with the divide-and-conquer approach to problem solving, a recursive result is presented in the domain of stochastic modelling that derives product-form solutions for the steady state probabilities of certain networks composed from interacting Markov chains. Practical applications include multi-tasking operating systems, communication channels and multi-tiered storage systems. The approach is also applied to the computation of response time quantiles, which are vital in transaction processing, computer communication service level agreements and other operational systems. The joint probability distribution of the sojourn times of a tagged task at each node in a network is determined by noting that this is the same in both the forward and reversed processes. In this way, existing results for response time probability densities in tandem, tree-like, and overtake-free Markovian queueing networks are quickly and systematically obtained. We further show how to apply the method in more general networks.