Structured Markov Chains Arising from Finite-Source Retrial Queues with Orital Search

We consider retrial queueing systems with a finite number of homogeneous sources of calls, a single reliable server, and the search for orbiting customers by the server after job completion. During this investigation, the infinitesimal generator of the underlying (finite) continuous-time Markov chain takes a (level-dependent) QBD-like form. After solving for the steady state probabilities using the MOSEL-2 tool, the results show a surprising maximum of the mean response time. This maximum was already discovered by other researchers dealing with finite-source retrial queues. However, to our best knowledge, no thorough investigation was done yet why this maximum exists and in which way it depends on the system parameters. In the talk, after introducing the backgrounds of finite-source retrial queues with orbital search, a generalized stochastic Petri net is used to derive the underlying continuous-time Markov chain and its generator. Finally, using the seminar, we can hopefully bring forward discussions how to make more general statements on the parameter-dependent behavior of the response time’s maximum.