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.