Evsey Morozov (Karelian Research Centre, Russia)

Regenerative queues: stability analysis and simulation

We present a general approach to stability of regenerative queueing systems, which is based on the properties of the embedded renewal process of regenerations. Such a process obeys a useful characterization of the limiting remaining renewal time allowing in many cases to establish minimal stability conditions by a two-step procedure. At first step, a negative drift condition is used to prove that the basic process does not go to infinity (in probability), and at the second step, the finiteness of the mean regeneration period is proved. This approach has lead to the effective stability analysis of some models describing, in particular, such modern telecommunication systems as retrial queues and queues with optical buffers.

Moreover, we discuss regenerative simulation method including both classical and non-classical (extended) regeneration allowing a dependence between regeneration cycles.