REGENERATIVE QUEUEING PROCESSES

    Evsey Morozov, Petrozavodsk State University


We discuss the notion regeneration with applications to the
basic stochastic processes describing queueing systems and
networks. These processes are usually too complex to be
studied by the i.i.d. techniques only. The main idea of the
regenerative approach is to detect  so-called regeneration
points when the process under investigation starts anew (in
probabilistic sense). Such points generate i.i.d. regeneration
cycles (the parts of trajectory between these points), and it
gives solid basis that the classical methods may be applied.

To explain this idea we show typical regenerative processes
in a separate queueing node and in a network. Moreover, we
discuss briefly the so-called weak regeneration which is the
natural extention of the classic one and often more suitable
for complex networks. Some statistical properties of
regenerative processes are considered too.