Modelling M/G/1 queueing systems with server vacations using stochastic Petri nets

The theory of non-Markovian stochastic Petri nets is employed in this paper to derive an alternative method for studying the steady state behaviour of the M/G/1 vacation queueing system with a limited service discipline. Three types of vacation schemes are considered, and systems with both a finite population and those with an infinite population (but finite capacity) are considered. Simple numerical examples are also provided to illustrate the functionality of the methods and some useful performance measures for the system are obtained.