A Universal Me Solution for an M/g/1 Queue with Vacation Periods

In this paper the information theoretic principle of Maximum Entropy (ME) is applied, as a method of inference, towards the study of the M/G/1 queueing model at equilibrium with either single or multiple server vacation periods under both exhaustive and non-exhaustive scheduling schemes. An analytic ME approximation for the characterisation of a universal form for the queue length distribution of the M/G/1 queue is derived, based on mean queue length value constraints and the decomposition property of queueing systems with server vacation. Moreover, the particular form of the ME solution in some special cases of vacation schemes is also determined. An exhaustive validation study of the credibility of the ME solution against simulation is included together with suggestions towards the approximate analysis of queueing networks with server vacations.