A maximum entropy analysis of the single server queue

Demanding a certain structural property, derived by applying the principle of maximum entropy to single server systems, from the equilibrium-queue-length distribution of the M/G/1 system leads to the generalized exponential (GE) service time distribution. The G/GE/1 queue is analysed by means of spectrum factorization of Lindley´s integral equation. We obtain explicit expressions for a job´s waiting time and sojourn time distribution, and for the equilibrium-queue-length distribution seen by an arriving job as well as seen at an arbitrary instant of time; the last one satisfies the structural property for arbitrary arrival processes. Moreover, the G/GE/1 queue can play a central role in the maximum entropy analysis of general open queueing networks with FCFS single server stations