On homogeneity in M/G/1 queueing systems

Operational analysis replaces certain classical gueueing theory assumptions with the condition of “homogeneous service times.” In this paper, we show that the sample paths of an M/G/1 queueing system have this property with non-zero probability if and only if the service time distribution is exponential. We also consider the relationship of the operational performance measures S(n) and the mean service time. This relationship is shown to depend on the form of the service distribution. It follows that using operational analysis to predict the performance of an M/G/1 queueing system when the mean service time is changed will be most successful when the service time distribution is exponential. Simulation evidence is presented which supports this claim.