Further Stochastic Order Relations among GI/GI/1 Queues with a Common Traffic Intensity

Abstract

Using two relations between virtual and actual waiting time distribution, it is shown that the stationary waiting times in GI/GI/1 queues, where both service and inter-arrival time distributions are of type 1SFBUE, are stochastically smaller than in M/M/1 with the same traffic intensity. Furthermore, a relation between virtual waiting time and distribution of number of customers m system is discussed.Finally, using a result of Köllerström a bound for the stationary waiting time distribution being a rational function is given, and it is shown that the coefficient of variation of stationary waiting times is greater than one.

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