Technical Note—On the Comparison of Waiting Times inGI/G/1 Queues

Abstract

Let W 1 , W 2 be the distribution functions of the waiting time in two queuing systems. We develop sufficient conditions for the stochastic inequalities W 1 ( x ) ≧ W 2 ( x ) and ∫ 0 ∞ xdW 1 ( x ) ≦ ∫ 0 ∞ xdW 2 ( x ) when both systems are of the type GI / G /1, GI / M /1 or M / G /1.