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

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.