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

Let W₁, W₂ be the distribution functions of the waiting time in two queuing systems. We develop sufficient conditions for the stochastic inequalities W₁(x) ≧ W₂(x) and ∫₀^∞xdW₁(x) ≦ ∫₀^∞xdW₂(x) when both systems are of the type GI/G/1, GI/M/1 or M/G/1.