摘要
In this paper, we compare queueing systems that differ only in their arrivalprocesses, which are special forms of doubly stochastic Poisson (DSP) processes. Wedefine a special form of stochastic dominance for DSP processes which is based onthe well-known variability or convex ordering for random variables. For two DSPprocesses that satisfy our comparability condition in such a way that the first processis more 'regular' than the second process, we show the following three results: (i) Ifthe two systems are DSP/GI/1 queues, then Ef(V1)) Ef(V(2)) for all f increasingconvex, with V('), i = 1 and 2, representing the workload (virtual waiting time) insystem. (ii) If the two systems are DSP/M(k)/1--+/M(k)/1--- --- /M(k)/1 tandem systems, with M(k) representing an exponential service time distributionwith a rate that is increasing concave in the number of customers, k, present at thestation, then Ef(Q(')) 5Ef(Q~2)) for all f increasing convex, with Q('), i = 1 and 2,being the total number of customers in the two systems. (iii) If the two systems areDSP/M(k)/1/N systems, with N being the size of the buffer, then P,) = P(), wherePA) denotes the blocking (loss) probability of the two systems. A model consideredbefore by Ross (1978) satisfies our comparability condition;a conjecture stated byhim is shown to be true.