Author:
Chang Cheng-Shang,Chao Xiu Li,Pinedo Michael
Abstract
In this paper, we compare queueing systems that differ only in their arrival processes, which are special forms of doubly stochastic Poisson (DSP) processes. We define a special form of stochastic dominance for DSP processes which is based on the well-known variability or convex ordering for random variables. For two DSP processes that satisfy our comparability condition in such a way that the first process is more ‘regular' than the second process, we show the following three results: (i) If the two systems are DSP/GI/1 queues, then for all f increasing convex, with V(i), i = 1 and 2, representing the workload (virtual waiting time) in system. (ii) If the two systems are DSP/M(k)/1→ /M(k)/l ∞ ·· ·∞ /M(k)/1 tandem systems, with M(k) representing an exponential service time distribution with a rate that is increasing concave in the number of customers, k, present at the station, then for all f increasing convex, with Q(i), i = 1 and 2, being the total number of customers in the two systems. (iii) If the two systems are DSP/M(k)/1/N systems, with N being the size of the buffer, then where denotes the blocking (loss) probability of the two systems. A model considered before by Ross (1978) satisfies our comparability condition; a conjecture stated by him is shown to be true.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
39 articles.
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