In:
Advances in Applied Probability, Cambridge University Press (CUP), Vol. 23, No. 1 ( 1991-03), p. 210-228
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.
Type of Medium:
Online Resource
ISSN:
0001-8678
,
1475-6064
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1991
detail.hit.zdb_id:
1474602-5
Permalink