Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks
J. George Shanthikumar, David D. Yao
Operations Research · 1987 · Volume 35 · Issue 4
Abstract
We study a Gordon-Newell type of closed queueing network that frequently arises in modeling manufacturing and computer systems. We are concerned with the transient and equilibrium behavior of the joint and individual queue lengths in the network when the job population increases. We show that increasing the job population will stochastically increase the queue-length vector process, provided that all stations have nondecreasing service rates. Single and multivariate likelihood ratio orderings are also established for the joint queue lengths in equilibrium. Our results extend the applicability of previously known results in the literature.
Keywords
697 closed queueing network, 706 stochastic monotonicity
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