New Linear Program Performance Bounds for Closed QueueingNetworks

Authors:
J. R. Morrison;P. R. Kumar
Affiliations:
University of Illinois, Coordinated Science Laboratory, 1308 West Main Street, Urbana, Illinois 61801, USA;University of Illinois, Coordinated Science Laboratory, 1308 West Main Street, Urbana, Illinois 61801, USA Web: black.csl.uiuc.edu/~prkumar
Venue:
Discrete Event Dynamic Systems
Year:
2001

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Abstract

We develop new linear program performance bounds for closed reentrantqueueing networks based on an inequality relaxation of the averagecost equation. The approach exploits the fact that the transitionprobabilities under certain policies of closed queueing networksare invariant within certain regions of the state space. Thisinvariance suggests the use of a piecewise quadratic functionas a surrogate for the differential cost function. The linearprogramming throughput bounds obtained are provably tighter thanpreviously known bounds at the cost of increased computationalcomplexity. Functional throughput bounds parameterized by thefixed customer population N are obtained, alongwith a bound on the limiting throughput as N \to + \infty.We show that one may obtain reduced complexity bounds while stillretaining superiority.