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Exact-Order Asymptotic Analysis for Closed Queueing Networks

Part of: Operations research and management science Computer system organization Special processes

Published online by Cambridge University Press:  04 February 2016

David K. George ,
Cathy H. Xia  and
Mark S. Squillante
David K. George*
Affiliation:
The Ohio State University
Cathy H. Xia*
Affiliation:
The Ohio State University
Mark S. Squillante*
Affiliation:
IBM Thomas J. Watson Research Center
*
∗ Postal address: Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43201, USA.
∗ Postal address: Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43201, USA.
∗∗∗∗ Postal address: Mathematical Sciences Department, IBM Thomas J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA. Email address: mss@us.ibm.com
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Abstract

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In this paper we study the asymptotic behavior of a general class of product-form closed queueing networks as the population size grows large. We first characterize the asymptotic behavior of the normalization constant for the stationary distribution of the network in exact order. This result then enables us to establish the asymptotic behavior of the system performance metrics, which extends a number of well-known asymptotic results to exact order. We further derive new, computationally simple approximations for performance metrics that significantly improve upon existing approximations for large-scale networks. In addition to their direct use for the analysis of large networks, these new approximations are particularly useful for reformulating large-scale queueing network optimization problems into more easily solvable forms, which we demonstrate with an optimal capacity planning example.

Keywords

Closed queueing networklarge populationasymptotic analysisexact-order asymptoticsapproximation methods

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 503 - 520
Copyright
© Applied Probability Trust 

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