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Concavity of queueing systems with NBU service times

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

Published online by Cambridge University Press:  01 July 2016

Rajendran Rajan  and
Rajeev Agrawal
Rajendran Rajan*
Affiliation:
IBM
Rajeev Agrawal*
Affiliation:
University of Wisconsin-Madison
*
∗ Postal address: IBM T.J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA. Email address: [email protected]
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691, USA. Email address: [email protected]
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Abstract

This paper establishes structural properties for the throughput of a large class of queueing networks with i.i.d. new-better-than-used service times. The main result obtained in this paper is applied to a wide range of networks, including tandems, cycles and fork-join networks with general blocking and starvation (as well as certain networks with splitting and merging of traffic streams), to deduce the concavity of their throughput as a function of system parameters, such as buffer and initial job configurations, and blocking and starvation parameters. These results have important implications for the optimal design and control of such queueing networks by providing exact solutions, reducing the search space over which optimization need be performed, or establishing the convergence of optimization algorithms. In order to obtain results for such disparate networks in a unified manner, we introduce the framework of constrained discrete event systems (CDES), which enables us to characterize any permutable and non-interruptive queueing network through its constraint set. The main result of this paper establishes comparison properties of the event occurrence processes of CDES as a function of the constraint sets, which are then translated into the above-mentioned concavity of the throughput as a function of system parameters in the context of queueing networks.

Keywords

Queueing networksnew-better-than-usedthroughputmonotonicityconcavitydiscrete parameter optimizationwork-in-progressbuffer allocationtimed discrete event systemsgeneralized semi-Markov processes

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M10: Network design and communication 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 551 - 567
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Research supported in part by NSF Grant No. NCR-9305018.

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