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Stability of multiclass queueing networks under longest-queue and longest-dominating-queue scheduling

Part of: Operations research and management science Special processes Stochastic processes

Published online by Cambridge University Press:  21 June 2016

Ramtin Pedarsani  and
Jean Walrand
Ramtin Pedarsani*
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
* Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
* Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
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Abstract

We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routeing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routeing decisions at the queues are independent, stationary, and ergodic. A scheduling policy is called robust if it does not depend on the arrival and service rates nor on the routeing probabilities. A policy is called throughput-optimal if it makes the system stable whenever the parameters are such that the system can be stable. We propose two robust policies: longest-queue scheduling and a new policy called longest-dominating-queue scheduling. We show that longest-queue scheduling is throughput-optimal for two groups of two queues. We also prove the throughput-optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.

Keywords

Stabilitylongest-queue schedulingqueueing networkfluid model

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B15: Network models, stochastic 60G17: Sample path properties
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 421 - 433
Copyright
Copyright © Applied Probability Trust 2016 

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