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

Part of:Operations research and management scienceStochastic processesSpecial 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

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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, stochastic60G17: Sample path properties

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016, pp. 421 - 433
Copyright
Copyright © Applied Probability Trust 2016 

References

[1]Baharian, G. and Tezcan, T. (2011).Stability analysis of parallel server systems under longest queue first.Math. Meth. Operat. Res. 74, 257–279.Google Scholar
[2]Bramson, M. (2008).Stability of queueing networks.Prob. Surveys 5, 169–345.Google Scholar
[3]Dai, J. G. (1995).On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models.Ann. Appl. Prob. 5, 49–77.CrossRefGoogle Scholar
[4]Dai, J. G. (1999).Stability of fluid and stochastic processing networks. Res. Rep. MPS-misc 1999-9, MaPhySto, University of Aarhus.Google Scholar
[5]Dai, J. G. and Lin, W. (2005).Maximum pressure policies in stochastic processing networks.Operat. Res. 53, 197–218.CrossRefGoogle Scholar
[6]Dai, J. G. and Vande Vate, J. H. (2000).The stability of two-station multitype fluid networks.Operat. Res. 48, 721–744.Google Scholar
[7]Dai, J. G. and Weiss, G. (1996).Stability and instability of fluid models for reentrant lines.Math. Operat. Res. 21, 115–134.Google Scholar
[8]Dimakis, A. and Walrand, J. (2006).Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits.Adv. Appl. Prob. 38, 505–521.Google Scholar
[9]Joo, C., Lin, X. and Shroff, N. (2009).Understanding the capacity region of the greedy maximal scheduling algorithm in multihop wireless networks.IEEE/ACM Trans. Networking 17, 1132–1145.Google Scholar
[10]Kumar, P. R. and Meyn, S. P. (1995).Stability of queuing networks and scheduling policies.IEEE Trans. Automatic Control 40, 251–260.Google Scholar
[11]Kumar, S. and Kumar, P. R. (1996).Fluctuation smoothing policies are stable for stochastic re-entrant lines.J. Discrete Event Dynamic Systems 6, 361–370.CrossRefGoogle Scholar
[12]Kumar, S., Giaccone, P. and Leonardi, E. (2002).Rate stability of stable marriage scheduling algorithms in input-queued switches. In Proc. 40th Annual Allerton Conference on Computers, Communication, and Control, University of Illinois, Urbana-Champaign.Google Scholar
[13]Lu, S. H. and Kumar, P. R. (1991).Distributed scheduling based on due dates and buffer priorities.IEEE Trans. Automatic Control 36, 1406–1416.CrossRefGoogle Scholar
[14]Malyshev, V. A. (1993).Networks and dynamical systems.Adv. Appl. Prob. 25, 140–175.Google Scholar
[15]McKeown, N. (1995).Scheduling algorithms for input-queued cell switches. Doctoral Thesis, University of California, Berkeley.Google Scholar
[16]Plemmons, R. J. (1977).M-matrix characterizations. I. Nonsingular M-matrices.Linear Algebra Appl. 18, 175–188.CrossRefGoogle Scholar
[17]Stolyar, A. L. (1995).On the stability of multiclass queueing networks: a relaxed sufficient condition via limiting fluid processes.Markov Process. Relat. Fields 1, 491–512.Google Scholar
[18]Tassiulas, L. and Ephremides, A. (1992).Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks.IEEE Trans. Automatic Control 37, 1936–1948.CrossRefGoogle Scholar
[19]Tassiulas, L. and Ephremides, A. (1993).Dynamic server allocation to parallel queues with randomly varying connectivity.IEEE Trans. Inf. Theory 39, 466–478.Google Scholar
[20]Yang, J. and Hu, Y. (2015).Stability of Kumar–Seidman networks under longest queue first policy.J. Systems Sci. Complexity 28, 848–856.Google Scholar