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Stability of Processor Sharing Networks with Simultaneous Resource Requirements

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jennie Hansen ,
Cian Reynolds  and
Stan Zachary
Jennie Hansen*
Affiliation:
Heriot-Watt University
Cian Reynolds*
Affiliation:
Heriot-Watt University
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗ Postal address: Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
∗ Postal address: Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
∗ Postal address: Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
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Abstract

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We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through poor control, and that, for a variety of network topologies, only small modifications to controls are required in order to ensure stability. For controls which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability.

Keywords

Processor sharing networkstabilityentrainment

MSC classification

Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K25: Queueing theory

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 636 - 651
Copyright
Copyright © Applied Probability Trust 2007 

References

Asmussen, S. (2003). Applied Probability and Queues. Springer, New York.Google Scholar
Bonald, T. and Massoulié, L. (2001). Impact of fairness on Internet performance. In Proc. ACM SIGMETRICS 2001, ACM, New York, pp. 82–91.Google Scholar
Bonald, T. and Proutière, A. (2004). On stochastic bounds for monotonic processor sharing networks. Queueing Systems 47, 81–106.CrossRefGoogle Scholar
Borovkov, A. A. (1998). Ergodicity and Stability of Stochastic Processes. John Wiley, Chichester.Google Scholar
Dai, J. (1995). On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5, 49–77.CrossRefGoogle Scholar
De Veciana, G., Lee, T.-J. and Konstantopoulos, T. (2001). Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networking 9, 2–14.CrossRefGoogle Scholar
Kelly, F. P. and Williams, R. J. (2004). Fluid model for bandwidth sharing. Ann. Appl. Prob. 14, 1055–1083.CrossRefGoogle Scholar
Kelly, F. P., Maulloo, A. K. and Tan, D. K. H. (1998). Rate control in communication networks: shadow prices, proportional fairness and stability. J. Operat. Res. Soc. 49, 237–252.CrossRefGoogle Scholar
Mo, J. and Walrand, J. (2000). Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networking 8, 556–567.CrossRefGoogle Scholar
Roberts, J. W. and Massoulié, L. (2000). Bandwidth sharing and admission control for elastic traffic. Telecommun. Systems 15, 185–201.Google Scholar