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Stability of a Processor-Sharing Queue with Varying Throughput

Part of:Limit theoremsSpecial processesProbability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

Pascal Moyal
Pascal Moyal*
Affiliation:
UTC Compiègne
*
∗ Postal address: Laboratoire de Mathématiques Appliquées de Compiègne, Université de Technologie de Compiègne, Département Génie Informatique, Centre de Recherches de Royallieu, BP 20 529, 60 205 Compiegne Cedex, France. Email address: moyalpas@dma.utc.fr
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Abstract

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In this paper we present a stability criterion for processor-sharing queues, in which the throughput may depend on the number of customers in the system (such as in the case of interferences between users). Such a system is represented by a point measure-valued stochastic recursion keeping track of the remaining processing times of the customers.

Keywords

Queueing systemstabilitymeasure-valued processstochastic recurrenceprocessor sharing

MSC classification

Secondary:60F17: Functional limit theorems; invariance principles60K25: Queueing theory60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008, pp. 953 - 962
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Baccelli, F. and Brémaud, P. (2002). Elements of Queueing Theory. 2nd edn. Springer, Berlin.Google Scholar
[2] Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.Google Scholar
[3] Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory. Springer, New York.Google Scholar
[4] Borovkov, A. A. and Foss, S. (1992). Stochastically recursive sequences and their generalizations. Siberian Adv. Math., 2, 16–81.Google Scholar
[5] Decreusefond, L. and Moyal, P. (2007). A functional central limit theorem for the M/{GI}/∞ queue. To appear in Ann. Appl. Prob. Google Scholar
[6] Loynes, R. M. (1962). The stability of queues with non-independent interarrivals and service times. Proc. Camb. Phil. Soc. 58, 497–520.Google Scholar
[7] Moyal, P. (2007). Construction of a stationary FIFO queue with impatient customers. Preprint. Available at http://arxiv.org/abs/0802.2495.Google Scholar