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A Note on Insensitivity in Stochastic Networks

Part of:Special processes

Published online by Cambridge University Press:  14 July 2016

Stan Zachary
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗ Postal address: Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email address: s.zachary@hw.ac.uk
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Abstract

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We give a simple and direct treatment of insensitivity in stochastic networks which is quite general and provides probabilistic insight into the phenomenon. In the case of multi-class networks, our results generalise those of Bonald and Proutière (2002), (2003).

Keywords

Insensitivitystochastic networkpartial balance

MSC classification

Primary:60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007, pp. 238 - 248
Copyright
Copyright © Applied Probability Trust 2007 

References

Bonald, T. and Massoulié, L. (2001). Impact of fairness on Internet performance. In Proc. ACM SIGMETRICS 2001 (Cambridge, MA), ACM Press, New York.Google Scholar
Bonald, T. and Proutière, A. (2002). Insensitivity in processor-sharing networks. Performance Evaluation 49, 193–209.CrossRefGoogle Scholar
Bonald, T. and Proutière, A. (2003). Insensitive bandwidth sharing in data networks. Queueing Systems 44, 69–100.CrossRefGoogle Scholar
Burman, D. Y. (1981). Insensitivity in queueing systems. Adv. Appl. Prob. 13, 846–859.CrossRefGoogle Scholar
Burman, D. Y., Lehoczky, J. P. and Lim, Y. (1984). Insensitivity of blocking probabilities in a circuit switching network. J. Appl. Prob. 21, 850–859.Google Scholar
Davis, M. H. A. (1984). Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Statist. Soc. B 46, 353–388.Google Scholar
Davis, M. H. A. (1993). Markov Models and Optimization. Chapman & Hall, London.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.Google Scholar
Kelly, F. P. (1979). Reversibility and Stochastic Networks. John Wiley, Chichester.Google Scholar
Kelly, F. P. (1986). Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.CrossRefGoogle Scholar
Pechinkin, A. V. (1983). An invariant queueing system. Math. Operationsforsch. Statist. Ser. Optim. 14, 433–444.Google Scholar
Pechinkin, A. V. (1987). A new proof of Erlang's formula for a lossy multichannel queueing system. Soviet J. Comput. System Sci. 25, 165–168.Google Scholar
Schassberger, R. (1978). Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
Schassberger, R. (1986). Two remarks on insensitive stochastic models. Adv. Appl. Prob. 18, 791–814.Google Scholar
Serfozo, R. F. (1999). Introduction to Stochastic Networks. Springer, Berlin.CrossRefGoogle Scholar
Sevastyanov, B. A. (1957). An ergodic theory for Markov processes and its application to a telephone system with refusals. Theory Prob. Appl. 2, 104–112.Google Scholar
Whittle, P. (1985). Partial balance and insensitivity. J. Appl. Prob. 22, 168–176.Google Scholar