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Rate of convergence of the fluid approximation for generalized Jackson networks

Part of: Special processes Limit theorems Computer system organization

Published online by Cambridge University Press:  14 July 2016

Hong Chen
Hong Chen*
Affiliation:
University of British Columbia
*
∗ Postal address: Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, B.C. Canada.
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Abstract

It is known that a generalized open Jackson queueing network after appropriate scaling (in both time and space) converges almost surely to a fluid network under the uniform topology. Under the same topology, we show that the distance between the scaled queue length process of the queueing network and the fluid level process of the corresponding fluid network converges to zero in probability at an exponential rate.

Keywords

RATE OF CONVERGENCEFLUID APPROXIMATIONQUEUEING NETWORK

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K25: Queueing theory 60F10: Large deviations 68M20: Performance evaluation; queueing; scheduling

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 804 - 814
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Supported in part by a Killam Faculty Research Fellowship and a grant from NSERC (Canada).

References

Bertsimas, D., Paschalidis, I. Ch. and Tsitsiklis, J. N. (1994) On the large deviations behaviour of acyclic networks of G/G/1 queues. Working paper. Operations Research Center, MIT, Cambridge, MA.Google Scholar
Chen, H. and Mandelbaum, A. (1991) Discrete flow networks: Bottleneck analysis and fluid approximations. Math. Operat. Res. 16, 408–446.CrossRefGoogle Scholar
Chen, H. and Mandelbaum, A. (1994) Hierarchical modelling of stochastic networks, part II: strong approximations. In Stochastic Modeling and Analysis of Manufacturing Systems , ed. Yao, D. D. Springer, Berlin. pp. 107–131.CrossRefGoogle Scholar
Chung, K. L. (1974) A Course in Probability Theory. Academic Press, New York.Google Scholar
De Veciana, G., Courcoubetis, C. and Walrand, J. (1993) Decoupling bandwidths for networks: a decomposition approach to resource management. IEEE/ACM Trans. Networking (submitted).Google Scholar
Dembo, and Zeitouni, (1993) Large Deviations Techniques and Applications. Jones and Bartlett, Boston.Google Scholar
Harrison, J. M. and Reiman, M. I. (1981) Reflected Brownian motion on an orthant. Ann. Prob. 9, 302–308.CrossRefGoogle Scholar
Heyman, D. P. and Sobel, M. J. (1982) Stochastic Models in Operations Research, Volume I: Stochastic Processes and Operating Characteristics. McGraw-Hill, New York.Google Scholar
Johnson, D. P. (1983) Diffusion approximations for optimal filtering of jump processes and for queueing networks. Ph.D. dissertation. University of Wisconsin.Google Scholar
Puhalskii, A. (1994) Large deviation analysis of the single server queue. Preprint. Google Scholar
Reiman, M. I. (1984) Open queueing networks in heavy traffic. Math. Operat. Res. 9, 441–458.CrossRefGoogle Scholar
Whitt, W. (1974) Preservation of rates of convergence under mappings. Z. Wahrscheinlichkeitsth. 29, 39–44.CrossRefGoogle Scholar