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Light traffic approximations for regenerative queueing processes

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Chia-Li Wang
Chia-Li Wang*
Affiliation:
National Dong Hwa University
*
*Postal address: Institute of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, Republic of China.
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Abstract

We consider a regenerative queueing process that is (partially) generated by an embedded phase-type renewal process. We show that, under some specified conditions, a performance measure is an analytic function of the rate of the renewal process. We then develop several methods for deriving its Taylor polynomial in the renewal rate. These polynomials are asymptotically exact as the rate decreases, and, thus, are called light traffic approximations of the performance measure. We show via examples that these new methods are not only more efficient compared to existing ones, but also more versatile due to their general settings, such as to conduct perturbation analysis and study transient behavior.

Keywords

QUEUEING THEORYLIGHT TRAFFIC APPROXIMATIONSREGENERATIVE PROCESSESANALYTIC FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 4 , December 1997 , pp. 1060 - 1080
Copyright
Copyright © Probability Trust 1997 

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References

Asmussen, S. (1992) Light traffic equivalence in single server queues. Ann. Appl. Prob. CrossRefGoogle Scholar
Blaszczyszyn, B., Rolski, T. and Schmidt, V. (1995) Light traffic approximation in queues and related stochastic models. In Advances in Queueing. ed. Dshalalow, J. H. CRC Press, Boca Raton, FL.Google Scholar
Daley, D. and Rolski, T. (1984) A light traffic approximation for a single-server queue. Math. Operat. Res. 9, 624–628.CrossRefGoogle Scholar
Daley, D. and Rolski, T. (1991) Light traffic approximations in queues. Math. Operat. Res. 16, 57–71.CrossRefGoogle Scholar
Kovalenko, I. N. (1995) Approximation at queues via small parameter method. In Advances in Queueing. ed. Dshslalow, J. H. CRC Press, Boca Raton, FL.Google Scholar
Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore, MD.Google Scholar
Reiman, ?. I. and Simon, B. (1988) Light traffic limits of sojourn time distribution in Markovian queueing networks. Stoch. Models 4, 191–233.Google Scholar
Reiman, ?. I. and Simon, B. (1989) Open queueing systems in light traffic. Math. Operat. Res. 14, 26–59.Google Scholar
Reiman, ?. I. and Weiss, A. (1989) Light traffic derivatives via likelihood ratios. IEEE Trans. Info. Theory 35, 648–654.Google Scholar
Wang, C. (1994) PhD dissertation. University of California, Berkeley.Google Scholar
Wang, C. and Wolff, R. W. (1995) The M/G/c queue in light traffic. Preprint. University of California, Berkeley.Google Scholar
Widder, D. V. (1941) The Laplace Transform. Princeton University Press, Princeton, NJ.Google Scholar
Wolff, R. W. (1982) Tandem queues with dependent services times in light traffic. Operat. Res. 30, 619–635.Google Scholar
Wolff, R. W. (1989) Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Zazanis, M. A. (1992) Analyticity of Poisson-driven stochastic systems. Adv. Appl. Prob. 24, 532–541.Google Scholar