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Derivatives of the expected delay in the GI/G/1 Queue

Published online by Cambridge University Press:  14 July 2016

Hong Chen  and
David D. Yao
Hong Chen
Affiliation:
Harvard University
David D. Yao
Affiliation:
Harvard University
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Abstract

Consider the GI/G/1 queue in which the interarrival/service times are parameterized. The derivatives (with respect to the parameter) of the expected delay of the nth job and its limit are derived and expressed in terms of the expectation of certain stochastic derivatives. Applications of these derivatives in stochastic optimization and random walk are illustrated.

Keywords

STOCHASTIC DERIVATIVERANDOM WALK
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 899 - 907
Copyright
Copyright © Applied Probability Trust 1990 

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References

Asmussen, S. (1987) Applied Probability and Queues. Wiley, Chichester.Google Scholar
Cao, X. R. (1985) Convergence of parameter sensitivity estimates in a stochastic experiment. IEEE Trans. Autom. Control 30, 845–853.Google Scholar
Glasserman, P. (1988) Performance continuity and differentiability in Monte Carlo optimization. Proc. 1988 Winter Simulation Conf, 518–524.Google Scholar
Glynn, P. W. (1986) Optimization of stochastic systems. Proc. 1986 Winter Simulation Conf., 52–59.CrossRefGoogle Scholar
Heidelberger, P., Cao, X. R., Zazanis, M. and Suri, R. (1988) Convergence properties of infinitesimal perturbation analysis estimates. Management Sci. 34, 563–572.Google Scholar
Ho, Y. C. (1987) Performance evaluation and perturbation analysis of discrete event dynamic systems. IEEE Trans. Autom Control 32, 583–572.Google Scholar
Kushner, H. J. and Clark, D. S. (1978) Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer-Verlag, New York.Google Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.CrossRefGoogle Scholar
Reiman, M. I. and Weiss, A. (1986) Sensitivity analysis via likelihood ratio. Proc. 1986 Winter Simulation Conf., 285–289.CrossRefGoogle Scholar
Royden, H. L. (1963) Real Analysis. Macmillan, New York.Google Scholar
Rubinstein, R. Y. (1986) Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks. Wiley, New York.Google Scholar
Siegmund, D. (1985) Sequential Analysis. Springer-Verlag, New York.CrossRefGoogle Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Suri, R. and Zazanis, M. (1988) Perturbation analysis gives strongly consistent sensitivity estimates for the M/G/1 queue. Management Sci. 34, 39–64.CrossRefGoogle Scholar