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On the structure of value functions for threshold policies in queueing models

Published online by Cambridge University Press:  14 July 2016

Sandjai Bhulai
Affiliation:
Vrije Universiteit Amsterdam
Ger Koole*
Affiliation:
Vrije Universiteit Amsterdam
*
∗∗Postal address: Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

Abstract

We study the multiserver queue with Poisson arrivals and identical independent servers with exponentially distributed service times. Customers arriving at the system are admitted or rejected according to a fixed threshold policy. Moreover, the system is subject to holding, waiting, and rejection costs. We give a closed-form expression for the average costs and the value function for this multiserver queue. The result will then be used in a single step of policy iteration in the model where a controller has to route to several finite-buffer queues with multiple servers. We numerically show that the improved policy has a close to optimal value.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

Current address: Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Room 2C-313, Murray Hill, NJ 07974-0636, USA. Email address: [email protected]

References

Bertsekas, D. P., and Tsitsiklis, J. N. (1996). Neuro-Dynamic Programming. Athena Scientific, Belmont, MA.Google Scholar
Gross, D., and Harris, C. M. (1985). Fundamentals of Queueing Theory, 2nd edn. John Wiley, New York.Google Scholar
Koole, G. M., and Nain, P. (2000). On the value function of a priority queue with an application to a controlled polling model. Queueing Systems 34, 199214.CrossRefGoogle Scholar
Koole, G. M., and Spieksma, F. (2001). On deviation matrices for birth-death processes. Prob. Eng. Inf. Sci. 15, 239258.Google Scholar
Mickens, R. E. (1990). Difference Equations: Theory and Applications, 2nd edn. Van Nostrand Reinhold, New York.Google Scholar
Ott, T. J., and Krishnan, K. R. (1992). Separable routing: a scheme for state-dependent routing of circuit switched telephone traffic. Ann. Operat. Res. 35, 4368.CrossRefGoogle Scholar
Puterman, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley, New York.CrossRefGoogle Scholar
Stidham, S. Jr, and Weber, R. R. (1993). A survey of Markov decision models for control of networks of queues. Queueing Systems 13, 291314.CrossRefGoogle Scholar