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Average optimal policies in a controlled queueing system with dual admission control

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Mark E. Lewis
Mark E. Lewis*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA. Email address: melewis@engin.umich.edu
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Abstract

We consider a controlled M/M/1 queueing system where customers may be subject to two potential rejections. The first occurs upon arrival and is dependent on the number of customers in the queue and the service rate of the customer currently in service. The second, which may or may not occur, occurs immediately prior to the customer receiving service. That is, after each service completion the customer in the front of the queue is assessed and the service rate of that customer is revealed. If the second decision-maker recommends rejection, the customer is denied service with a fixed probability. We show the existence of long-run average optimal monotone switching-curve policies. Further, we show that the average reward is increasing in the probability that the second decision-maker's recommendation of rejection is honored. Applications include call centers with delayed classifications and manufacturing systems when the server is responsible for multiple tasks.

Keywords

Markov and semi-Markov processesqueueing theory

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 369 - 385
Copyright
Copyright © Applied Probability Trust 2001 

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References

Altman, E. (1996). Non zero-sum stochastic games in admission, service, and routing control in queueing systems. Queueing Systems 23, 256–279.Google Scholar
Altman, E. (1999). A Markov game approach for optimal routing into a queueing network. In Stochastic and Differential Games (Ann. Int. Soc. Dynamic Games 5), eds Bardi, M., Raghavan, T. E. S. and Parthasarathy, T. Birkhäuser, Boston, pp. 359–376.Google Scholar
Altman, E. (2001). Applications of Markov decision processes in telecommunications: a survey. To appear in Markov Decision Processes: Models, Methods, Directions and Open Problems, eds Feinberg, E. and Schwartz, A. Kluwer, Dordrecht.Google Scholar
Altman, E., and Stidham, S. Jr. (1995). Optimality of monotonic policies for two-action Markovian decision processes, with applications to control of queues with delayed information. Queueing Systems 21, 267–291.Google Scholar
Ghoneim, H. A., and Stidham, S. Jr. (1985). Control of arrivals to two queues in series. Eur. J. Operat. Res. 21, 399–409.Google Scholar
Hajek, B. (1984). Optimal control of two interacting service stations. IEEE Trans. Automatic Control 29, 491–499.Google Scholar
Helm, W. E., and Waldmann, K.-H. (1984). Optimal control of arrivals to multi-server queues in a random environment. J. Appl. Prob. 21, 602–615.Google Scholar
Hernández-Lerma, O., and Lasserre, J. B. (1996). Discrete-Time Markov Control Processes: Basic Optimality Criteria. Springer, New York.Google Scholar
Heyman, D. P. (1968). Optimal operating policies for M/G/1 queueing systems. Operat. Res. 16, 362–382.Google Scholar
Lewis, M. E., and Puterman, M. L. (2000). A note on bias optimality in controlled queueing systems. J. Appl. Prob. 37, 300–305.Google Scholar
Lewis, M. E., and Puterman, M. L. (2001). A probabilistic analysis of bias optimality in unichain Markov decision processes. IEEE Trans. Automatic Control 46, 1–5.Google Scholar
Lippman, S. A. (1975). Applying a new device in the optimization of exponential queueing systems. Operat. Res. 23, 687–712.Google Scholar
Lippman, S. A., and Ross, S. M. (1971). The streetwalker's dilemma: a job shop model. SIAM J. Appl. Math. 20, 336–342.Google Scholar
Miller, B. L. (1969). A queueing reward system with several customer classes. Management Sci. 16, 234–245.CrossRefGoogle Scholar
Puterman, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley, New York.CrossRefGoogle Scholar
Stidham, S. Jr. (1985). Optimal control of admission to a queueing system. IEEE Trans. Automatic Control 30, 705–713.Google Scholar
Xu, S. H., and Shanthikumar, J. G. (1993). Optimal expulsion control—a dual approach to admission control of an ordered-entry system. Operat. Res. 41, 1137–1152.Google Scholar
Yadin, M., and Naor, P. (1963). Queueing systems with a removable service station. Operat. Res. Quart. 14, 393–405.Google Scholar