Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-25T04:50:17.087Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMALITY OF RANDOMIZED TRUNK RESERVATION FOR A PROBLEM WITH MULTIPLE CONSTRAINTS

Published online by Cambridge University Press:  27 February 2007

Xiaofei Fan-Orzechowski  and
Eugene A. Feinberg
Xiaofei Fan-Orzechowski
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, E-mail: [email protected]; [email protected]
Eugene A. Feinberg
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the optimal admission of arriving customers to a Markovian finite-capacity queue (e.g., M/M/c/N queue) with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The penalties are modeled by a K-dimensional cost vector, K ≥ 1. The goal is to maximize the average rewards per unit time subject to the K constraints on the average costs per unit time. Let Km denote min{K,m − 1}, where m is the number of customer types. For a feasible problem, we show the existence of a Km-randomized trunk reservation optimal policy, where the acceptance thresholds for different customer types are ordered according to a linear combination of the service rewards and rejection costs. Additionally, we prove that any Km-randomized stationary optimal policy has this structure.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 2 , April 2007 , pp. 189 - 200
Copyright
© 2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Altman, E. (2002). Applications of Markov decision processes in telecommunications: A survey. In E. Feinberg & A. Shwartz (eds.), Handbook on Markov decision processes. New York: Kluwer, pp. 489–536.CrossRef
Altman, E., Jimenez, T., & Koole, G. (2001). On optimal call admission control in a resource-sharing system. IEEE Transactions on Communications 49: 1659–1668.Google Scholar
Fan-Orzechowski, X. & Feinberg, E. A. (2006). Optimality of randomized trunk reservation for a problem with a single constraint. Advances in Applied Probability 38: 199–220.Google Scholar
Feinberg, E.A. (1994). Constrained semi-Markov decision processes with average rewards. Mathematical Methods of Operations Research 39: 257–288.Google Scholar
Feinberg, E.A. (2002). Constrained finite continuous-time Markov decision processes with average rewards. In Proceedings of IEEE 2002 Conference on Decisions and Control, December 10–13, 2002, Las Vegas, pp. 3805–3810.
Feinberg, E.A. (2004). Continuous time discounted jump Markov decision processes: A discrete-event approach. Mathematics of Operations Research 29: 492–524.Google Scholar
Feinberg, E.A. & Reiman, M.I. (1994). Optimality of randomized trunk reservation. Probability in the Engineering and Informational Sciences 8: 463–489.Google Scholar
Lewis, M.E. (2001). Average optimal policies in a controlled queueing system with dual admission control. Journal of Applied Probability 38: 369–385.Google Scholar
Lewis, M.E., Ayhan, H., & Foley, R.D. (1999). Bias optimality in a queue with admission control. Probability in the Engineering and Informational Sciences 13: 309–327.Google Scholar
Lewis, M.E., Ayhan, H., & Foley, R.D. (2002). Bias optimal admission policies for a nonstationary multi-class queueing system. Journal of Applied Probability 39: 20–37.Google Scholar
Lin, K.Y. & Ross, S.M. (2003). Admission control with incomplete information of a queueing system. Operations Research 51: 645–654.Google Scholar
Lin, K.Y. & Ross, S.M. (2004). Optimal admission control for a single-server loss queue. Journal of Applied Probability 41: 535–546.Google Scholar
Miller, B.L. (1969). A queueing reward system with several customer classes. Management Science 16: 235–245.Google Scholar
Ross, K.W. (1995). Multiservice loss models for broadband telecommunication networks. London: Springer-Verlag.CrossRef