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OPTIMALITY OF TRUNK RESERVATION FOR AN M/M/K/N QUEUE WITH SEVERAL CUSTOMER TYPES AND HOLDING COSTS

Published online by Cambridge University Press:  21 July 2011

Eugene A. Feinberg  and
Fenghsu Yang
Eugene A. Feinberg
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, NY 11794-3600, Stony Brook, USA E-mail: Eugene.Feinberg@sunysb.edu; fyang@ic.sunysb.edu
Fenghsu Yang
Affiliation:
Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, NY 11794-3600, Stony Brook, USA E-mail: Eugene.Feinberg@sunysb.edu; fyang@ic.sunysb.edu
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Abstract

In this article we study optimal admission to an M/M/k/N queue with several customer types. The reward structure consists of revenues collected from admitted customers and holding costs, both of which depend on customer types. This article studies average rewards per unit time and describes the structures of stationary optimal, canonical, bias optimal, and Blackwell optimal policies. Similar to the case without holding costs, bias optimal and Blackwell optimal policies are unique, coincide, and have a trunk reservation form with the largest optimal control level for each customer type. Problems with one holding cost rate have been studied previously in the literature.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 4 , October 2011 , pp. 537 - 560
Copyright
Copyright © Cambridge University Press 2011

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