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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: xfan@ams.sunysb.edu; Eugene.Feinberg@sunysb.edu
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: xfan@ams.sunysb.edu; Eugene.Feinberg@sunysb.edu
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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

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