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Optimality of Randomized Trunk Reservation

Published online by Cambridge University Press:  27 July 2009

Eugene A. Feinberg  and
Martin I. Reiman
Eugene A. Feinberg
Affiliation:
W. A. Harriman School for Management and Policy, SUNY at Stony Brook, Stony Brook, New York 11794–3775.
Martin I. Reiman
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
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Abstract

We consider a controlled queueing system that is a generalization of the M/M/c/W queue. There are m types of customers that arrive according to independent Poisson processes. Service times are exponential and independent and do not depend on the customer type. There is room in the system for a total of N customers; if there are N customers in the system, new arrivals are lost. Type j customers are more profitable than type (j + 1 ) customers, j = 2,…, m —, and type 1 customers are at least as profitable as type 2 customers. The allowed control is to accept or reject customers at arrival. No preemption of customers in service is allowed. The goal is to maximize the average reward per unit of time subject to a constraint that the blocking probability of type 1 customers is no greater than a given level.

For an M/M/c/c system without a constraint, Miller [12] proved that an optimal policy has a simple threshold structure. We show that, for the constrained problem described above, an optimal policy has a similar structure, but one of the thresholds might have to be randomized. We also derive an algorithm that constructs an optimal policy and describe other forms of optimal policies.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 4 , October 1994 , pp. 463 - 489
Copyright
Copyright © Cambridge University Press 1994

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