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Title:An M/M/1 dynamic priority queue with optional promotion / BEBR No. 524
Author(s):Kofman, Ehud, 1945-; Lippman, Steven A.
Contributor(s):University of Illinois at Urbana-Champaign. College of Commerce and Business Administration
Subject(s):Queuing theory.
Customer services.
Issue Date:Ot 25 1978
Publisher:[Urbana, Ill.] : College of Commerce and Business Administration, University of Illinois at Urbana-Champaign,
Series/Report:Faculty working papers ; no. 524
Description:"This research was partially supported by the National Science Foundation through Grant SOC-7808985."
Includes bibliographical references (p. 29-30).
"We consider an M/M/1 queue with two types of customers: priority customers and regular customers. They arrive at the service facility according to two independent Poisson streams and form a single queue according to the order in which they arrive. The two types of customers are distinguished by the holding costs charged per unit time that each of them resides in the queue. The server can either serve customers according to the order in which they arrive or pay a fixed fee R and promote a priority customer, bypassing the customers ahead of him. The server selects the customers to be served so as to minimize the expected average cost per unit of time of operating the system. We show that whenever the number of regular customers bypassed in a promotion times the expected holding costs per priority customer per service period is greather than or equal to R, promotion is strictly optimal. Moreover, for each state there exists a value of R, with R exceeding the number of regular customers bypassed in a promotion times the expected holding costs per priority customer per service period, for which promotion is optimal. This result contradicts previous work in the literature. In addition, we demonstrate that the set of states from which promotion is optimal decreases in the sense of set inclusion as R increases. This fact is the key to an efficient algorithm."
Rights Information:In copyright. Digitized with permission of the University of Illinois Board of Trustees. Contact for information.
Copyright Ot 25 1978 Board of Trustees University of Illinois.
Date Available in IDEALS:2011-09-15
Has Version(s):
Identifier in Online Catalog:91602
OCLC Identifier:(OCoLC)ocm05121031

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