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Some Pitfalls of Black Box Queue Inference: The Case of State-Dependent Server Queues

Published online by Cambridge University Press:  27 July 2009

Sheldon M. Ross ,
J. George Shanthikumar  and
Xiang Zhang
Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
J. George Shanthikumar
Affiliation:
Walter A. Haas School of Business, University of California, Berkeley, California 94720
Xiang Zhang
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
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Abstract

In several queueing systems the service rate of a server is affected by the work load present in the system. For example, a teller at a bank or a checker at a check-out counter in a supermarket may change the service rate depending on the number of customers present in the system. But the service rate as a function of the number in the system can rarely be measured. Consequently, in a typical model of such a system it is assumed that the service rate is constant. Hence, such systems with a single stage are often modeled by GI/GI/c queueing systems with mutually independent arrival and service processes. Then the observed service times are used to find a sample distribution that will represent the distribution of the assumed i.i.d. service times. The purpose of this paper is to explore the effect of this black box queue inference (BBQI) in its ability to predict the performance of the actual system. In this regard, we have shown that when the arrival process is Poisson, if the servers react favorably [unfavorably] to higher work loads (i.e., if the server increases [decreases] the service rate as the number of customers in the system increases) then the BBQI predictions will be pessimistic [optimistic]. This result can be used to identify the server's attitude toward higher work load.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 149 - 157
Copyright
Copyright © Cambridge University Press 1993

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