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WAITING TIME ANALYSIS OF MULTI-CLASS QUEUES WITH IMPATIENT CUSTOMERS

Published online by Cambridge University Press:  28 March 2013

Vahid Sarhangian  and
Bariş Balciog̃lu
Vahid Sarhangian
Affiliation:
Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, M5S 3E6, Canada E-mail: [email protected]
Bariş Balciog̃lu
Affiliation:
Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı-Tuzla, 34956 Istanbul, Turkey E-mail: [email protected]
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Abstract

In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single- and multi-server settings. In all models, we obtain the Laplace transform of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 333 - 352
Copyright
Copyright © Cambridge University Press 2013 

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