On priority queues with impatient customers |
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Authors: | Foad Iravani Bar?? Balc?og?lu |
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Institution: | (1) UCLA Anderson School of Management, 110 Westwood Plaza, Los Angeles, CA 90095-1481, USA;(2) Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Rd., Toronto, ON, M5S 3G8, Canada |
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Abstract: | In this paper, we study three different problems where one class of customers is given priority over the other class. In the
first problem, a single server receives two classes of customers with general service time requirements and follows a preemptive-resume
policy between them. Both classes are impatient and abandon the system if their wait time is longer than their exponentially
distributed patience limits. In the second model, the low-priority class is assumed to be patient and the single server chooses
the next customer to serve according to a non-preemptive priority policy in favor of the impatient customers. The third problem
involves a multi-server system that can be used to analyze a call center offering a call-back option to its impatient customers.
Here, customers requesting to be called back are considered to be the low-priority class. We obtain the steady-state performance
measures of each class in the first two problems and those of the high-priority class in the third problem by exploiting the
level crossing method. We furthermore adapt an algorithm from the literature to obtain the factorial moments of the low-priority
queue length of the multi-server system exactly.
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Keywords: | Call centers M/GI/1+M queue Priority queues Impatient customers Level-crossing method Call-back |
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