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Waiting time in the M/M/\( m \) LCFS nonpreemptive priority queue with impatient customers

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Abstract

As a model of a service center with multiple servers and prioritized impatient customers served in reverse order of arrival such as the 9-1-1 call center in the United States, we study an M/M/\( m \) nonpreemptive priority (last-come, first-served within the same class) queueing system with impatient customers in the steady state. We analyze the waiting time for those customers who are served successfully and the time to abandonment for those customers who leave the system while waiting. Explicit formulas are given for the probabilities of service and abandonment as well as the mean and second moment of the waiting time for customers of each class. Numerical examples are shown in order to demonstrate the computation of theoretical formulas. The difference in the behavior of the waiting time from that in the corresponding first-come, first-served system is discussed.

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Acknowledgments

I would like to thank the guest editors and anonymous reviewers for many valuable comments including the notification of references Jouini (2012), Jouini and Roubos (2014) in the reviewing process.

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  1. Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba Science City, Ibaraki, 305-8573, Japan

    Hideaki Takagi

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  1. Hideaki Takagi
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Correspondence to Hideaki Takagi.

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Takagi, H. Waiting time in the M/M/\( m \) LCFS nonpreemptive priority queue with impatient customers. Ann Oper Res 247, 257–289 (2016). https://doi.org/10.1007/s10479-015-1876-7

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  • DOI: https://doi.org/10.1007/s10479-015-1876-7

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