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Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions

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  • Walsh Zuñiga, Alexander

Abstract

This paper extends the works of Kang and Ramanan (2010) and Kaspi and Ramanan (2011), removing the hypothesis of absolute continuity of the service requirement and patience time distributions. We consider a many-server queueing system in which customers enter service in the order of arrival in a non-idling manner and where reneging is considerate. Similarly to Kang and Ramanan (2010), the dynamics of the system are represented in terms of a process that describes the total number of customers in the system as well as two measure-valued processes that record the age in service of each of the customers being served and the “potential” waiting times. When the number of servers goes to infinity, fluid limit is established for this triple of processes. The convergence is in the sense of probability and the limit is characterized by an integral equation.

Suggested Citation

  • Walsh Zuñiga, Alexander, 2014. "Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1436-1468.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:3:p:1436-1468
    DOI: 10.1016/j.spa.2013.11.008
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    References listed on IDEAS

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    1. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    2. O. Garnet & A. Mandelbaum & M. Reiman, 2002. "Designing a Call Center with Impatient Customers," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 208-227, October.
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