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Personalized queues: the customer view, via a fluid model of serving least-patient first

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Abstract

In personalized queues, information at the level of individuals—customers or servers—affects system dynamics. Such information is becoming increasingly accessible, directly or statistically, as exemplified by personalized/precision medicine (customers) or call center workforce management (servers). In the present work, we take advantage of personalized information about customers, specifically knowledge of their actual (im)patience while waiting to be served. This waiting takes place in a many-server queue that alternates between over- and underloaded periods, hence a fluid view provides a natural modeling framework. The parsimonious fluid view enables us to parameterize and analyze partial information, and consequently calculate and understand the benefits from personalized customer information. We do this by comparing least-patience first (LPF) routing (personalized) against FCFS (relatively info-ignorant). An example of a resulting insight is that LPF can provide significant advantages over FCFS when the durations of overloaded periods are comparable to (im)patience times.

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Acknowledgements

The work of A. M. has been partially supported by BSF Grants 2008480 and 2014180, ISF Grants 1357/08 and 1955/15 and by the Technion funds for promotion of research and sponsored research. Some of the research was funded by and carried out while A. M. was visiting the Statistics and Applied Mathematical Sciences Institute (SAMSI) of the NSF; the Department of Statistics and Operations Research (STOR), the University of North Carolina at Chapel Hill; the Department of Information, Operations and Management Sciences (IOMS), Leonard N. Stern School of Business, New York University; and the Department of Statistics, The Wharton School, University of Pennsylvania—the wonderful hospitality of all four institutions is gratefully acknowledged and truly appreciated. The work of P. M. has been partially supported by the NSF Grant CMMI-1362630 and the BSF Grant 2014180. Finally, the authors thank the 2012 SAMSI Working Group on Data-Based Patient Flow in Hospitals, which provided an encouraging forum for our research as it evolved. In particular, Jamol Pender suggested, during a SAMSI meeting, the MPF policy as a benchmark.

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, 3200, Haifa, Israel

    Avishai Mandelbaum

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Petar Momčilović

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  1. Avishai Mandelbaum
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Correspondence to Petar Momčilović.

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Mandelbaum, A., Momčilović, P. Personalized queues: the customer view, via a fluid model of serving least-patient first. Queueing Syst 87, 23–53 (2017). https://doi.org/10.1007/s11134-017-9537-y

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  • DOI: https://doi.org/10.1007/s11134-017-9537-y

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