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A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems

Vile, J. L., Gillard, J. W. ORCID:, Harper, P. R. ORCID: and Knight, V. A. ORCID: 2017. A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems. Decision Sciences 48 (4) , pp. 766-794. 10.1111/deci.12236

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This article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time-dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time-dependent dual-class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete-continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST).

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Publisher: Wiley
ISSN: 0011-7315
Funders: EPSRC
Date of First Compliant Deposit: 16 June 2016
Date of Acceptance: 16 May 2016
Last Modified: 05 May 2023 22:15

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