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A Queueing Theoretic Approach to Set Staffing Levels in Time-Dependent Dual-Class Service Systems

机译：在时间相关的双级服务系统中设置人员编制水平的排队论方法

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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).
机译：本文针对具有两个客户类别和时间依赖性到达率的非抢占式优先级队列，解决了最佳人员配备问题。该问题与几个重要的服务设置有关，例如呼叫中心和紧急部门，其中将客户分为高优先级和低优先级两类，并且通常根据目标响应中响应的客户比例来评估服务次。迄今为止，仅探索了近似方法来生成与时间相关的双级服务的人员配备要求，但是我们提出了一种易于处理的数值方法，用于使用混合离散连续时间马尔可夫链（MDCTMC）评估系统行为并生成安全的最低人员配备水平。我们的方法之所以精巧，是因为它根据许多不同的规则来解释系统的行为，这些规则可能会在员工因休假而忙碌时施加于他们身上，并明确计算两个客户类别的延迟分布。最终，我们将方法论嵌入到拟议的Euler方法扩展（即Euler Pri）中，该方法可以处理两个客户类别，并使用它为威尔士救护车服务信托（WAST）推荐人员水平。

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  • 来源
    《Decision sciences》 |2017年第4期|1-25|共25页
  • 作者

    Vile J. L.; Gillard J. W.; Harper P. R.; Knight V. A.;

  • 作者单位

    Cardiff Univ, Sch Math, Cardiff, S Glam, Wales;

    Cardiff Univ, Sch Math, Cardiff, S Glam, Wales;

    Cardiff Univ, Sch Math, Cardiff, S Glam, Wales;

    Cardiff Univ, Sch Math, Cardiff, S Glam, Wales;

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