A Queueing Theoretic Approach to Set Staffing Levels in Time‐Dependent Dual‐Class Service Systems*
针对两类顾客（高优先级和低优先级）且到达率随时间变化的服务系统，提出一种基于混合离散连续时间马尔可夫链的数值方法，用于计算安全的最低人员配置水平，并应用于威尔士救护服务信托。
ABSTRACT 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).