Abstract

The Accumulating Priority Queue model, in which customers accumulate priority as a linear function of their time in the queue, was first introduced by Kleinrock in 1964 under another name. All publications addressing the APQ since then have assumed that customers start accumulating priority credits upon arrival. The model we present herein, called the Delayed Accumulating Priority Queue, entails an initial delay prior to priority accumulation for low-priority customers. The waiting time distribution for the lower class of customers in such an APQ is determined, and the impact of the initial delay upon that distribution is assessed. The equivalence to another model, the Affine Accumulating Priority Queue, is established. A motivation for our work is the potential for very long waiting times for low-acuity patients in health care systems operating at very high utilization. We test cases in an idealized setting motivated by access targets which differ by a factor of two (as occurs in the Canadian Triage and Acuity Scale (CTAS)). This work also considers the problem of finding the minimal lower-class priority accumulation rate which allows for the lower-class customers to meet their access target, as a function of the duration of the initial delay involved.

摘要

累积优先级队列模型由客户Kleinrock于1964年首次提出，在该模型中，客户将优先级作为其在队列中时间的线性函数进行累积。从那时起，所有针对APQ的出版物都假定客户在抵达时就开始积累优先积分。我们在此介绍的模型称为“延迟累积优先级队列”，对于低优先级客户而言，在优先级累积之前需要进行初始延迟。确定此类APQ中较低级别客户的等待时间分配，并评估初始延迟对该分配的影响。建立与另一个模型（仿射累积优先级队列）的对等关系。我们工作的动力在于，在利用率很高的医疗保健系统中，低敏患者可能需要很长的等待时间。我们在理想的环境中测试案例，这些案例是由访问目标驱动的，目标相差两个因数（如加拿大分类和敏锐度表（CTAS）中所发生的情况）。这项工作还考虑了一个问题，即根据所涉及的初始延迟的持续时间，找到最低的下层优先级累积速率，该速率允许下层客户满足其访问目标。