Abstract: This article addresses the optimal staffing problem for a non-preemptive priority queue with two customer classes and a time-dependent arrival rate. The problem is related to several important service settings such as call centres and emergency departments, where customers are grouped into two classes of 'high priority' and 'low priority', and services are typically evaluated according to the proportion of customers 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 behaviour and generate safe minimum staffing levels using mixed discrete-continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behaviour 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 the two customer classes. We embed our methodology in a proposed extension of the Euler method, which we call Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST).
@article{vile2016queueing,
title = {A queueing theoretic approach to set staffing levels in
time-dependent dual-class service systems},
author = {Vile, Julie L. and Gillard, Jonathan W. and Harper, Paul R. and
Knight, Vincent A.},
journal = {Decision Sciences},
volume = {48},
number = {4},
pages = {766--794},
year = {2016},
doi = {10.1111/deci.12236},
url = {https://doi.org/10.1111/deci.12236},
}