Of Queuing Theory in Healthcare a Novel Approach

This paper surveys the contributions and applications of queuing theory in the field of healthcare. The paper summarizes a range of queuing theory results in the following areas: waiting time and utilization analysis, system design, and appointment systems. The paper also considers results for systems at different scales, including individual departments (or units), healthcare facilities, and regional healthcare systems. The goal is to provide sufficient information to analysts who are interested in using queuing theory to model a healthcare process and want to locate the details of relevant models. INTRODUCTION The organizations that care for persons who are ill and injured vary widely in scope and scale, from specialized outpatient clinics to large, urban hospitals to regional healthcare systems. Despite these differences, one can view the healthcare processes that these organizations provide as queuing systems in which patients arrive, wait for service, obtain service, and then depart. The healthcare processes also vary in complexity and scope, but they all consist of a set of activities and procedures (both medical and non-medical) that the patient must undergo in order to receive the needed treatment. The resources (or servers) in these queuing systems are the trained personnel and specialized equipment that these activities and procedures require. A considerable body of research has shown that queuing theory can be useful in real-world healthcare situations, and some reviews of this work have appeared. McClain (1976) reviews research on models for evaluating the impact of bed assignment policies on utilization, waiting time, and the probability of turning away patients. Nosek and Wilson (2001) review the use of queuing theory in pharmacy applications with particular attention to improving customer satisfaction. Customer satisfaction is improved by predicting and reducing waiting times and adjusting staffing. Preater (2002) presents a brief history of the use of queuing theory in healthcare and points to an extensive bibliography of the research that lists many papers (however, it provides no description of the applications or results). Green (2006a) presents the theory of queuing as applied in healthcare. She discusses the relationship amongst delays, utilization and the number of servers; the basic M/M/ s model, its assumptions and extensions; and the applications of the theory to determine the required number of servers. This paper surveys the contributions and applications of queuing theory in the field of healthcare. The reviews mentioned above focus on presenting mathematical models or limit their scope to a single type of application. This paper, however, seeks to show the applicability of queuing theory from the perspective of healthcare organizations. Thus, this paper summarizes a range of queuing theory results in the following areas: waiting time and utilization analysis, system design, and appointment systems. This covers processes that provide direct patient treatment and processes that provide auxiliary services such as pharmacy and medical laboratory processing. The paper also considers results for systems at different scales, including individual departments (or units), healthcare facilities, and regional health systems. The goal is to provide sufficient information to analysts who are interested in using queuing theory to model ahealthcare process and want to locate the details of relevant models. We assume that the reader isfamiliar with healthcare organizations and the basic concepts of queuing theory. This survey covers analytical queuing theory models applied directly to healthcare APPLICATIONS OF QUEUING THEORY IN HEALTHCARE A NOVEL APPROACH