An Emergency Department Patient Flow Model Based on Queueing Theory Principles

Abstract

Objectives: The objective was to derive and validate a novel queuing theory-based model that predicts the effect of various patient crowding scenarios on patient left without being seen (LWBS) rates.Methods: Retrospective data were collected from all patient presentations to triage at an urban, academic, adult-only emergency department (ED) with 87,705 visits in calendar year 2008. Data from specific time windows during the day were divided into derivation and validation sets based on odd or even days. Patient records with incomplete time data were excluded. With an established call center queueing model, input variables were modified to adapt this model to the ED setting, while satisfying the underlying assumptions of queueing theory. The primary aim was the derivation and validation of an ED flow model. Chi-square and Student's t-tests were used for model derivation and validation. The secondary aim was estimating the effect of varying ED patient arrival and boarding scenarios on LWBS rates using this model. Results:The assumption of stationarity of the model was validated for three time periods (peak arrival rate = 10:00 a.m. to 12:00 p.m.; a moderate arrival rate = 8:00 a.m. to 10:00 a.m.; and lowest arrival rate = 4:00 a.m. to 6:00 a.m.) and for different days of the week and month. Between 10:00 a.m. and 12:00 p.m., defined as the primary study period representing peak arrivals, 3.9% (n = 4,038) of patients LWBS. Using the derived model, the predicted LWBS rate was 4%. LWBS rates increased as the rate of ED patient arrivals, treatment times, and ED boarding times increased. A 10% increase in hourly ED patient arrivals from the observed average arrival rate increased the predicted LWBS rate to 10.8%; a 10% decrease in hourly ED patient arrivals from the observed average arrival rate predicted a 1.6% LWBS rate. A 30-minute decrease in treatment time from the observed average treatment time predicted a 1.4% LWBS. A 1% increase in patient arrivals has the same effect on LWBS rates as a 1% increase in treatment time. Reducing boarding times by 10% is expected to reduce LWBS rates by approximately 0.8%. Conclusions:This novel queuing theory-based model predicts the effect of patient arrivals, treatment time, and ED boarding on the rate of patients who LWBS at one institution. More studies are needed to validate this model across other institutions.ACADEMIC EMERGENCY MEDICINE 2013; 20:939-946

Operations research/management contributions to emergency department patient flow optimization: Review and research prospects

“…One of these blocking models identifies three major sources throughout the hospital from which blocking occurs (Osorio and Bierlaire, 2009). Wiler et al (2013) also focus on minimizing patient boarding with a queueing perspective. Marshall et al (2005) assess that simulation will be used in the future to carry out complexities of patient queueing systems like bed-block.…”

“…Time dependency is also captured in the modeling of clinical wards, where it is recognized that understanding variability outside of the ED is essential for capacity planning (Bekker and de Bruin, 2009). Wiler et al (2013) incorporate patient abandonment (LWBS) by using a M/G I/r/s + G I model introduced by Whitt (2005), where patient arrival follows a Poisson distribution, service times are a general distribution i.i.d, with r bed servers, s waiting area capacity and abandonment times are a general distribution i.i.d. Batt and Terwiesch (2013) provide innovative work in patient waiting, noting that factors beyond waiting time affect abandonment.…”

Emergency department crowding: Time to shift the paradigm from predicting and controlling to analysing and managing

“…The required key definitions and metrics for operational performance are already available in the literature Welch et al, 2006Welch et al, , 2011aWelch et al, , 2011bWiler et al, 2013).…”

Population Health and the Academic Medical Center

“…12 Examples range from applying queuing theory to improve emergency department throughput, to reducing the potential for severe medication interactions by verifying electronic medication lists against those populated by patients through a Web-based portal. 13,14 Indeed, leveraging the vast array of data generated in the process of care with the goal of refining and continuously improving performance—transforming into a “learning health system”—is emerging as a vital goal for large delivery systems. 15 Regional linkages between delivery system health information technology (HIT) networks, or health information exchanges, offer new tools for identifying emerging trends and targeting subgroups that may benefit from tailored interventions.…”