Forecasting emergency department crowding: a discrete event simulation

Abstract

Study objective: To develop a discrete event simulation of emergency department (ED) patient flow for the purpose of forecasting near-future operating conditions and to validate the forecasts with several measures of ED crowding.

Methods: We developed a discrete event simulation of patient flow with evidence from the literature. Development was purely theoretical, whereas validation involved patient data from an academic ED. The model inputs and outputs, respectively, are 6-variable descriptions of every present and future patient in the ED. We validated the model by using a sliding-window design, ensuring separation of fitting and validation data in time series. We sampled consecutive 10-minute observations during 2006 (n=52,560). The outcome measures--all forecast 2, 4, 6, and 8 hours into the future from each observation--were the waiting count, waiting time, occupancy level, length of stay, boarding count, boarding time, and ambulance diversion. Forecasting performance was assessed with Pearson's correlation, residual summary statistics, and area under the receiver operating characteristic curve.

Results: The correlations between crowding forecasts and actual outcomes started high and decreased gradually up to 8 hours into the future (lowest Pearson's r for waiting count=0.56; waiting time=0.49; occupancy level=0.78; length of stay=0.86; boarding count=0.79; boarding time=0.80). The residual means were unbiased for all outcomes except the boarding time. The discriminatory power for ambulance diversion remained consistently high up to 8 hours into the future (lowest area under the receiver operating characteristic curve=0.86).

Conclusion: By modeling patient flow, rather than operational summary variables, our simulation forecasts several measures of near-future ED crowding, with various degrees of good performance.

Figure 1.

Conceptual process of using a simulation model to forecast ED operations. The model would take past and present patient-level data as input and would give future patient-level data as output. Any outcome measure of interest could theoretically be calculated using this information to obtain a forecast.

Figure 2.

Diagram of patient flow through the ForecastED simulation. Six random processes, marked by circled letters, drive all aspects of patient flow. A, Patient arrivals as a nonstationary Poisson process, dependent on the time of the day and day of the week; B, decisions to leave without being seen as a Bernoulli trial, dependent on the waiting room count; C, patient acuity levels as a multinomial distribution; D, duration of evaluation and treatment as a log-normal distribution, dependent on the acuity level; E, hospital admission decisions as a Bernoulli trial, dependent on the acuity level; and F, hospital bed openings as a nonstationary Poisson process, dependent on the time of the day and day of the week.

Figure 3.

Example application of the sliding-window validation technique. At consecutive 10-minute observations, the distribution parameters were reestimated with 4 weeks of historical patient data. The simulation forecast the operating conditions at various points in the future. This technique ensured the data used for fitting and validation never overlapped.

Figure 4.

Observed (dark shading) and theoretical (light shading) distributions of the random processes in ForecastED. A, Time between patient arrivals, B, probability of leaving without being seen as a function of the waiting room count, C, probability of being assigned to each triage category, D, duration of ED evaluation and treatment, E, probability of hospital admission as a function of the acuity level, and F, time between hospital bed openings. All acuity levels are described according to the Emergency Severity Index (ESI).

Figure 5.

Receiver operating characteristic curves of the simulation forecast of ambulance diversion at various points in the future. The area under the receiver operating characteristic curve with 95% CI is shown in parentheses.