Category Archives: Simulation

Use of Simulation to Reduce Hospital Emergency Department Waiting Times

The next posts will focus on the effective use of simulation to improve Emergency Department (ED) performance and use an optimization procedure with respect to controllable variables and constants.   Clark (2016) describes the approach and a case study illustrating its application.   Long waiting times and length of stay at hospital emergency departments is an important public health problem. This post describes the use of simulation to improve ED performance. The approach described was applied at the Saint Camille hospital in Paris.   The hospital has about 300 beds and its ED operates 24 hours per day and serves more than 60,000 patients per year.

Long wait times is an increasing problem in the United States, and visits to Hospital EDs has been increasing.   From 1999 to 2009, it had increased by 32% to 136 million annual visits (Hing, Bhuiya 2012).   That is, it increased at annual rate of 2.8%.   For some hospitals, this increase has resulted in crowding and longer wait times to see a provider.   Between 2003 and 2009, the mean wait time to be examined by a provider increased by 25% to 58.1 minutes. However, the distributions of wait times are highly skewed since more serious conditions are treated more quickly.   The median wait time increased by 22% to 33 minutes.

The National Academy of Engineering and the Institute of Medicine prepared a report presenting the importance of systems engineering tools in improving health care processes (Reid, Compton, Grossman et all 2005). They emphasized the use of simulation. A discrete-event simulation of patient flow through an ED represents the ED as it evolves over time. The simulation’s state is stochastic since the processes such as patient arrival times, patient severity, and treatment times are stochastic and represented by random variables.   Thus one must replicate the simulation model to estimate performance measures such as the average waiting time, the histogram of waiting times for a specified set of ED resources such as number of beds, doctor availability and nurse availability.


  1. Clark, Gordon (2016). “Statistics for Quality Improvement” ASQ Statistics Division Digest, 35(2): 22-26.
  2. E. Hing, F. Bhuiya (2012). “Wait Time for Treatment in Hospital Emergency Departments: 2009” National Center for Health Statistics Data Brief, No. 102, August 2012.
  3. P. P. Reid, W. D. Compton, J. H. Grossman et al (2005). Building a Better Delivery System: A New Engineering/Health Care Partnership, National Academies Press, Washington, DC.

Simulation Model Building

This posting illustrates the use of model building to study cause and effect and reduce common-cause variation.  One approach to model building is to build a model such as a regression model based on either results from an experimental design or observed process data.  Another approach illustrated in this posting is to construct a simulation model based on the system flow chart or process map.    One application of a simulation model is to predict flow times or service times for complex systems.   In service or health system applications customer service or wait times could be useful quality measures.   One uses the simulation model by varying input variables such as the number of servers to predict their effect on customer service times.

Davies (2007) describes a case study involving the treatment of minor injuries and medical problems in an emergency department in England.   Receptionists route arriving patients with minor injuries or medical conditions are routed to the “Minors” department.   The standard processing procedure has receptionists in the Minors department assign patients to a queue for triage nurses who assess the patient condition and needs.   Then the triage nurse routes the patients to a doctor or nurse for treatment.   The nurses are qualified to assess and treat minor injuries but not to handle minor medical conditions which are handled by doctors.   These nurses are Emergency Nurse Practitioners (EPNs).  Call this procedure “See” and “Treat”.   The UK national health service recommended that emergency departments skip the triage nurse step.   The health service recommended that receptionists route patients to a doctor or ENP for diagnosis and treatment.  Call this procedure “See & Treat”.   The intent was to reduce patient system time by eliminating a step and its associated queuing time.   The following figure depicts the “See & Treat” patient flow.



Davies describes a simulation model for comparing the two procedures.   This model represents the processing of individual patients, their waiting times, and individual task processing times.   Inputs to the model would include distributions for task times, distributions for times between patient arrivals, and the numbers of doctors and EPNs.  The following figure presents some of the simulation results.   The new procedure “See & Treat” that eliminates the triage step gives the lowest system time.




  1. Davies, R. (2007). “See and Treat” or “See” and “Treat” in an Emergency Department. 2007 Winter Simulation Conference. Washington, DC.