Rescue Squad Simulation Michael C. Jones MSIM 852 Fall 2007 Prof: Bailey

Motivation “Of 13,822 cardiac arrests not witnessed by ambulance crews but attended by them within 15 minutes, complete data were available for 10,554 (76%). Of these patients, 653 (6%) survived to hospital discharge. After other significant covariates were adjusted for, shorter response time was significantly associated with increased probability of receiving defibrillation and survival to discharge among those defibrillated. Reducing the response time to 8 minutes increased the predicted survival to 8%, and reducing it to 5 minutes increased survival to 10-11%.” Source: http://www.bmj.com/cgi/content/abstract/322/7299/1385

System Description One Rescue Squad, composed of three ambulances, is responsible for responding to emergencies in four neighborhoods. Currently, all three ambulances work out of the station. There is an opportunity to move some of them to another building. Would this improve response time? Statistics of interest are: Mean response time, and percent of responses within 7 minutes of being dispatched. (Based on interviews, 1 minute must be allowed for dispatch to process the call and assign a unit.)

Distances:

Arena Model

Observation: - Ambulances are a critical asset. Long wait times are not acceptable. Therefore, in order to achieve the required response time, “excess” capacity is built into the system. This means that the system naturally returns to the “empty and idle” state. Therefore, startup transients, normally a problem for modelers, are not a problem in the case.

Lessons Learned: (AKA: Room For Improvement) The matrix for distances is N2, and the number of paths to animate is also N2, so reducing the number of stations through VV&A is important. Actual calls are NOT iid. (For example, heavy rain causes slick roads, therefore more calls from all stations. Summer causes more traffic at the beach, therefore more calls from the Ocean Front than normal.) I modeled ambulance speed as a constant. It should be random.

i.i.d.? Since the response time of the ith patient, and the treatment time for that patient, may prolong the response time for the (i+1)th patient, the response time of these two patients are NOT independent. Since the system routinely returns to the empty and idle state, the response times of two patients, ti and t(i+x) are iid if x is “large enough” to ensure the two patients are separated by an empty and idle state. By inspection, x must be greater than about 10. I used internal batches 250 patients long and averaged across the batches. All subsequent calculations are based on these batched means.

Ranking and Selection Single Stage Bechhofer-Elmaghraby-Morse (BEM). Two-stage Rinott.

Results:

Hypothesis Testing Ho: Stationing an ambulance at the new building will not improve response time as determined by: mean response time and percent of responses slower than 7 minutes. Ha: Stationing an ambulance at the new building will improve response time. Desired significance: 1%.

Hypothesis Testing Mean Response Time Therefore: The new station does improve response time.

Hypothesis Testing Mean Satisfactory Response Therefore: The new station does reduce the number of responses taking greater than 7 minutes.

Conclusion The rescue squad should put one of the ambulances at the new location.