```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-ElmaghrabyMorse (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
X  7.37
ˆ  3.25
N  250
7.37  8.5
Z
3.25 / 250
Z  5.49
Therefore: The new station does improve
response time.
Hypothesis Testing
Mean Satisfactory Response
X  0.17
ˆ  0.12
N  250
0.17  0.12
Z
0.31 / 250
Z  1000
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.
```