stat 340 project
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Walk-In Clinic
SimulationTeam 14:
Archit AgnihotriJawed Karim
Salman Asif
Umer Iqbal
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Introduction
Medical attention and health care are two vital factors that influence ones life. The
amount of time one spends waiting to see a doctor is at times boundless.
The objective of our project is to analyze the waiting and service time at a clinic for
a patient, in an attempt to find the optimal number of doctors working at different
times during the day.
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Reception
Waiting Lounge
Doctor 3Doctor 2
Departure
Entrance
Doctor 1
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Data - VariablesEvent Counter System State Output
Arrival timeNumber of
arrivals
Patients at
Reception
Cost per
patient
Departure timeNumber ofdepartures
Patients inWaiting lounge
Number ofdoctors
Patients beingServed
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Assumptions Maximum capacity of the sitting area is K i.e. there cannot be more than K number of
patients waiting at any one time
Maximum number of doctors is N (corresponding to the total number of doctors offices)
We assume that patients have made no appointments with the doctor. Patients are served
on a first come, first serve basis.
Patients arrive one at a time i.e. no groups of sick people
One queue, multiserver system
Patients arrive independent of each other
The service time of all doctors is independent and identically distributed
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Summary of waiting timeMean 19.57
Var 571.19
Median 12.77
First Quartile 2.79
Third Quartile 23.55
Fourth Quartile 97.72
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Summary of service time
Mean 12.72
Var 85.16
Median 13.1
First Quartile 3.56
Third Quartile 20.43
Fourth Quartile 30.94
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Validation
Waiting times and Service Times follow exponential distribution.
Kolmogorov-Smirnov (K-S) test statistic
Sample means and variances using these values would not be adequate
Reliance on plots to determine the distribution
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Waiting time plot
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
20
40
60
80
100
120
Wating time
Wa ting time
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Service time plot
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
5
10
15
20
25
30
35
S ervic e Time
S ervice Time
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Simulation In order to improve the estimate of the average
waiting and service times, we simulated two
thousand data points
> mean(simulated.wait)
[1] 22.14312
> mean(simulated.serv)
[1] 12.57606
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Preliminary Conclusion
Average waiting time follows an exponential distribution with mean
(19.57) Minutes
Average service time follows an exponential distribution with mean
(12.72) - Minutes
Simulated mean for the waiting time - 22.14
Simulated mean for the service time - 12.57
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Recommendations
Collect more data points to avoid sampling errors and improve accuracy
Visit walk-in clinics across the country in order to collect data which is unbiased
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