Question 3 A A private bank has installed an ATM in the city bazaar area. It was found that the time between an arrival and completion of transaction varies from one minute to seven minutes. The arrival and service distribution times are given below. Probability Tine (aninutes) Arrival Service 0.10 0.05 2-3 0.15 0.15 3-4 0.30 0.30 4-3 0.25 0.20 3-6 0.10 0.15 6-7 0.10 0.15
Question 3 A A private bank has installed an ATM in the city bazaar area. It was found that the time between an arrival and completion of transaction varies from one minute to seven minutes. The arrival and service distribution times are given below. Probability Tine (aninutes) Arrival Service 0.10 0.05 2-3 0.15 0.15 3-4 0.30 0.30 4-3 0.25 0.20 3-6 0.10 0.15 6-7 0.10 0.15
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Question 3 A
A private bank has installed an ATM in the city bazaar area. It was found that the time between an arrival
and completion of transaction varies from one minute to seven minutes. The arrival and service
distribution times are given below.
Probability
Tine (aninutes)
Arrival
Service
1-2
0.10
0.05
2-3
0.15
0.15
3-4
0.30
0.30
4-5
0.25
0.20
3-6
O.10
0.15
0.15
6-7
0.10
a) Compute the average time for arrival and service times and construct the appropriate
random number mappings using the average times for the random variables starting
from random number mappings for the random variables starting from 00.
b) Simulate 15 customers arriving at the using the random numbers given below. (12
c) What is the average time a customer waits for service? (
d) What is the average time a customer is in the system (wait plus service time) (
e) What is the percent of time the clerk is busy with customers?
Hint – average for time is using the mid point of time interval i.e 6-7 is 6.5
Random Numbers To Be Used in the Simulation
12 3 4 56 7
Customer
8 9 10 1i| 12 13
14 15
Interarrival time
0.08
0.87
0.15
0.04
0.52
0.46
0.96
0.1
0.02
0.76
0.32
0.1
0.62
0.25
09
Service Time
0.72
0.46
0.96
00
0,27 0.73
0.76
0.25
0.11
0.47
0.28 0.83
0.52
0.39
0.68
Use the following headings to complete the simulation
Time
Wait
Time
Customer RN
Between
Arrival Begin
for
RN Service
End
in
Arrivals
Time Service service
Time
Service System
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