Required a) Compute the midpoints for arrival and service times and apply it to construct the appropriate random number mappings for the random variables starting from 00. (3 marks) b) Simulate 15 customers arriving at the using the random numbers given below. (12 marks) c) What is the average time a customer waits for service? (1 mark) d) What is the average time a customer is in the system (wait plus service time) (2 marks) e) What is the percent of time the clerk is busy with customers? (2 marks)
Required a) Compute the midpoints for arrival and service times and apply it to construct the appropriate random number mappings for the random variables starting from 00. (3 marks) b) Simulate 15 customers arriving at the using the random numbers given below. (12 marks) c) What is the average time a customer waits for service? (1 mark) d) What is the average time a customer is in the system (wait plus service time) (2 marks) e) What is the percent of time the clerk is busy with customers? (2 marks)
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
Related questions
Question
THIS IS FOR REVISION PURPOSES. NOT GRADED
Transcribed Image Text:Required
a) Compute the midpoints for arrival and service times and apply it to construct the
appropriate random number mappings for the random variables starting from 00. (3
marks)
b) Simulate 15 customers arriving at the using the random numbers given below. (12
marks)
c) What is the average time a customer waits for service? (1 mark)
d) What is the average time a customer is in the system (wait plus service time) (2 marks)
e) What is the percent of time the clerk is busy with customers? (2 marks)
Hint (midpoint for 60 to under 90= (60+90)/2=75 sec)
Customer
Interarrival time
Service Time
Random Numbers To Be Used in the Simulation
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15
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 0.9
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
Between
Customer RN
Arrivals
Wait
for RN Service
Time
in
End
Time Service System
Arrival Begin
Time Service service
Transcribed Image Text:Question 3 A
Passengers arriving at a suburban rail ticket office during the morning peak commuter period
frequently have to wait for service. There is one clerk who issues tickets and provides an
information service for passengers. The manager has received complaints regarding the time
passengers spend in the queue waiting to be served, and she wishes to investigate possible methods
of reducing the queueing time. Possible ideas include employing a second ticket clerk who could
either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be
to collect fares on the train. The manager decided to collect data on arrivals and service times over
a number of days, and her figures are summarized
Inter-arrival time
(secs)
0 to under 30
30 to under 60
60 to under 90
90 to under 120
Frequency
(%)
55
30
10
5
Service time
(secs)
20 to under 30
30 to under 40
40 to under 50
50 to under 60
60 to under 90
Frequency
(%)
17
28
25
20
10
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