1. Given the following values: Compute the following values: i) Average waiting time ii) Probability (wait) iii) Probability of Idle Server iv) Average service time(minutes) Total Number of customers = 20 Total Idle time of server = 14 Total run time of simulation = 86 Number of customers who wait = 11 Total service time=68 Total time customer wait in the queue = 30

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.4: Important Queueing Relationships
Problem 6P
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Please, I want a complete answer to this question, with a correct and clear solution to all paragraphs. The question is one question, but it has multiple paragraphs. Please solve it completely. And correctly.
1. Given the following values:
Compute the following values:
i) Average waiting time
ii) Probability(wait)
iii) Probability of Idle Server
iv) Average service time(minutes)
Customer
1. Fill in the following simulation table:
1
2
3
4
5
6
0
Time
Customer
Waits in
Arrival
Queue
Time (Minutes) Begins (Minutes)
7
15
16
18
25
1
2
3
4
5
6
Service
Time
1
4
3
4
Number of customers who wait = 11
Total service time = 68
Total time customer wait in the queue = 30
4
1
Total Number of customers = 20
Total Idle time of server = 14
Total run time of simulation = 86
2. Given below Simulation table emphasizing clock times :
Customer Arrival Time
Number (Clock)
Time Service
Begins(Clock)
0
1
3
7
9
15
Time
Service
Time
Service
Ends
Service Time
(Duration)
2
4
3
2
1
4
Time
Customer
Spends in
System
(Minutes)
Time
Service
Ends(Clock)
Transcribed Image Text:1. Given the following values: Compute the following values: i) Average waiting time ii) Probability(wait) iii) Probability of Idle Server iv) Average service time(minutes) Customer 1. Fill in the following simulation table: 1 2 3 4 5 6 0 Time Customer Waits in Arrival Queue Time (Minutes) Begins (Minutes) 7 15 16 18 25 1 2 3 4 5 6 Service Time 1 4 3 4 Number of customers who wait = 11 Total service time = 68 Total time customer wait in the queue = 30 4 1 Total Number of customers = 20 Total Idle time of server = 14 Total run time of simulation = 86 2. Given below Simulation table emphasizing clock times : Customer Arrival Time Number (Clock) Time Service Begins(Clock) 0 1 3 7 9 15 Time Service Time Service Ends Service Time (Duration) 2 4 3 2 1 4 Time Customer Spends in System (Minutes) Time Service Ends(Clock)
Q. Answer the following questions.
Q.1 Complete the Simulation table for a single channel by computing Time service begins, Time
Customer Waits in Queue, Time Service Ends, Time Customer Spends in System and Idle Time of
Server:
A
Arrival
Customer Time
1
0
7
2
3
4
5
6
7
8
9
10
11
12
13
14
B
15
14
16
23
30
33
37
39
42
47
49
51
59
66
с
Time
Service
Time
(Minutes) Begins
Service
1
2
4
3
3
2
3
4
4
3
3
1
4
3
D
4
E
F
Time
Customer
Waits in
Queue
(Minutes) Ends
Time
Service
G
Time
Customer
Spends in
System
(Minutes)
Answer the following questions:
a. What is the average waiting time for a customer?
b. What is the probability that a customer has to wait in the queue?
c. What is the Probability of idle time of the server?
d. What is the average service time?
e. What is the average time between arrivals?
f. What is the average waiting time of those who wait?
g. What is the average time a customer spends in the system?
H
Idle Time
of Server
(Minutes)
Transcribed Image Text:Q. Answer the following questions. Q.1 Complete the Simulation table for a single channel by computing Time service begins, Time Customer Waits in Queue, Time Service Ends, Time Customer Spends in System and Idle Time of Server: A Arrival Customer Time 1 0 7 2 3 4 5 6 7 8 9 10 11 12 13 14 B 15 14 16 23 30 33 37 39 42 47 49 51 59 66 с Time Service Time (Minutes) Begins Service 1 2 4 3 3 2 3 4 4 3 3 1 4 3 D 4 E F Time Customer Waits in Queue (Minutes) Ends Time Service G Time Customer Spends in System (Minutes) Answer the following questions: a. What is the average waiting time for a customer? b. What is the probability that a customer has to wait in the queue? c. What is the Probability of idle time of the server? d. What is the average service time? e. What is the average time between arrivals? f. What is the average waiting time of those who wait? g. What is the average time a customer spends in the system? H Idle Time of Server (Minutes)
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Cengage,