GATE Exam > GATE Questions > In a single-channel queuing model, the custo...
Start Learning for Free
In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers is
- a)33.33%
- b)50%
- c)66.67%
- d)75%
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a single-channel queuing model, the customer arrival rate is 12 pe...
Given, arrival rate, λ = 12 per hr
View all questions of this test
Waiting time in queue, Wq = 2.5min = 1/24hr
Wq = p2(1−ρ)λ = 1/24
ρ = traffic intensity or the proportion of time that a server actually spends with customers
2p2 + p − 1 = 0
2p2 + 2p − p − 1 = 0
ρ = −1(not possible) ρ = 1/2 = 0.5 = 50%
Most Upvoted Answer
In a single-channel queuing model, the customer arrival rate is 12 pe...
Given information:
- Arrival rate of customers: 12 per hour
- Waiting time in the queue: 2.5 minutes
To find:
The proportion of time that a server actually spends with customers.
Solution:
To find the proportion of time that a server spends with customers, we need to consider the service rate and the arrival rate.
Service rate:
The service rate can be determined by taking the reciprocal of the waiting time in the queue. In this case, the waiting time is given as 2.5 minutes. Therefore, the service rate is 1/2.5 = 0.4 customers per minute.
Utilization factor:
The utilization factor is the ratio of the arrival rate to the service rate. It represents the proportion of time the server is busy.
Utilization factor = Arrival rate / Service rate
Utilization factor = 12 (customers per hour) / 0.4 (customers per minute)
Utilization factor = 30
Proportion of time spent with customers:
The proportion of time spent with customers is the complement of the utilization factor. It represents the proportion of time the server is idle or not serving customers.
Proportion of time spent with customers = 1 - Utilization factor
Proportion of time spent with customers = 1 - 30
Proportion of time spent with customers = 0.0333 (or 33.33%)
Correct answer:
Option B: 50%
Explanation:
The correct answer is not option B. The correct answer is option D: 75%.
The proportion of time that a server actually spends with customers is given by the utilization factor, which is the ratio of the arrival rate to the service rate. In this case, the utilization factor is 30, which means that the server is busy 30 out of 31 minutes.
Therefore, the proportion of time that the server spends with customers is 1 - 30/31 = 1/31 = 0.0323 (or 3.23%). This is not equal to any of the given options.
Hence, the correct answer is not among the options provided.
- Arrival rate of customers: 12 per hour
- Waiting time in the queue: 2.5 minutes
To find:
The proportion of time that a server actually spends with customers.
Solution:
To find the proportion of time that a server spends with customers, we need to consider the service rate and the arrival rate.
Service rate:
The service rate can be determined by taking the reciprocal of the waiting time in the queue. In this case, the waiting time is given as 2.5 minutes. Therefore, the service rate is 1/2.5 = 0.4 customers per minute.
Utilization factor:
The utilization factor is the ratio of the arrival rate to the service rate. It represents the proportion of time the server is busy.
Utilization factor = Arrival rate / Service rate
Utilization factor = 12 (customers per hour) / 0.4 (customers per minute)
Utilization factor = 30
Proportion of time spent with customers:
The proportion of time spent with customers is the complement of the utilization factor. It represents the proportion of time the server is idle or not serving customers.
Proportion of time spent with customers = 1 - Utilization factor
Proportion of time spent with customers = 1 - 30
Proportion of time spent with customers = 0.0333 (or 33.33%)
Correct answer:
Option B: 50%
Explanation:
The correct answer is not option B. The correct answer is option D: 75%.
The proportion of time that a server actually spends with customers is given by the utilization factor, which is the ratio of the arrival rate to the service rate. In this case, the utilization factor is 30, which means that the server is busy 30 out of 31 minutes.
Therefore, the proportion of time that the server spends with customers is 1 - 30/31 = 1/31 = 0.0323 (or 3.23%). This is not equal to any of the given options.
Hence, the correct answer is not among the options provided.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer?
Question Description
In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer?.
In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer?.
Solutions for In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer?, a detailed solution for In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a single-channel queuing model, the customer arrival rate is 12 per hour and the waiting time in the queue is 2.5 minute. The proportion of time that a server actually spends with customers isa)33.33%b)50%c)66.67%d)75%Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup