Mechanical Engineering Exam > Mechanical Engineering Questions > The number of customers arriving at a railway...
Start Learning for Free
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will be
- a)3
- b)3.2
- c)4
- d)4.2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of customers arriving at a railway reservation counter is P...
Most Upvoted Answer
The number of customers arriving at a railway reservation counter is P...
Solution:
Given:
Arrival rate (λ) = 8 customers/hour
Service rate (μ) = 6 minutes/customer
To find: Average number of customers in the queue
- Arrival rate (λ) can be converted to arrival rate per minute by dividing it by 60 (since 1 hour = 60 minutes):
Arrival rate per minute (λ') = 8/60 = 0.1333 customers/minute
- Service rate (μ) can be converted to service rate per minute by dividing it by 60:
Service rate per minute (μ') = 6/60 = 0.1 customers/minute
- Utilization factor (ρ) can be calculated using the formula:
ρ = λ'/μ'
Substitute the values:
ρ = 0.1333/0.1 = 1.33
- Using the formula for the average number of customers in the queue (Lq) for a M/M/1 queue:
Lq = ρ^2 / (1 - ρ)
Substitute the value of ρ:
Lq = (1.33)^2 / (1 - 1.33) = 1.77 / (-0.33) = -5.36
- The negative value for Lq indicates that the system is not stable and the queue length is not defined.
Since the negative value of Lq is not valid, we need to check for any errors in the calculations.
- Utilization factor (ρ) cannot exceed 1, so it seems there is an error in the calculation of ρ.
- Recalculate ρ using the correct values:
ρ = λ/μ
Substitute the values:
ρ = 8/6 = 1.33
- Now recalculate Lq using the correct ρ value:
Lq = ρ^2 / (1 - ρ)
Substitute the value of ρ:
Lq = (1.33)^2 / (1 - 1.33) = 1.77 / (-0.33) = -5.36
Again, the negative value for Lq indicates an error in the calculations.
However, in the given options, we can see that the correct answer is option B, which suggests that the average number of customers in the queue is 3.2.
It seems there is an error in the question or the provided options. The correct answer cannot be determined based on the given information and calculations.
Given:
Arrival rate (λ) = 8 customers/hour
Service rate (μ) = 6 minutes/customer
To find: Average number of customers in the queue
- Arrival rate (λ) can be converted to arrival rate per minute by dividing it by 60 (since 1 hour = 60 minutes):
Arrival rate per minute (λ') = 8/60 = 0.1333 customers/minute
- Service rate (μ) can be converted to service rate per minute by dividing it by 60:
Service rate per minute (μ') = 6/60 = 0.1 customers/minute
- Utilization factor (ρ) can be calculated using the formula:
ρ = λ'/μ'
Substitute the values:
ρ = 0.1333/0.1 = 1.33
- Using the formula for the average number of customers in the queue (Lq) for a M/M/1 queue:
Lq = ρ^2 / (1 - ρ)
Substitute the value of ρ:
Lq = (1.33)^2 / (1 - 1.33) = 1.77 / (-0.33) = -5.36
- The negative value for Lq indicates that the system is not stable and the queue length is not defined.
Since the negative value of Lq is not valid, we need to check for any errors in the calculations.
- Utilization factor (ρ) cannot exceed 1, so it seems there is an error in the calculation of ρ.
- Recalculate ρ using the correct values:
ρ = λ/μ
Substitute the values:
ρ = 8/6 = 1.33
- Now recalculate Lq using the correct ρ value:
Lq = ρ^2 / (1 - ρ)
Substitute the value of ρ:
Lq = (1.33)^2 / (1 - 1.33) = 1.77 / (-0.33) = -5.36
Again, the negative value for Lq indicates an error in the calculations.
However, in the given options, we can see that the correct answer is option B, which suggests that the average number of customers in the queue is 3.2.
It seems there is an error in the question or the provided options. The correct answer cannot be determined based on the given information and calculations.
|
Explore Courses for Mechanical Engineering exam
|
|
Top Courses for Mechanical EngineeringView all
Question Description
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer?.
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will bea)3b)3.2c)4d)4.2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup