Mechanical Engineering Exam > Mechanical Engineering Questions > A maintenance service facility has Poisson ar...
Start Learning for Free
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a 'first come first served' queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be
[2004]
- a)1/6 day
- b)1/3 day
- c)1 day
- d)3 day
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A maintenance service facility has Poisson arrival rates, negative exp...
Most Upvoted Answer
A maintenance service facility has Poisson arrival rates, negative exp...
Given:
- Poisson arrival rates
- negative exponential service time
- first come first served queue discipline
- Break-downs occur on an average of 3 per day with a range of zero to eight.
- Maintenance crew can service an average of 6 machines per day with a range of zero to seven.
To find:
- Mean waiting time for an item to be serviced
Solution:
- We can use Little's Law to find the mean waiting time, which states that the mean number of items in a queue (L) is equal to the mean arrival rate (λ) multiplied by the mean waiting time (W).
- We can also use the fact that the arrival rate (λ) is equal to the mean number of arrivals per unit time. In this case, since we are given the average number of break-downs per day, we can assume that the arrival rate is λ = 3 per day.
- Similarly, we can use the fact that the service rate (μ) is equal to the mean number of items serviced per unit time. In this case, since we are given the average number of machines serviced per day, we can assume that the service rate is μ = 6 per day.
- The utilization factor (ρ) can be calculated as ρ = λ/μ = 0.5.
- Using Little's Law, we can find the mean waiting time as W = L/λ. We already know λ and we can find L using the formula L = ρ^2/(1-ρ) = 0.5^2/(1-0.5) = 0.5.
- Therefore, the mean waiting time is W = 0.5/3 = 1/6 day.
Answer: Option A (1/6 day)
- Poisson arrival rates
- negative exponential service time
- first come first served queue discipline
- Break-downs occur on an average of 3 per day with a range of zero to eight.
- Maintenance crew can service an average of 6 machines per day with a range of zero to seven.
To find:
- Mean waiting time for an item to be serviced
Solution:
- We can use Little's Law to find the mean waiting time, which states that the mean number of items in a queue (L) is equal to the mean arrival rate (λ) multiplied by the mean waiting time (W).
- We can also use the fact that the arrival rate (λ) is equal to the mean number of arrivals per unit time. In this case, since we are given the average number of break-downs per day, we can assume that the arrival rate is λ = 3 per day.
- Similarly, we can use the fact that the service rate (μ) is equal to the mean number of items serviced per unit time. In this case, since we are given the average number of machines serviced per day, we can assume that the service rate is μ = 6 per day.
- The utilization factor (ρ) can be calculated as ρ = λ/μ = 0.5.
- Using Little's Law, we can find the mean waiting time as W = L/λ. We already know λ and we can find L using the formula L = ρ^2/(1-ρ) = 0.5^2/(1-0.5) = 0.5.
- Therefore, the mean waiting time is W = 0.5/3 = 1/6 day.
Answer: Option A (1/6 day)
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer?
Question Description
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer?.
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. 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 A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a first come first served queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven.The mean waiting time for an item to be serviced would be[2004]a)1/6 dayb)1/3 dayc)1 dayd)3 dayCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
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