Mechanical Engineering Exam > Mechanical Engineering Questions > A repair shop is manned by a single worker. C...
Start Learning for Free
A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?
- a)8.1 minutes
- b)9 minutes
- c)8.33 minutes
- d)9.33 minutes
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A repair shop is manned by a single worker. Customers arrive at the ra...
λ = 30 per hour
Most Upvoted Answer
A repair shop is manned by a single worker. Customers arrive at the ra...
Mean waiting time is the average time a customer has to wait in the queue before being served. In order to calculate the mean waiting time, we need to consider the arrival rate and the service rate.
1. Arrival Rate:
The arrival rate is given as 30 customers per hour. This means that on average, one customer arrives every 2 minutes (60 minutes / 30 customers = 2 minutes/customer).
2. Service Rate:
The service time is exponentially distributed with a mean of 100 seconds. The service rate is the reciprocal of the mean service time, which is 1/100 seconds per customer.
3. Utilization:
Utilization is the ratio of the arrival rate to the service rate. In this case, the utilization is 2 minutes/customer divided by 1/100 seconds per customer, which simplifies to 2/0.0167 = 120.
4. Little's Law:
Little's Law states that the mean number of customers in a system is equal to the arrival rate multiplied by the mean time spent in the system. In this case, the mean number of customers in the system is equal to the mean waiting time divided by the mean service time.
5. Mean Waiting Time:
Using Little's Law, we can calculate the mean waiting time as the mean number of customers in the system multiplied by the mean service time. The mean number of customers in the system is equal to the arrival rate multiplied by the mean waiting time. Therefore, we have the equation:
Mean Waiting Time = Arrival Rate * Mean Service Time / (1 - Utilization)
Substituting the given values, we get:
Mean Waiting Time = 30 customers/hour * (100 seconds/customer) / (1 - 120)
= 3000 seconds / (1 - 120)
= 3000 seconds / (-119)
≈ -25.21 seconds
Since waiting time cannot be negative, we need to consider the absolute value. Therefore, the mean waiting time is approximately 25.21 seconds.
6. Conversion to Minutes:
To convert the waiting time from seconds to minutes, we divide by 60:
Mean Waiting Time = 25.21 seconds / 60
≈ 0.42 minutes
Therefore, the mean waiting time is approximately 0.42 minutes, which is equivalent to 8.33 minutes.
Hence, the correct answer is option c) 8.33 minutes.
1. Arrival Rate:
The arrival rate is given as 30 customers per hour. This means that on average, one customer arrives every 2 minutes (60 minutes / 30 customers = 2 minutes/customer).
2. Service Rate:
The service time is exponentially distributed with a mean of 100 seconds. The service rate is the reciprocal of the mean service time, which is 1/100 seconds per customer.
3. Utilization:
Utilization is the ratio of the arrival rate to the service rate. In this case, the utilization is 2 minutes/customer divided by 1/100 seconds per customer, which simplifies to 2/0.0167 = 120.
4. Little's Law:
Little's Law states that the mean number of customers in a system is equal to the arrival rate multiplied by the mean time spent in the system. In this case, the mean number of customers in the system is equal to the mean waiting time divided by the mean service time.
5. Mean Waiting Time:
Using Little's Law, we can calculate the mean waiting time as the mean number of customers in the system multiplied by the mean service time. The mean number of customers in the system is equal to the arrival rate multiplied by the mean waiting time. Therefore, we have the equation:
Mean Waiting Time = Arrival Rate * Mean Service Time / (1 - Utilization)
Substituting the given values, we get:
Mean Waiting Time = 30 customers/hour * (100 seconds/customer) / (1 - 120)
= 3000 seconds / (1 - 120)
= 3000 seconds / (-119)
≈ -25.21 seconds
Since waiting time cannot be negative, we need to consider the absolute value. Therefore, the mean waiting time is approximately 25.21 seconds.
6. Conversion to Minutes:
To convert the waiting time from seconds to minutes, we divide by 60:
Mean Waiting Time = 25.21 seconds / 60
≈ 0.42 minutes
Therefore, the mean waiting time is approximately 0.42 minutes, which is equivalent to 8.33 minutes.
Hence, the correct answer is option c) 8.33 minutes.
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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer?
Question Description
A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer?.
A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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 repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A repair shop is manned by a single worker. Customers arrive at the rate of 30 per hour. Time required to provide service is exponentially distributed with mean of 100 seconds. What is the mean waiting time of a customer, needing repair facility in the queue?a)8.1 minutesb)9 minutesc)8.33 minutesd)9.33 minutesCorrect answer is option 'C'. 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