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A machine receives jobs at a rate of 20 per hour and the processing rate is 30 per hour. How much time (in minutes) on an average does a job have to wait before it gets loaded on to the machine?
- a)4
- b)3
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A machine receives jobs at a rate of 20 per hour and the processing r...
λ = 20/hour
μ = 30/hour
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A machine receives jobs at a rate of 20 per hour and the processing r...
Given:
- Job arrival rate = 20 per hour
- Processing rate = 30 per hour
To find:
- Average waiting time for a job before it gets loaded onto the machine
Explanation:
The average waiting time for a job can be calculated using Little's Law, which states that the average number of jobs in a system is equal to the arrival rate multiplied by the average time a job spends in the system.
Step 1: Calculate the average number of jobs in the system:
The arrival rate is given as 20 jobs per hour, so the average arrival rate per minute can be calculated by dividing it by 60 (since there are 60 minutes in an hour):
Average arrival rate = 20 / 60 = 1/3 jobs per minute
The processing rate is given as 30 jobs per hour, so the average processing rate per minute can be calculated by dividing it by 60:
Average processing rate = 30 / 60 = 1/2 jobs per minute
The average number of jobs in the system can be calculated as the ratio of the arrival rate to the processing rate:
Average number of jobs in the system = Average arrival rate / Average processing rate = (1/3) / (1/2) = 2/3 jobs
Step 2: Calculate the average time a job spends in the system:
The average time a job spends in the system can be calculated as the reciprocal of the processing rate:
Average time a job spends in the system = 1 / Average processing rate = 1 / (1/2) = 2 minutes
Step 3: Calculate the average waiting time for a job:
The average waiting time for a job can be calculated using Little's Law:
Average waiting time = Average number of jobs in the system * Average time a job spends in the system = (2/3) * 2 = 4/3 minutes
Therefore, the average waiting time for a job before it gets loaded onto the machine is 4/3 minutes, which is approximately 1.33 minutes.
- Job arrival rate = 20 per hour
- Processing rate = 30 per hour
To find:
- Average waiting time for a job before it gets loaded onto the machine
Explanation:
The average waiting time for a job can be calculated using Little's Law, which states that the average number of jobs in a system is equal to the arrival rate multiplied by the average time a job spends in the system.
Step 1: Calculate the average number of jobs in the system:
The arrival rate is given as 20 jobs per hour, so the average arrival rate per minute can be calculated by dividing it by 60 (since there are 60 minutes in an hour):
Average arrival rate = 20 / 60 = 1/3 jobs per minute
The processing rate is given as 30 jobs per hour, so the average processing rate per minute can be calculated by dividing it by 60:
Average processing rate = 30 / 60 = 1/2 jobs per minute
The average number of jobs in the system can be calculated as the ratio of the arrival rate to the processing rate:
Average number of jobs in the system = Average arrival rate / Average processing rate = (1/3) / (1/2) = 2/3 jobs
Step 2: Calculate the average time a job spends in the system:
The average time a job spends in the system can be calculated as the reciprocal of the processing rate:
Average time a job spends in the system = 1 / Average processing rate = 1 / (1/2) = 2 minutes
Step 3: Calculate the average waiting time for a job:
The average waiting time for a job can be calculated using Little's Law:
Average waiting time = Average number of jobs in the system * Average time a job spends in the system = (2/3) * 2 = 4/3 minutes
Therefore, the average waiting time for a job before it gets loaded onto the machine is 4/3 minutes, which is approximately 1.33 minutes.
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A machine receives jobs at a rate of 20 per hour and the processing rate is 30 per hour. How much time (in minutes) on an average does a job have to wait before it gets loaded on to the machine?a) 4b) 3c) 5d) 6Correct answer is option 'A'. Can you explain this answer?
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A machine receives jobs at a rate of 20 per hour and the processing rate is 30 per hour. How much time (in minutes) on an average does a job have to wait before it gets loaded on to the machine?a) 4b) 3c) 5d) 6Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A machine receives jobs at a rate of 20 per hour and the processing rate is 30 per hour. How much time (in minutes) on an average does a job have to wait before it gets loaded on to the machine?a) 4b) 3c) 5d) 6Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A machine receives jobs at a rate of 20 per hour and the processing rate is 30 per hour. How much time (in minutes) on an average does a job have to wait before it gets loaded on to the machine?a) 4b) 3c) 5d) 6Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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