GATE ME 2024 Set 1 — Question 35
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Industrial Engineering → Operations Research → Queuing Models (M/M/1)
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Question
A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queueing system, the probability that the server is not busy at any point in time is
Correct answer
(C) 0.50
Solution
This is an queueing model.
Arrival rate, jobs/hour.
Mean service time minutes hours hours.
Service rate, jobs/hour.
Utilization factor, .
The probability that the server is not busy (idle) is .
Arrival rate, jobs/hour.
Mean service time minutes hours hours.
Service rate, jobs/hour.
Utilization factor, .
The probability that the server is not busy (idle) is .
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