GATE 2021 ME (ME1) – Question 52
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is _____ (round off to the nearest integer).
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Correct answer: 4
Explanation
Service rate is μ=60/4=15 jobs/hour and utilisation is ρ=12/15=0.8. For an M/M/1 system, mean jobs including the one in service is $L=\rho/(1-\rho)$.
Thus L=0.8/0.2=**4**. Queue-only mean would be 3.2, which is a different quantity.