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A queueing system has one single server work station 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

1. 0.20
2. 0.17
3. 0.50
4. 0.83

Correct answer: 0.50

Solution

lambda = 5 jobs/hr; mean service 6 min gives mu = 10 jobs/hr, so utilization rho = 5/10 = 0.5. The probability the server is idle is P0 = 1 - rho = 0.5, option 2. The stored 0.83 is wrong.

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