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Consider Bernoulli single-server queuing system with the arrival rate of 6 jobs per hour, service rate of 10 jobs per hour, 3-minute frames, and capacity

Consider Bernoulli single-server queuing system with the arrival rate of 6 jobs per hour, service rate of 10 jobs per hour, 3-minute frames, and capacity limited by 2 job. Let X(n) be the number of jobs in the system after n frames.

(a) Compute the transition probability matrix of X.

(b) Compute the steady state distribution of X. (c) In a long run, what portion of the time is the server running idle?

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