Question: Consider an M/M/1 queueing system with mean arrival rate and mean service time 1/. The system provides bulk service in the following manner. When

Consider an M/M/1 queueing system with mean arrival rate λ and mean service time 1/μ. The system provides bulk service in the following manner.

When the server completes any service, the system returns to the empty state if there are no waiting customers. Customers who arrive while the server is busy join a single queue. At the end of a service completion, all waiting customers enter the service area to begin receiving a bulk service.

a. Give the state-transition-rate diagram of the process.

b. What is the probability that the server is idle?

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