Question: Consider an M/M/1 queueing system with mean arrival rate and mean service time 1/ that operates in the following manner. When the number of

Consider an M/M/1 queueing system with mean arrival rate λ and mean service time 1/μ that operates in the following manner. When the number of customers in the system is greater than three, a newly arriving customer joins the queue with probability p and balks (i.e., leaves without joining the queue) with probability 1 − p.

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

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

c. Find the actual arrival rate of customers in the system.

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