Consider an M/M/1/5 queueing system with mean arrival rate and mean service time 1/ that operates in the following manner. When any customer is

Consider an M/M/1/5 queueing system with mean arrival rate λ and mean service time 1/μ that operates in the following manner. When any customer is in queue, the time until he defects (i.e., leaves the queue without receiving service) is exponentially distributed with a mean of 1/β. It is assumed that when a customer begins receiving service he does not defect.

Markovian Queueing Systems 151

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

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

c. Find the average number of customers in the system.