7.14 Consider an M/M/1 queueing system with mean arrival rate and mean service time 1= that...

7.14 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 2 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.