Customers arrive at a service facility with one server according to a Poisson process with a rate of 5 per hour. The service times are i.i.d. exponential r.v.’s, and on the average, the server can serve 7 customers per hour. Suppose that the system is in the stationary regime.

(a) What is the probability that at a particular time moment, there will be no queue?

(b) What is the probability that at a particular time moment, there will be more than three customers waiting for service?

(c) What is the mean proportion of time when the server is idle?