33.

(a) The arrivals at a desk are Poisson distributed with a mean of one customer every two minutes.

The service times are exponentially distributed with an average of 15 seconds per customer. You are required to calculate:

(i) Overall system utilisation.

(ii) Expected number of customers in the system.

(iii) Expected length of queues.

(iv) Expected time a customer spends in the system.

(v) Expected time a customer spends in the queue.

(vi) Probability that the system is completely idle.

(vii) Probability that an arriving customer waits.

(b) Recalculate the parameters given in

(a) assuming, first, that the server works twice as fast and, second, that two servers each work at the original rate, and compare them.