1. At a certain petrol pump, customers arrive in a Poisson process with an average time of five minutes between successive arrivals. The time taken at the petrol pump to serve customers follows exponential distribution with an average of two minutes. You are required to obtain the following:

(a) Arrival and service rates.

(b) The utilisation parameter.

(

c) Probability that there shall be four customers in the system.

(d) Probability that there are more than four customers in the system.

(

e) Expected queue length.

(t) Expected number of customers in the system.

(g) Expected time that a customer has to wait in the queue.

(h) Expected time that a customer has to spend in the system.

(i) It is decided to open a new service point when the customers' expected waiting time rises to three times the present level. What increased flow of customers will justify this?