Customers arrive at a single-server station in accordance with a Poisson process having rate . Each customer

Customers arrive at a single-server station in accordance with a Poisson process having rate λ. Each customer has a value. The successive values of customers are independent and come from a uniform distribution on (0, 1). The service time of a customer having value x is a random variable with mean 3+4x and variance 5.

(a) What is the average time a customer spends in the system?

(b) What is the average time a customer having value x spends in the system?