Suppose that customers arrive at a service facility with a single server according to a Poisson process with rate λ. The server waits until there are four customers in the system before beginning to serve them, all at once. The service times are independent random variables, all having a

uniform distribution on the interval (0,1). Moreover, the system capacity is equal to four customers. What fraction of time, , are there i customer(s) in the system, over a long period?

Indication, Use the results on renewal processes.