Consider a M/G/1 system with E[S] < 1. (a) Suppose that service is about to begin at

Consider a M/G/1 system with λE[S] < 1.

(a) Suppose that service is about to begin at a moment when there are n customers in the system.

(i) Argue that the additional time until there are only n −1 customers in the system has the same distribution as a busy period.

(ii) What is the expected additional time until the system is empty?

(b) Suppose that the work in the system at some moment is A. We are interested in the expected additional time until the system is empty—call it E[T ]. Let N denote the number of arrivals during the first A units of time.

(i) Compute E[T |N].

(ii) Compute E[T ].