* 3 0 . Consider an M/G/l system in which the first customer in a busy period has service distribution Gx and all others have distribution G2. Let C denote the number of customers in a busy period, and let 5 denote the service time of a customer chosen at random.

Argue that

(a) a0 = P0 = 1 - XE[S].

(b) E[S] = ctoElSi] + (1 - a0)E[S2] where Sf has distribution G,.

(c) Use

(a) and

(b) to show that E[B], the expected length of a busy period, is given by

(d) Find Å[C].