29. For the M/G/l queue, let Xn denote the number in the system left behind by the nth departure.

(a) If 1 + Yn i f * „ > 1 if Xn = 0 what does Yn represent?

(b) Rewrite the preceding as X, n+l — ׄ-1 + Õç + ä, ç (8.58)

where 0, 1, i f * „ > 1 iiXn = 0 Take expectations and let ç -* oo in Equation (8.58) to obtain E[ÔJ = 1 - A£[S]

(c) Square both sides of Equation (8.58), take expectations, and then let ç -• oo to obtain E V U - 2(1 - L[5|> + i E li S

(d) Argue that E[X^y the average number as seen by a departure, is equal to L.