38. For the M/G/1 queue, let Xn denote the number in the system left behind by the nth departure.

(a) If

(c) Square both sides of Equation (8.64), take expectations, and then let n→∞
to obtain

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

Transcribed Image Text:

Xn-1+ Yn, if Xn 1 Xn+1 = Yns if Xn = 0 what does Y, represent? (b) Rewrite the preceding as Xn+1=X-1+ Yn + 8n where 1, if X=0 = if X, 1 Take expectations and let n in Equation (8.64) to obtain E[8] 1 E[S]