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

(a) If

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

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Xn-1+Yn, if Xn 1 Xn+1 Yn, what does Yn represent? (b) Rewrite the preceding as Xn+1=Xn-1+ Yn +8n where 1, n if X, = 0 = 10, if X, 1 if X = 0 (8.64) Take expectations and let n in Eq. (8.64) to obtain E[800] 1 E[S] (c) Square both sides of Eq. (8.64), take expectations, and then let n to obtain E[X] = x E[S] 2(1 AE[S]) +E[S]