Question: . M/ M/1 queue: waiting time in the system for an arrival at instant t, (virtual waiting time in the system). Show that = F(x,

. M/ M/1 queue: waiting time in the system for an arrival at instant t,

(virtual waiting time in the system).

Show that = F(x, t) P{W, x|t} = 1-eux and the PDF

Show that = F(x, t) P{W, x|t} = 1-eux and the PDF of W, is given by (x) s! Pn(t), n=0s=0 d w(x, t) = F(x, t) dx = e 00 " (ux)s Pn(t)- n=0s=0 s! 11 n=0 s=1 (x)- (s 1)! - Pn(t).

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