Question: . Show that for the M/ M/1 queueing system starting with k customers at time 0, the joint distribution of the busy period Ti, and

. Show that for the M/ M/1 queueing system starting with k customers at time 0, the joint distribution of the busy period Ti, and the number N(TR) served during the busy period initiated by k customers is given by P[+

dt.

n!(n - k)!

Hence, find the marginal distributions, that is, the PDF for Ti (busy period initiated by a single customer) and the distribution of N(Ti) = N (Prabhu, 1965).

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