Busy Period in an M/G/1 System. Suppose Q(t) is an M/G/1 queueing process with Poisson arrival times 0 τ1 : Q(t)=0}, which is the time at which the system first becomes empty. Now T = τ1 + Y , where Y...

Busy Period in an M/G/1 System. Suppose Q(t) is an M/G/1 queueing process with Poisson arrival times 0 <><><><>τ1 : Q(t)=0}, which is the time at which the system first becomes empty. Now T =
_τ1
+ Y , where Y is the duration of the busy period for the server. Find E[T ] and show that E[Y ] = ρ/λ(1 − ρ).