170B Note

• (inter-arrival times and arrival times) – Arrival times T1,T2, · · · are i.i.d. and have Exp(λ) distribution. – The kth arrival time Yk = T1 + · · · + Tk is called to have the Erlang distribution of order k. • (merging of Poisson processes) If (At ) and (Bt ) are independent Poisson processes of rate α and β, resp., then – Nt = At + Bt is a Poisson process of rate λ = α + β. – If (Xn )∞ n=1 is defined as