Properties of the Poisson process Merging property )→∑k k Let A1, A2,... Ak be independent Poisson Processes of rate 2122..k A=∑A1 is also poisson of rate=∑41 Splitting property Suppose that every arrival is randomly routed with probability P to stream 1 and(1-P)to stream 2 Streams 1 and 2 are Poisson of rates Ph and (1-P)h respectively 入P 入 p(1-P)Properties of the Poisson process • Merging Property λ1 λ2 ∑ λi λk Let A1, A2, … Ak be independent Poisson Processes of rate λ1, λ2, … λk A = ∑ Ai is also Poisson of rate = ∑ λi • Splitting property – Suppose that every arrival is r andomly routed with probability P to stream 1 and (1-P) to stream 2 – Streams 1 and 2 are Poisson of rates P λ and (1-P) λ respectively P 1-P λP λ λ(1−P) Eytan Modiano Slide 9