Properties of the Poisson process Merging Property A2●→∑ Let A1, A2,... Ak be independent Poisson Processes of rate 21. 72....nk A=∑ A is also poisson of rate=∑ Splitting property Suppose that every arrival is randomly routed with probability pto stream 1 and (1-P) to stream 2 Streams 1 and 2 are Poisson of rates Ph and (1-p)n respectively AP 入 1-PEytan Modiano Slide 9 Properties of the Poisson process • Merging Property Let A1, A2, … Ak be independent Poisson Processes of rate λ1, λ2, … λ k • 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 P λ and (1-P) λ respectively A = A is also Poisson of rate = ∑ ∑ i i λ λ P 1-P λ P λ(1−P) λ1 λ 2 λ k λ ∑ i