Random events Arrival process Packets arrive according to a random process Typically the arrival process is modeled as Poisson The Poisson process Arrival rate of n packets per second Over a small interval s P(exactly one arrival)=n8+oo) P(O arrivals)=1-n8+o(8 P(more than one arrival =08 Where0(6y6→>08→>0. It can be shown that: 27 P(n arrivalsininterval T (r)eRandom events • Arrival process – Packets arrive according to a random process – Typically the arrival process is modeled as Poisson • The Poisson process – Arrival rate of λ packets per second – Over a small interval δ, P(exactly one arrival) = λδ + ο(δ) P(0 arrivals) = 1 - λδ + ο(δ) P(more than one arrival) = 0(δ) Where 0(δ)/ δ −> 0 �� δ −> 0. – It can be shown that: P(n arrivalsininterval T)= ( λT)n e−λT n! Eytan Modiano Slide 4