TRAFFIC MODELS MPEG2 (sport) Voice Data MPEG2 (news) Poisson Distribution Poisson process Discrete events in an interval The probability of one success in an interval is stable The probability of more than one success in this interval is 0 The probability of success is independent from interval to interval e.g.: The number of customers arriving in 15 minutes PXx x x (| ! e - e.g.: Find the probability of four customers arriving in three minutes when the mean is 3.6. Poisson Distribution Formula where: X = number of successes per time period = expected number of successes per time period e = base of the natural logarithm system ( ) Graph of Poisson Probabilities X = P(X = 2) =.0758 Graphically: =.50 Poisson Distribution Shape The shape of the Poisson Distribution depends on the parameter : = 0.50 = 3.00 In-Class Exercises: 1a. If calls to your cell phone are a Poisson process with a constant rate =2 calls per hour, whats the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? 1b. How many phone calls do you expect to get during the movie? Answer 1a. If calls to your cell phone are a Poisson process with a constant rate =2 calls per hour, whats the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? X ~ Poisson ( =2 calls/hour) P(X1)=1 P(X=0) P(X1)=1 .05 = 95% chance 1b. How many phone calls do you expect to get during the movie? E(X) = t = 2(1.5) = 3
