Poisson process

A stochastic, renewal-counting point process beginning from time t = 0 with N(0) = 0 that satisfies the following assumptions is called a Poisson process with rate λ: (1) the probability of one event happening in the interval (t, t + h]is λ h + o(h), where o(h) is a function which goes to zero faster than h; (2) the probability of more than one event happening in (t, t + h]iso(h); and (3) events happening in non-overlapping intervals are statistically independent. (Either (1) or (2) can be replaced by: the probability of no event happening in the interval (t, t + h]is 1 − λ h + o(h)). The number of arrivals to a M/G/1 queueing system is a Poisson process. If the arrival process to a queueing system is a Poisson process with rate λ, then the interarrival times are independent and identically, exponentially distributed with mean 1/λ. Markov chains; Markov processes; Queueing theory.