When customers interarrival times to a queueing system are defined by a sequence of independent and identically distributed exponential random variables. If a system has exponential interarrival times with distribution function A(t) = 1 − exp(−λ), then the number of arrivals to the system in any period of time t has the Poisson distribution with probability function p_n(t) − exp(−λt)(λt)ⁿ/n!.  Poisson arrivals;  Queueing theory.