When interarrival times between successive customers coming to a queueing system are independent and identical exponential random variables, it follows that the number of arrivals to the system in a given period of time has a Poisson distribution (i.e., is a Poisson process). As a result, we would say that this queueing system has Poisson arrivals.  Exponential arrivals; Poisson process;  Queueing theory.