When a Queue Looks the Same to an Arriving Customer as to an Observer.
A brief proof demonstrating Poisson arrival distribution. The arrival of each customer is shown to be independent of anything occurring in the queue, i.e., numbers and types of servers available, discipline and distribution of service, as well as customer behavior after entering the queue or number of different types of customers. To ensure that the probability distribution of states of the queue at a given time is the same regardless of whether or not an arrival occurs at that time, two requirements are needed: (1) the state of the queue given in the past must not be dependent on the new arrival; (2) the arrival distribution must be Poisson. A corollary to the proof postulates stationary distribution. 3 pp. (KB)