Letter to the Editor—The Output of an M/G/∞ Queuing System is Poisson

Burke [Burke, P. J. 1956. The output of a queuing system. Opns. Res.4 699–704.] has shown that, in steady state, a queuing system with a Poisson input and independent (negative) exponential service times has an output that is also a Poisson process with a rate equal to the input rate, regardless of the number of channels. He has also shown that the interdeparture interval is independent of the state of the system at the end of the interval.

We will show that if a queuing system has a Poisson input and an infinite number of channels, the output is also Poisson, regardless of the distribution of service times, provided that these times are independent.