Output Distribution of a Single-Channel Queue

The interdeparture-time distribution of a single-channel queuing system with general arrival and service time distribution is derived by applying the complex-variable theory. It is important in studying the queues in series, since the output from one channel comprises the input into the subsequent channel. An example is given on the exponential channel. This shows that the output from such a system with a Poisson input is itself a Poisson. The interdeparture times fail to be statistically independent if the interarnval times and the service times are other than exponentially distributed.