On the input-output map of aG/G/1 queue

Abstract

In this note, we considerG/G/1 queues with stationary and ergodic inputs. We show that if the service times are independent and identically distributed with unbounded supports, then for a given mean of interarrival times, the number of sequences (distributions) of interarrival times that induce identical distributions on interdeparture times is at most 1. As a direct consequence, among all theG/M/1 queues with stationary and ergodic inputs, theM/M/1 queue is the only queue whose departure process is identically distributed as the input process.