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

Published online by Cambridge University Press:  14 July 2016

Cheng-Shang Chang*
Affiliation:
National Tsing Hua University
*
Postal address: Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.

Abstract

In this note, we consider G/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 the G/M/1 queues with stationary and ergodic inputs, the M/M/1 queue is the only queue whose departure process is identically distributed as the input process.

MSC classification

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1994 

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