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

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

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

Keywords

STATIONARY AND ERGODIC INPUTSDEPARTURE PROCESS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1128 - 1133
Copyright
Copyright © Applied Probability Trust 1994 

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