Some invariance properties of monotone failure rate in the M/G/1 queue

Yoav Kerner

Some invariance properties of monotone failure rate in the M/G/1 queue

Department of Industrial Engineering and Management

Research output: Other contribution › peer-review

Abstract

We show that in the stationary M/G/1 queue, if the service time distribution is with increasing (decreasing) failure rate (IFR (DFR)), then (a) The distribution of the number of customers in the system is also IFR (DFR), (b) The conditional distribution of the remaining service time given the number of customers in the system is also IFR (DFR) and (c) The conditional distribution of the remaining service time given the number of customers in the system, is stochastically decreasing (increasing) with the number of customers in the system.

Original language	English GB
Publisher	Eurandom, Workshop Center in the area of Stochastics
Number of pages	7
State	Published - 2009

Publication series

Name	Report Eurandom
Volume	2009018
ISSN (Print)	1389-2355

Cite this

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Some invariance properties of monotone failure rate in the M/G/1 queue

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