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

Y. Kerner

Research output: Book/ReportReportAcademic

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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 re- maining 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 languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages7
Publication statusPublished - 2009

Publication series

NameReport Eurandom
Volume2009018
ISSN (Print)1389-2355

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