DFR property of first-passage times and its preservation under geometric compounding
type: Item
instance of: scholarly article
title: DFR property of first-passage times and its preservation under geometric compounding
zbMATH Open document ID: 0636.60075
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: If the transition survival probability matrix of a discrete-time Markov chain on the non-negative integers is \(TP_ 2\), then the author proves that the first passage time from state 1 to state 0 is DFR. The transition survival probability matrix \(Q:=\| Q(i,j)\|\) corresponding to a Markov matrix \(P:=\| P(i,j)\|\) is defined by \(Q(i,j):=\sum_{k\geq j}P(i,k)\). Related consequences/results derived are: (i) the DFR property is closed under geometric compounding, (ii) in an M/G/1 queue with IFR service times, the number of customers served during a busy period is DFR, (iii) the stationary waiting time in a GI/G/1 (M/G/1) queue with DFR (IMRL respectively) service times is DFR, (iv) sufficient conditions on inter-renewal times for a concave renewal function.
reviewed by: Manish C. Bhattacharjee
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 4036857
zbMATH Keywords: first passage time
zbMATH Keywords: geometric compounding
zbMATH Keywords: inter-renewal times
zbMATH Keywords: concave renewal function
author: J. George Shanthikumar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991910
OpenAlex ID: W2011840488
Wikidata QID: Q56427824
DOI: 10.1214/AOP/1176991910
description: scientific article; zbMATH DE number 4036857