Higher-order Lindley equations
type: Item
instance of: scholarly article
title: Higher-order Lindley equations
zbMATH Open document ID: 0840.60084
DOI: 10.1016/0304-4149(94)90058-2
author: F. I. Karpelevich
author: Yuri Suhov
author: Mark Kelbert
published in: Stochastic Processes and their Applications
publication date: 1994-12-07T00:00:00Z
review text: This article is devoted to an analysis of the generalized Lindley equation \[ w \cong \max \bigl[ w^{(1)} + s^{(1)} - \tau^{(1)}, \dots, w^{(m)} + s^{(m)} - \tau^{(m)} \bigr] \] where the \(w\) all have the same unknown distribution, and the \(s\) as well as the \(\tau\) are i.i.d. The authors begin by pointing out that this equation is applicable to queueing network problems in areas such as operations research and computer systems. They then apply the theory of random marked flows to state conditions under which there is weak convergence to the minimal solution of the above equation. They further characterize this solution in terms of the unique probability one solution to another equation. It follows also that if the fundamental stability condition (earlier required for existence) is violated, then no solution to the generalized Lindley equation exists. Finally, the nature of the solution is further characterized and described.
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 691018
zbMATH Keywords: queueing network
zbMATH Keywords: waiting time
zbMATH Keywords: generalized Lindley equation
reviewed by: Frederick J. Beutler
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90058-2
OpenAlex ID: W1987266626
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description: scientific article; zbMATH DE number 691018