A non-increasing Lindley-type equation

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Abstract

In this paper we study the Lindley-type equation W=max¿{0,B-A-W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do so. We also examine stability issues, derive the tail behaviour of W, and briefly discuss how one can iteratively solve this equation by using a contraction mapping.
Original languageEnglish
Pages (from-to)41-52
JournalQueueing Systems: Theory and Applications
Volume56
Issue number1
DOIs
Publication statusPublished - 2007

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