A non-increasing Lindley-type equation

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.

16 pages, 1 figure, 20 references

References in corpus (3)

• On the minimal travel time needed to collect n items on a circle
• Time-dependent behaviour of an alternating service queue
• An alternating service problem

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