A non-increasing Lindley-type equation

Authors:
Maria Vlasiou
Affiliations:
Georgia Institute of Technology, H. Milton Stewart School of Industrial & Systems Engineering, Atlanta, USA 30332-0205
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Abstract

In this paper we study the Lindley-type equation W=max驴{0,B驴A驴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.