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.
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This research has been carried out when the author was affiliated with EURANDOM, The Netherlands.
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Vlasiou, M. A non-increasing Lindley-type equation. Queueing Syst 56, 41–52 (2007). https://doi.org/10.1007/s11134-007-9029-6
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DOI: https://doi.org/10.1007/s11134-007-9029-6
Keywords
- Lindley’s recursion
- Alternating service
- Carousel
- Rational Laplace transform
- Generalised Wiener–Hopf equation
- Fredholm integral equations