Abstract
The present paper considers the class of polling systems that allow a multi-type branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times tend to infinity. The motivation to study these setup time asymptotics in polling systems is based on the specific application area of base-stock policies in inventory control. Our analysis provides new and more general insights into the behavior of polling systems with large setup times.
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Acknowledgments
The author wishes to thank Sem Borst, Onno Boxma and Rob van derMei for valuable discussions and for useful comments on earlier drafts of the present paper. Moreover, Sem Borst is thanked for the derivation of (18). Furthermore, the author is indebted to Marcel van Vuuren for his assistance in using the simulation program used in Sect. 4.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Winands, E.M.M. Branching-type polling systems with large setups. OR Spectrum 33, 77–97 (2011). https://doi.org/10.1007/s00291-009-0174-7
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DOI: https://doi.org/10.1007/s00291-009-0174-7