@article{3deabd613af342e081095add6fb70ade,
title = "Performance analysis of polling systems with retrials and glue periods",
abstract = "We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.",
keywords = "Glue periods, Polling system, Retrials",
author = "Abidini, {Murtuza Ali} and Onno Boxma and Bara Kim and Jeongsim Kim and Jacques Resing",
note = "Funding Information: Acknowledgements We are grateful to the reviewer and the associate editor for valuable comments and suggestions, which considerably improved this paper. The research is supported by the IAP program BEST-COM, funded by the Belgian government, and by the Gravity program NETWORKS, funded by the Dutch government. The authors gratefully acknowledge several discussions with Professor Ton Koonen (TU Eindhoven) about optical communications. B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542). Funding Information: We are grateful to the reviewer and the associate editor for valuable comments and suggestions, which considerably improved this paper. The research is supported by the IAP program BESTCOM, funded by the Belgian government, and by the Gravity program NETWORKS, funded by the Dutch government. The authors gratefully acknowledge several discussions with Professor Ton Koonen (TU Eindhoven) about optical communications. B. Kim?s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim?s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542). Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media, LLC.",
year = "2017",
month = dec,
day = "1",
doi = "10.1007/s11134-017-9545-y",
language = "English",
volume = "87",
pages = "293--324",
journal = "Queueing Systems",
issn = "0257-0130",
publisher = "Springer Netherlands",
number = "3-4",
}