Random fluid limit of an overloaded polling model

Authors :: Bert Zwart
Serguei Foss
Maria Remerova
Stochastics
Mathematics
Eurandom
Stochastic Operations Research
Source :: Advances in Applied Probability, 46, 76-101, Advances in Applied Probability, ResearcherID, Remerova, M, Foss, S & Zwart, A P 2014, ' Random fluid limit of an overloaded polling model. ', Advances in Applied Probability, vol. 46, no. 1, pp. 76-101 . https://doi.org/10.1239/aap/1396360104, Adv. in Appl. Probab. 46, no. 1 (2014), 76-101, Advances in Applied Probability, 46(1), 76-101. University of Sheffield
Publication Year :: 2014
Publisher :: University of Sheffield, 2014.
Abstract: In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage to the fluid dynamics, the server switches between the queues infinitely many times in any finite time interval causing frequent oscillatory behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid limit is random. Additionally, we suggest a method that establishes finiteness of moments of the busy period in an M/G/1 queue.<br />Comment: 36 pages, 2 pictures