1. Random fluid limit of an overloaded polling model
- Author
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Bert Zwart, Serguei Foss, Maria Remerova, Stochastics, Mathematics, Eurandom, and Stochastic Operations Research
- Subjects
Statistics and Probability ,Mathematical optimization ,Primary 60K25, 60F17, Secondary 90B15, 90B22 ,overload ,0211 other engineering and technologies ,90B22 ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,random fluid limit ,60K25 ,FOS: Mathematics ,Fluid dynamics ,multi-stage gated discipline ,0101 mathematics ,Queue ,Mathematics ,Branching process ,Fluid limit ,busy period moment ,021103 operations research ,Applied Mathematics ,Probability (math.PR) ,Mathematical analysis ,90B15 ,branching process ,Polling system ,60F17 ,Finite time ,Cyclic polling ,Mathematics - Probability - 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., Comment: 36 pages, 2 pictures
- Published
- 2014
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