Random Fluid Limit of an Overloaded Polling Model

@article{Remerova2014RandomFL,
  title={Random Fluid Limit of an Overloaded Polling Model},
  author={Maria Remerova and Sergey Foss and Bert Zwart},
  journal={Advances in Applied Probability},
  year={2014},
  volume={46},
  pages={76 - 101}
}
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. In addition, we suggest… 

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