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Random fluid limit of an overloaded polling model. (English) Zbl 1292.60093

The paper under review studies the series of overloaded cyclic polling queueing system with Poisson arrivals that starts empty. In the queueing literature, it is well known the connection between this type of polling queueing systems and multitype branching processes, e.g. see [V. A. Vatutin, Theory Probab. Appl. 55, No. 4, 631–660 (2011); translation from Teor. Veroyatn. Primen. 55, No. 4, 644–679 (2010; Zbl 1244.60089); R. D. van der Mei, Queueing Syst. 57, No. 1, 29–46 (2007; Zbl 1150.90002)]. Exploiting a connection between polling queueing systems and multitype branching processes, the paper under review derives fluid asymptotics for the joint queue-length process, and the fluid limit is random. As well, the paper suggests a method that establishes finiteness of moments of the busy period in an \(\mathrm{M}/\mathrm{G}/1\) queueing system.

MSC:

60K25 Queueing theory (aspects of probability theory)
60F17 Functional limit theorems; invariance principles
90B15 Stochastic network models in operations research
90B22 Queues and service in operations research

References:

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