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# Point Processes in Fast Jackson Networks

Abstract : We consider a Jackson-type network, each of whose nodes contains $N$ identical channels with a single server. Upon arriving at a node, a task selects $m$ of the channels at random, and joins the shortest of the $m$ queues observed. We fix a collection of channels in the network, and analyse how the queue-length processes at these channels vary as $N\to\infty$. If the initial conditions converge suitably, the distribution of these processes converges in local variation distance to a limit under which each channel evolves independently. We discuss the limiting processes which arise, and in particular we investigate the point processes of arrivals and departures at a channel when the networks are in equilibrium, for various values of the system parameters.
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https://hal.inria.fr/inria-00072602
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Submitted on : Wednesday, May 24, 2006 - 10:22:29 AM
Last modification on : Friday, February 4, 2022 - 3:16:48 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:15:09 PM

### Identifiers

• HAL Id : inria-00072602, version 1

### Citation

James B. Martin. Point Processes in Fast Jackson Networks. RR-4036, INRIA. 2000. ⟨inria-00072602⟩

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