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Reports Year : 2000

Point Processes in Fast Jackson Networks


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.


Other [cs.OH]
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Dates and versions

inria-00072602 , version 1 (24-05-2006)


  • HAL Id : inria-00072602 , version 1


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