The Annals of Applied Probability

Point processes in fast Jackson networks

James B. Martin

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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 analyze 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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Ann. Appl. Probab., Volume 11, Number 3 (2001), 650-663.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 90B15: Network models, stochastic 60G55: Point processes

Queueing network point process Jackson network


Martin, James B. Point processes in fast Jackson networks. Ann. Appl. Probab. 11 (2001), no. 3, 650--663. doi:10.1214/aoap/1015345344.

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