The Annals of Applied Probability

Point processes in fast Jackson networks

James B. Martin

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 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.

Article information

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

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015345344

Digital Object Identifier
doi:10.1214/aoap/1015345344

Mathematical Reviews number (MathSciNet)
MR1865019

Zentralblatt MATH identifier
1021.90007

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

Citation

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

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