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August 2001 Point processes in fast Jackson networks
James B. Martin
Ann. Appl. Probab. 11(3): 650-663 (August 2001). DOI: 10.1214/aoap/1015345344


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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James B. Martin. "Point processes in fast Jackson networks." Ann. Appl. Probab. 11 (3) 650 - 663, August 2001.


Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1021.90007
MathSciNet: MR1865019
Digital Object Identifier: 10.1214/aoap/1015345344

Primary: 60G55 , 90B15

Keywords: Jackson network , point process , Queueing network

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 3 • August 2001
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