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Propagation of chaos for a fully connected loss network with alternate routing

Author

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  • Graham, Carl
  • Méléard, Sylvie

Abstract

We study a stochastic loss network of switched circuits with alternate routing. The processes of interest will be the loads of the links, forming a strongly interacting system which is neither exchangeable nor Markovian. We consider interaction graphs representing the past history of a collection of links and prove their convergence to a limit tree, using the notion of chain reactions. Thus we prove a propagation of chaos result in variation norm for the laws of the whole sample paths, for general initial conditions, and in the i.i.d. case we have speeds of convergence.

Suggested Citation

  • Graham, Carl & Méléard, Sylvie, 1993. "Propagation of chaos for a fully connected loss network with alternate routing," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 159-180, January.
    • Handle: RePEc:eee:spapps:v:44:y:1993:i:1:p:159-180
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    Cited by:

    1. A. Karthik & Arpan Mukhopadhyay & Ravi R. Mazumdar, 2017. "Choosing among heterogeneous server clouds," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 1-29, February.
    2. Tanabe, Yasuo, 2006. "The propagation of chaos for interacting individuals in a large population," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 125-152, March.
    3. Barbour, A.D. & Brightwell, Graham & Luczak, Malwina, 2022. "Long-term concentration of measure and cut-off," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 378-423.
    4. Weina Wang & Mor Harchol-Balter & Haotian Jiang & Alan Scheller-Wolf & R. Srikant, 2019. "Delay asymptotics and bounds for multitask parallel jobs," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 207-239, April.

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