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

DOI10.1016/0304-4149(93)90043-4zbMath0769.60093OpenAlexW2066945301MaRDI QIDQ1208939

Sylvie Méléard, Carl Graham

Publication date: 16 May 1993

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(93)90043-4

zbMATH Keywords

weak convergencecommunication networkcoupling argumentpure jump processfully connected networkmartingale formulation

Mathematics Subject Classification ID

Stochastic network models in operations research (90B15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Circuits, networks (94C99)

Related Items (12)

Choosing among heterogeneous server clouds ⋮ Fluctuations for a fully connected loss network with alternate routing ⋮ Chaos hypothesis for a system interacting through shared resources ⋮ Stochastic particle approximations for generalized Boltzmann models and convergence estimates ⋮ THE BOUNDED CONFIDENCE MODEL OF OPINION DYNAMICS ⋮ Long-term concentration of measure and cut-off ⋮ Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks ⋮ Nonregressivity in switched linear circuits and mechanical systems ⋮ The propagation of chaos for interacting individuals in a large population ⋮ Insensitivity of the mean field limit of loss systems under SQ(d) routeing ⋮ Delay asymptotics and bounds for multitask parallel jobs ⋮ The equilibrium states of large networks of Erlang queues

Cites Work

• Investigation of a fully connected channel switching network with many nodes and alternative routes
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• Arbres et processus de Galton-Watson. (Trees and Galton-Watson processes)
• A mean field limit for a lattice caricature of dynamic routing in circuit switched networks
• Nonlinear diffusion with jumps
• The Boltzmann equation and its applications
• A geometric rate of convergence to the equilibrium for Boltzmann processes with multiple particle interactions
• [https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
• Central limit theorem for a system of Markovian particles with mean field interactions
• Propagation of chaos for a system of annihilating brownian spheres
• Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-limit
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