Poisson Hypothesis for information networks (A study in non-linear Markov processes)
Rybko, Alexander ; Shlosman, Senya
arXiv, 0303010 / Harvested from arXiv
Text on arXiv
In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov processes, have a line of fixed points which are global attractors. To do this we derive the corresponding non-linear integral equation and we explore its self-averaging properties. Our derivation relies on a solution of a combinatorial problem of rode placements.
Publié le : 2003-03-04
Classification:  Mathematical Physics,  Mathematics - Probability,  82C20,  60J25 
@article{0303010,
     author = {Rybko, Alexander and Shlosman, Senya},
     title = {Poisson Hypothesis for information networks (A study in non-linear
  Markov processes)},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303010}
}

Rybko, Alexander; Shlosman, Senya. Poisson Hypothesis for information networks (A study in non-linear
  Markov processes). arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303010/