Limit theorems for one class of Polling models
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 585-593
Voir la notice de l'article provenant de la source Math-Net.Ru
The asymptotic independence of any finite set of random processes describing states of nodes is proved for an open transportation network with $N$ nodes and $M$ servers moving between them provided $N\to\infty$ and $M/N\to r$ ($0$). We determine that the limit flow of servers to a fixed node is a nonstationary Poisson process and describe behavior of the system in the thermodynamic limit. A system with Poisson input flow and a special kind of travel time distribution is examined as an example of such networks. The convergence to a limit dynamic system is proved for it. Also the steady point is specified and it is discovered that this point depends on the shape of travel time distribution only through its mean.
Keywords:
polling model, random process, asymptotic independence, thermodynamic limit.
@article{TVP_2005_50_3_a12,
author = {A. A. Sergeev},
title = {Limit theorems for one class of {Polling} models},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {585--593},
publisher = {mathdoc},
volume = {50},
number = {3},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a12/}
}
A. A. Sergeev. Limit theorems for one class of Polling models. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 585-593. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a12/