A scaling analysis of a star network with logarithmic weights

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Robert, Philippe¹  Veber, Amandine² 

[1] INRIA Paris, 2 Rue Simone Iff,CS 42112, F-75589 Paris 12, France

[2] Ecole Polytech, CMAP, Route Saclay, F-91128 Palaiseau, France

关键词: Communication networks;    Fluid scaling;    Separation of timescales;   

DOI  :  10.1016/j.spa.2018.06.002

来源: Elsevier

【 摘 要 】

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has L requests to transmit and is idle, it tries to access the channel at a rate proportional to log(1 + L). A stochastic model of such an algorithm is investigated in the case of the star network, in which J nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these J+1 interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter N being the norm of the initial state. It is shown that the asymptotic fluid behavior of the system is a consequence of the evolution of the state of the network on a specific time scale (N-t, t is an element of(0, 1)). The main result is that, on this time scale and under appropriate conditions, the state of a node with index j >= 1 is of the order of N-aj(t), with 0 <= a(j)(t) < 1, where t (bar right arrow) a(j)(t) is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free