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### International Journal of Mathematical Sciences and Computing(IJMSC)

ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)

IJMSC Vol.3, No.3, Jul. 2017

#### Graph Dynamic Threshold Model Resource Network: Key Features

Full Text (PDF, 436KB), PP.28-38

#### Author(s)

L. Yu. Zhilyakova

#### Index Terms

Graph dynamic models;threshold models;flows in networks;Markov chains;diffusion on graphs;resource networks

#### Abstract

In this paper, we describe a graph dynamic threshold model called resource network, and briefly present the main results obtained during several years of research. Resource Network is represented by a connected oriented with weighted graph with an arbitrary topology. Weights of edges denote their throughput capacities for an abstract resource. The resource is stored in vertices, which can contain its unlimited amount. Network operates in discrete time. The total amount of resource is constant, while pieces of resource are reallocating among vertices every time step, according to certain rules with threshold switching. The main objective of our research is to define for a network with an arbitrary topology all its basic characteristics: the vectors of limit state and flow for every total amount of resource W; the threshold value of total recourse T, which switches laws of operating of the network; description of these laws. It turned out that there exists several classes of networks depending on their topologies and capacities. Each class demonstrates fundamentally different behavior. All these classes and their characteristics will be reviewed below.

#### Cite This Paper

L. Yu. Zhilyakova,"Graph Dynamic Threshold Model Resource Network: Key Features", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.3, No.3, pp.28-38, 2017.DOI: 10.5815/ijmsc.2017.03.03

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