Uniform resource networks I. Complete graphs

Kuznetsov, O. P.

doi:10.1134/s0005117909110137

Cited by 12 publications

(9 citation statements)

References 4 publications

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“…Complete homogeneous networks with loops have three properties, which are derived from properties 1-3 formulated in Kuznetsov, 2009 for loopless networks, by virtue of substitution of rn for r(n-1).…”

Section: Homogeneous Complete Bidirectional Network With Loopsmentioning

confidence: 99%

“…The resource network represented in Kuznetsov, 2009, is a dynamic model, where the resources are exchanged between vertices under certain rules with the total resource being constant. The network is a bidirectional graph: adjacent vertices are connected by a pair of oppositely directed arcs.…”

Section: Introductionmentioning

confidence: 99%

“…In Kuznetsov, 2009 the complete homogeneous (with identical arc capacities) networks without loops were considered. Analysis of complete heterogeneous networks with loops and their limit states is made in Kuznetsov and Zhilyakova, 2010. In this paper, we consider the properties of bidirectional resource networks with loops, arbitrary connections, and various capacities.…”

Section: Introductionmentioning

confidence: 99%

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Flows and Limit States in Bidirectional Resource Networks

Kuznetsov

Zhilyakova

2011

IFAC Proceedings Volumes

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Section: Homogeneous Complete Bidirectional Network With Loopsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flows and Limit States in Bidirectional Resource Networks

Kuznetsov

Zhilyakova

2011

IFAC Proceedings Volumes

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“…For the first time, the resource network was introduced in [1], where a simple special case was considered-a complete uniform network with loops. Since then, the mathematical properties of networks for all graph topologies have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Single-Threshold Model Resource Network and Its Double-Threshold Modifications

Zhilyakova

2021

Mathematics

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A resource network is a non-classical flow model where the infinitely divisible resource is iteratively distributed among the vertices of a weighted digraph. The model operates in discrete time. The weights of the edges denote their throughputs. The basic model, a standard resource network, has one general characteristic of resource amount—the network threshold value. This value depends on graph topology and weights of edges. This paper briefly outlines the main characteristics of standard resource networks and describes two its modifications. In both non-standard models, the changes concern the rules of receiving the resource by the vertices. The first modification imposes restrictions on the selected vertices’ capacity, preventing them from accumulating resource surpluses. In the second modification, a network with so-called greedy vertices, on the contrary, vertices first accumulate resource themselves and only then begin to give it away. It is noteworthy that completely different changes lead, in general, to the same consequences: the appearance of a second threshold value. At some intervals of resource values in networks, their functioning is described by a homogeneous Markov chain, at others by more complex rules. Transient processes and limit states in networks with different topologies and different operation rules are investigated and described.

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“…It was first proposed in Kuznetsov, 2009. This pioneer work described a simple particular version of a model -complete uniform resource networks, networks represented by complete graphs with identical capacities for all edges.…”

Section: Introductionmentioning

confidence: 99%

Graph Dynamic Threshold Model Resource Network: Key Features

Zhilyakova¹

2017

IJMSC

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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.

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Uniform resource networks I. Complete graphs

Cited by 12 publications

References 4 publications

Flows and Limit States in Bidirectional Resource Networks

Flows and Limit States in Bidirectional Resource Networks

Single-Threshold Model Resource Network and Its Double-Threshold Modifications

Graph Dynamic Threshold Model Resource Network: Key Features

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