Nonsymmetric resource networks. The study of limit states

• Autorzy: Kuznetsov O. P. , Zhilyakova L. Yu.
• Języki publikacji: EN

Abstrakty

EN

A network model called a resource network and represented by an oriented weighted graph with loops is considered. In the bidirectional resource network: i) any two vertices are either not adjacent or connected by a pair of oppositely directed edges; ii) resources are assigned to vertices, which have unlimited volumes; the weights of arcs indicate their capacities. The total resource is constant, while resources at the vertices are reallocated according to certain rules in discrete time. The limit states of networks with arbitrary initial distribution of resource are analyzed. The threshold value T is proved to exist: when the total resource value is less than T the network with loops corresponds to a regular Markov chain; when the total resource value exceeds T the Markov property does not hold. The classification of vertices, depending on their ability to accumulate resources is given. The vertices capable to accumulate the amount of resource, surpassing their total output capacity was is were called the potential attractors. The criterion of attractiveness of vertices is formulated. The formulae of resource value at every vertex in limit state expressing its dependence on limit probabilities of corresponding Markov chain, the total resource value and total output capacity are derived.

Słowa kluczowe

EN

resource network; state of network; oriented weighted graph; criterion of attractiveness of vertices

PL

zasób sieciowy; model sieci; łańcuch Markowa

• Wydawca: Production Engineering Committee of the Polish Academy of Sciences ; Polish Association for Production Management
• Czasopismo: Management and Production Engineering Review
• Rocznik: 2011
• Tom: Vol. 2, No. 3
• Strony: 33--39
• Opis fizyczny: Bibliogr. 9 poz., tab.

Twórcy

autor

Kuznetsov O. P.

autor

Zhilyakova L. Yu.

• V.A. Trapeznikov Institute of Control Sciences, 65 Profsoyuznaya St., 117997 Moscow, Russia, phone: [phone],

Bibliografia

• [1] Kuznetsov O.P., Uniform Resource Networks. I. Complete Graphs, Automation and Remote Control, 70, 11, 1767-1775, 2009.
• [2] Ford L.R. Jr., Fulkerson D.R., Flows in Networks, Princeton Univ. Press, Princeton, 1962.
• [3] Ahuja R.K., Magnati T.L., Orlin J.B., Network Flows: Theory, Algorithms and Applications, Prentice Hall, New Jersey, 1993.
• [4] Szeto W., Iraqi Y., Boutaba R., A multi-commodity flow based approach to virtual network resource allocation, Proceedings of Global Telecommunications Conference, GLOBECOM ’03, IEEE, DOI: 10.1109/GLOCOM.2003.1258787, 2003.
• [5] Zhilyakova L.Yu., The Model of Distribution of Chemical Substances and Passive Biological Objects in an Aqueous Medium, Control Science, 2, 46-51, 2011 (in Russian).
• [6] Kuznetsov O.P., Zhilyakova L.Yu., Bidirectional Resource Networks: A New Flow Model, Doklady Mathematics, 82, 1, 643–646, 2010.
• [7] Zhilyakova L.Yu., Asymmetrical Resource Networks. I. Stabilization Processes for Low Resourses, Automation and Remote Control, 72, 4, 798-807, 2011.
• [8] Gantmacher F.R., The Theory of Matrices, Chelsea, New York, 1959.
• [9] Kemeny J.G., Snell J.L., Finite Markov Chains, Van Nostrand Reinhold, New York, 1959.