Solvable model for distribution networks on random graphs

Nasiev, D., van Mourik, Jort and Kühn, Reimer (2007). Solvable model for distribution networks on random graphs. Physical Review E, 76 (4), pp. 1-8.

Abstract

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

Publication DOI: https://doi.org/10.1103/PhysRevE.76.041120
Divisions: Engineering & Applied Sciences
Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: ©2007 American Physical Society. Solvable model for distribution networks on random graphs D. Nasiev, J. van Mourik, and R. Kühn Phys. Rev. E 76, 041120 – Published 12 October 2007
Uncontrolled Keywords: distribution network,blackouts,finite connectivity,nodes,graph,network,Physics and Astronomy(all),Condensed Matter Physics,Statistical and Nonlinear Physics,Mathematical Physics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://link.aps ... sRevE.76.041120 (Publisher URL)
Published Date: 2007-10-12
Authors: Nasiev, D.
van Mourik, Jort
Kühn, Reimer

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