Percolation thresholds for robust network connectivity

Arman Mohseni-Kabir, Mihir Pant, Don Towsley, Saikat Guha, Ananthram Swami

Research output: Contribution to journalArticlepeer-review

Abstract

Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation (resp., deletion) probability or an edge activation (resp., removal) probability above (resp., below) which there exists a giant connected component (GCC), a connected component comprising of a number of occupied nodes and active edges whose size is proportional to the size of the network itself. Any pair of occupied nodes in the GCC is connected via at least one path comprised of active edges and occupied nodes. The mere existence of the GCC itself does not guarantee that the long-range connectivity would be robust, e.g. to random link or node failures due to network dynamics. In this paper, we explore new percolation thresholds that guarantee not only spanning network connectivity, but also robustness. We define and analyze four measures of robust network connectivity, explore their interrelationships, and numerically evaluate the respective robust percolation thresholds for the 2D square lattice.

Original languageEnglish (US)
Article number013212
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2021
Issue number1
DOIs
StatePublished - Jan 2021

Keywords

  • Classical phase transitions
  • Communication
  • Critical exponents and amplitudes
  • Information networks
  • Percolation problems
  • Supply

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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