Fermi-Dirac statistics and traffic in complex networks

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35 Citations (Scopus)

Abstract

We propose an idealized model for traffic in a network, in which many particles move randomly from node to node, following the network's links, and it is assumed that at most one particle can occupy any given node. This is intended to mimic the finite forwarding capacity of nodes in communication networks, thereby allowing the possibility of congestion and jamming phenomena. We show that the particles behave like free fermions, with appropriately defined energy-level structure and temperature. The statistical properties of this system are thus given by the corresponding Fermi-Dirac distribution. We use this to obtain analytical expressions for dynamical quantities of interest, such as the mean occupation of each node and the transport efficiency, for different network topologies and particle densities. We show that the subnetwork of free nodes always fragments into small isolated clusters for a sufficiently large number of particles, implying a communication breakdown at some density for all network topologies. These results are compared to direct simulations
Original languageEnglish
Article number066114
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume71
Issue number6 Part 2
DOIs
Publication statusPublished - Jun 2005

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Fermi-Dirac statistics
Complex Networks
traffic
Paul Adrien Maurice Dirac
Traffic
Statistics
Vertex of a graph
topology
Network Topology
congestion
jamming
communication networks
occupation
Finite Capacity
breakdown
fermions
energy levels
communication
Jamming
fragments

Keywords

  • small-world networks
  • scale-free networks
  • betweenness centrality
  • packet transport
  • random-walks
  • congestion
  • navigation
  • load
  • web

Cite this

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title = "Fermi-Dirac statistics and traffic in complex networks",
abstract = "We propose an idealized model for traffic in a network, in which many particles move randomly from node to node, following the network's links, and it is assumed that at most one particle can occupy any given node. This is intended to mimic the finite forwarding capacity of nodes in communication networks, thereby allowing the possibility of congestion and jamming phenomena. We show that the particles behave like free fermions, with appropriately defined energy-level structure and temperature. The statistical properties of this system are thus given by the corresponding Fermi-Dirac distribution. We use this to obtain analytical expressions for dynamical quantities of interest, such as the mean occupation of each node and the transport efficiency, for different network topologies and particle densities. We show that the subnetwork of free nodes always fragments into small isolated clusters for a sufficiently large number of particles, implying a communication breakdown at some density for all network topologies. These results are compared to direct simulations",
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AB - We propose an idealized model for traffic in a network, in which many particles move randomly from node to node, following the network's links, and it is assumed that at most one particle can occupy any given node. This is intended to mimic the finite forwarding capacity of nodes in communication networks, thereby allowing the possibility of congestion and jamming phenomena. We show that the particles behave like free fermions, with appropriately defined energy-level structure and temperature. The statistical properties of this system are thus given by the corresponding Fermi-Dirac distribution. We use this to obtain analytical expressions for dynamical quantities of interest, such as the mean occupation of each node and the transport efficiency, for different network topologies and particle densities. We show that the subnetwork of free nodes always fragments into small isolated clusters for a sufficiently large number of particles, implying a communication breakdown at some density for all network topologies. These results are compared to direct simulations

KW - small-world networks

KW - scale-free networks

KW - betweenness centrality

KW - packet transport

KW - random-walks

KW - congestion

KW - navigation

KW - load

KW - web

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DO - 10.1103/PhysRevE.71.066114

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