### Abstract

Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.

Original language | English (US) |
---|---|

Article number | 026125 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*71*(2), [026125]. https://doi.org/10.1103/PhysRevE.71.026125

**Onset of traffic congestion in complex networks.** / Zhao, Liang; Lai, Ying-Cheng; Park, Kwangho; Ye, Nong.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 71, no. 2, 026125. https://doi.org/10.1103/PhysRevE.71.026125

}

TY - JOUR

T1 - Onset of traffic congestion in complex networks

AU - Zhao, Liang

AU - Lai, Ying-Cheng

AU - Park, Kwangho

AU - Ye, Nong

PY - 2005/2

Y1 - 2005/2

N2 - Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.

AB - Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.

UR - http://www.scopus.com/inward/record.url?scp=41349101297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349101297&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.026125

DO - 10.1103/PhysRevE.71.026125

M3 - Article

AN - SCOPUS:41349101297

VL - 71

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 026125

ER -