Phase transition and hysteresis in scale-free network traffic

Area of Science:

• Network science
• Information theory
• Traffic flow dynamics

Background:

• Scale-free networks are prevalent in real-world systems.
• Understanding information traffic dynamics is crucial for network efficiency.
• Previous models often simplify network topology and traffic behavior.

Purpose of the Study:

• To model information traffic on scale-free networks.
• To identify conditions for maximal system capacity.
• To characterize traffic flow behavior and identify distinct traffic states.

Main Methods:

• Developed a model where node queue length (L) is proportional to node degree.
• Node delivering ability (C) is proportional to queue length.
• Simulated traffic flow and analyzed phase transitions from free flow to congestion.

Main Results:

• Maximal system capacity is achieved with a local routing coefficient (phi) slightly above zero.
• Identified an optimal value for the local routing coefficient.
• Reported the fundamental diagram of flow against density, revealing hysteresis.

Conclusions:

• The study identifies four traffic states: free flow, saturated flow, bistable, and jammed.
• Optimal routing strategies can enhance information traffic capacity on scale-free networks.
• The observed hysteresis is a key characteristic of complex traffic systems.