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Area of Science:

  • Complex systems
  • Network science
  • Applied mathematics

Background:

  • Dynamical systems with queues, such as network traffic, often exhibit complex behaviors like jamming.
  • Accurate characterization of these jamming phenomena is crucial for system optimization and performance.
  • Existing methods may not fully capture the intricate topological properties of jamming transitions.

Purpose of the Study:

  • To introduce and validate an approach using algebraic topology for characterizing jamming in queueing dynamical systems.
  • To analyze information packet traffic on a network substrate as a prototype system.
  • To identify quantifiable measures that delineate different traffic regimes.

Main Methods:

  • Mapping temporal traffic density fluctuations to a mathematical graph where vertices represent system states.
  • Classifying high-dimensional clique agglomerates to reveal coupling complexity between states.
  • Quantifying complexity using geometrical and entropy measures.

Main Results:

  • Distinct graph structures were observed for free-flow, jamming, and congested traffic regimes.
  • The approach accurately characterized jamming transitions in the prototype network traffic system.
  • Largest geometrical complexity and minimum entropy were identified as indicators for the jamming region's edge.

Conclusions:

  • Algebraic topological methods provide an accurate framework for analyzing jamming in queueing dynamical systems.
  • The developed geometrical and entropy measures effectively distinguish traffic regimes.
  • This approach offers a powerful tool for understanding and managing complex network dynamics.