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This study models queueing networks with unreliable links, presenting mathematical tools to analyze performance and quantify outage impacts. It offers a diffusion limit for queue lengths in these dynamic systems.

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Area of Science:

  • Queueing theory
  • Stochastic processes
  • Network analysis

Background:

  • Queueing networks are essential for modeling systems with waiting lines.
  • Unreliable network links introduce complexities in performance analysis.
  • Dynamic graph structures model evolving network topologies.

Purpose of the Study:

  • To develop mathematical models for queueing networks with unreliable links.
  • To provide methods for evaluating performance measures and the impact of link failures.
  • To derive a diffusion limit for the queue length process.

Main Methods:

  • Formulating coupled partial differential equations for time-dependent behavior.
  • Developing ordinary differential equations for stationary behavior.
  • Designing algorithms for moment evaluation and performance measure computation.
  • Applying diffusion approximation techniques.

Main Results:

  • A system of PDEs and ODEs describing the probability generating function.
  • Algorithms for computing time-dependent and stationary moments.
  • Procedures for quantifying the impact of link outages on user-perceived performance.
  • A diffusion limit for the joint queue length process.

Conclusions:

  • The developed models and algorithms effectively analyze queueing networks with unreliable links.
  • The study quantifies the performance degradation caused by link outages.
  • The diffusion limit provides insights into the large-scale behavior of these systems.