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Weighted scheduled traffic process with asymptotic fractional dynamics
Marcin Magdziarz1, Wladyslaw Szczotka2
1Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
Chaos (Woodbury, N.Y.)
|October 24, 2025
Summary
This study analyzes a weighted scheduled traffic process with heavy-tailed perturbations. The rescaled process converges to fractional Brownian motion, offering insights into various fields.
Area of Science:
- Probability and Statistics
- Stochastic Processes
- Queueing Theory
Background:
- Traditional scheduled traffic models lack robustness to random perturbations.
- Variable weights and heavy-tailed distributions are common in real-world systems.
- Understanding asymptotic behavior is crucial for system analysis.
Purpose of the Study:
- To investigate the asymptotic behavior of a weighted scheduled traffic process.
- To extend the traditional scheduled traffic model by incorporating random perturbations and variable weights.
- To analyze the convergence properties under heavy-tailed distributions.
Main Methods:
- Mathematical modeling of the weighted scheduled traffic process.
- Analysis of asymptotic behavior using stochastic process theory.
- Weak convergence analysis to a fractional Brownian motion.
Main Results:
- Demonstration of weak convergence to fractional Brownian motion for the rescaled process.
- Characterization of the process's behavior under heavy-tailed perturbation assumptions.
- Identification of key parameters influencing the asymptotic behavior.
Conclusions:
- The weighted scheduled traffic process with heavy-tailed perturbations converges to fractional Brownian motion.
- This model provides a more realistic framework for analyzing complex systems.
- The findings have broad applications in queueing theory, telecommunications, finance, and healthcare.
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