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Departure Process of Actively Managed Queue with Dependent Job Sizes.

Andrzej Chydzinski1

  • 1Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.

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Summary

This study analyzes queueing systems with dependent job sizes and active queue management. We provide mathematical insights into job departures and rejections under various conditions.

Keywords:
actively managed queuedeparture processdependent job sizesdependent service timesperformance evaluationqueueing modelrejection processstationary analysistransient analysis

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Area of Science:

  • Queueing Theory
  • Performance Analysis
  • Computer Networks

Background:

  • Real-world queueing systems often exhibit stochastic dependence in job sizes.
  • Active management, where service denial probability depends on queue size, is common in systems like computer networks.

Purpose of the Study:

  • To conduct a comprehensive transient and stationary analysis of job departure and rejection processes.
  • To develop theorems for key performance metrics in a queueing model with dependent job sizes and active management.

Main Methods:

  • Mathematical analysis of a queueing model incorporating stochastic job size dependence.
  • Transient and stationary analysis techniques applied to job departure and rejection processes.

Main Results:

  • Theorems derived for expected job departures, departure intensity, and stationary departure rate.
  • Formulations for expected job rejections, transient rejection intensity, and stationary rejection rate.
  • Numerical examples illustrating the impact of job dependence, rejection probability, and system load.

Conclusions:

  • The study provides a robust analytical framework for queueing systems with complex characteristics.
  • Understanding departure and rejection dynamics is crucial for optimizing performance in dependent queueing systems.