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On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism
Martyna Kobielnik1, Wojciech Kempa1
1Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland.
Sensors (Basel, Switzerland)
|August 28, 2021
Summary
This study analyzes a GI/M/1 queue with a limited buffer and an energy-saving working vacation policy. It determines the time until the first packet loss, optimizing system performance and energy efficiency.
Area of Science:
- Queueing Theory
- Performance Analysis
- Energy Efficiency in Computing
Background:
- Modern communication systems face challenges with limited buffer capacity and the need for energy conservation.
- Single server queues with vacation policies are crucial for modeling various systems, including telecommunication networks and computer systems.
- Understanding packet loss and system uptime is vital for ensuring reliable service delivery.
Purpose of the Study:
- To analyze a single server GI/M/1 queue with a finite buffer and an energy-saving working vacation mechanism.
- To derive the performance metrics, specifically focusing on the transient time to the first buffer overflow (packet loss).
- To investigate the impact of system parameters on the duration of periods without packet loss.
Main Methods:
- Utilizing an embedded Markov chain and the continuous law of total probability to model the system's transient behavior.
- Developing a system of equations for the cumulative distribution functions of the time to the first buffer overflow.
- Employing a linear algebra-based approach to derive explicit representations for the Laplace transforms of key performance characteristics.
Main Results:
- The study provides a comprehensive analysis of a GI/M/1 queue with a working vacation policy and limited buffer capacity.
- Explicit formulas for the Laplace transforms of performance measures, including the time to the first buffer overflow, are derived.
- Numerical examples illustrate the model's behavior and the influence of various parameters on system performance and packet loss.
Conclusions:
- The developed analytical framework accurately models the transient behavior of the analyzed queueing system.
- The findings offer insights into optimizing the energy-saving working vacation policy to minimize packet loss and enhance system reliability.
- The research contributes to the understanding of queueing systems with finite buffers and energy-saving mechanisms, applicable to network performance optimization.
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