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Probabilistic Analysis of a Buffer Overflow Duration in Data Transmission in Wireless Sensor Networks
1Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland.
Sensors (Basel, Switzerland)
|October 15, 2020
Summary
This study models buffer overflows in wireless sensor networks. It provides a mathematical framework to calculate the probability distribution of overflow durations, crucial for network optimization.
Area of Science:
- Computer Science
- Electrical Engineering
- Applied Mathematics
Background:
- Periodic buffer overflows are a significant issue in packet networks, especially wireless sensor networks (WSNs).
- Buffer overflows lead to data loss, impacting network performance and reliability.
- Understanding the probabilistic nature of overflow duration is vital for network optimization.
Purpose of the Study:
- To develop a mathematical model for a WSN node experiencing buffer overflows.
- To derive the probability distribution for the duration of buffer overflow periods.
- To analyze both the first and subsequent overflow periods.
Main Methods:
- A finite-buffer discrete-time queueing system model was developed.
- Geometrically distributed interarrival times and general processing times were assumed.
- A system of equations for the tail cumulative distribution function was derived.
- Analytical solutions using embedded Markov chains and linear algebra were employed for probability generating functions.
Main Results:
- A mathematical model for WSN nodes with finite buffers was established.
- Equations for the probability distribution of buffer overflow durations were derived.
- The model provides insights into the probabilistic behavior of WSN data transmission.
Conclusions:
- The proposed model accurately captures the dynamics of buffer overflows in WSNs.
- The derived probability distributions are essential for optimizing WSN performance.
- This research contributes to a better understanding and management of data loss in WSNs.
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