# Performance Analysis of CSMA/NP under Finite Population Environments

## TL;DR

This paper studies how a wireless communication protocol behaves when the number of devices is limited, showing how performance changes with more devices.

## Contribution

The paper introduces a finite model for CSMA/NP, deriving a closed-form throughput expression for moderate node counts.

## Key findings

- Throughput behavior converges with Kleinrock’s infinite model as node count increases.
- A closed-form expression for finite node throughput is derived and numerically solved.
- The finite model better captures realistic dynamics in low-contention networks.

## Abstract

In this study, we analyze the CSMA Non-Persistent protocol with a finite number of nodes, providing more accurate results for applications like wireless sensor networks. The finite model addresses scenarios where the node count is moderate, capturing realistic system dynamics. Our analysis reveals a dependency on the node count, impacting system throughput. As the node count increases, throughput behavior aligns with Kleinrock’s infinite model. We derive a complex closed-form throughput expression for a finite quantity of nodes in the system, solved numerically, and offer an approximate expression for specific conditions. These insights advance understanding of low-contention network performance, especially in scenarios where the infinite model becomes inadequate.