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Summary

This study introduces a percolation model to understand how varying transmission ranges in mobile ad hoc networks impact connectivity. The research shows the percolation threshold continuously varies, offering insights into network reliability under environmental factors.

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Area of Science:

  • Computer Science
  • Network Science
  • Statistical Physics

Background:

  • Mobile ad hoc networks (MANETs) exhibit non-uniform transmission ranges due to environmental factors like temperature, humidity, and obstructions.
  • Understanding the impact of these variable transmission ranges on overall network connectivity is crucial for practical applications.

Purpose of the Study:

  • To theoretically model and analyze the effect of variable transmission ranges on global connectivity in mobile ad hoc networks.
  • To introduce a percolation model with an additional source of disorder to study network reliability.

Main Methods:

  • A percolation model on a square lattice is developed where occupied sites are assigned random disk radii.
  • Bonds are defined based on a condition related to the radii of disks at connected sites.
  • A general formulation divides the radius plane into regions to define occupied bonds, with three rules analyzed.

Main Results:

  • The percolation threshold is shown to vary continuously under the proposed model.
  • The threshold has two limiting values: the ordinary site percolation threshold and unity.
  • The approach to these limits is characterized by two exponents.

Conclusions:

  • The developed percolation model provides a theoretical framework for understanding network connectivity with variable transmission ranges.
  • The continuous variation of the percolation threshold highlights the complex relationship between individual element behavior and global network properties.
  • The model's findings are applicable to designing more robust mobile ad hoc networks in dynamic environments.