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Optimization of Wi-Fi Direct average time to discovery: a global channel randomization approach

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Abstract

The main objective of this work is to propose concrete time reduction strategies for discovery of Wi-Fi Direct in Android. To achieve our goals, we perform a fairly general mathematical modeling of the discovery of devices using Poisson processes. Subsequently, under asymptotic invariance hypotheses of certain distributions, we derive formulas for the expected time to discovery. We provide sufficient condition for fast convergence to an invariant distribution and determine key decision parameters (jumps intensities) that minimize the average time to discovery. We also propose a predictive model for rapid evaluation of these optimal discovery parameters. Experimental tests in an emulator are also conducted to validate the theoretical results obtained. A comparative performance study is done with some optimization approaches from literature. Compared with existing methods, the improvement of the average time discovery we obtained with the proposed method is above \(98.34\%\).

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Notes

  1. https://grouper.ieee.org/groups/802/11/Reports/802.11_Timelines.htm

  2. http://madwifi-project.org.

  3. http://wireless.kernel.org.

  4. \(1\text { }Time\text { } Unit=1024\,\upmu \text {s}\).

  5. See Sun et al. (2016).

  6. Significance codes under R software in terms of P-value : 0 “***" 0.001 “**" 0.01 “*"0.05 “\(\bullet\)" 0.1 " " 1

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Acknowledgements

The authors would like to thank engineer Freddy Emmanuel Ngasam for his great availability in terms of proofreading and criticism of this work.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, The University of Ngaoundere, Ngaoundere, Cameroun

    Rémy Maxime Mbala, David Jaurès Fotsa-Mbogne & Jean Michel Nlong

  2. Department of Mathematics and Computer Science, The University of Liverpool, Liverpool, United Kingdom

    Olivier Menoukeu-Pamen

  3. Department of Mathematics and Computer Science, Catholic University of Central Africa, Yaoundé, Cameroun

    Jean-Robert Kala-Kamdjoug

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  1. Rémy Maxime Mbala
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  2. David Jaurès Fotsa-Mbogne
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  3. Jean Michel Nlong
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  4. Olivier Menoukeu-Pamen
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Correspondence to David Jaurès Fotsa-Mbogne.

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Appendix A: Algorithms

Appendix A: Algorithms

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Mbala, R.M., Fotsa-Mbogne, D.J., Nlong, J.M. et al. Optimization of Wi-Fi Direct average time to discovery: a global channel randomization approach. Optim Eng 24, 1689–1717 (2023). https://doi.org/10.1007/s11081-022-09749-w

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