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Connectivity in Wireless Ad-hoc Networks with a Log-normal Radio Model

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Abstract

In this paper we study connectivity in wireless ad-hoc networks by modeling the network as an undirected geometric random graph. The novel aspect in our study is that for finding the link probability between nodes we use a radio model that takes into account statistical variations of the radio signal power around its mean value. We show that these variations, that are unavoidably caused by the obstructions and irregularities in the surroundings of the transmitting and the receiving antennas, have two distinct effects on the network. Firstly, they reduce the amount of correlation between links causing the geometric random graph tend to behave like a random graph with uncorrelated links. Secondly, these variations increase the probability of long links, which enhances the probability of connectivity for the network.

Another new result in our paper is an equation found for the calculation of the giant component size in wireless ad-hoc networks, that takes into account the level of radio signal power variations. With simulations we show that for the planning and design of wireless ad-hoc networks or sensor networks the giant component size is a good measure for “connectivity”.

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References

  1. IETF mobile ad-hoc networks (MANET) working group, http://www.ietf.org/html.charters/manet-charter.html.

  2. E. Royer and C.-K. Toh, A review of current routing protocols for ad-hoc mobile wireless networks, IEEE Personal Communications 6(2) (1999) 46–55.

    Article  Google Scholar 

  3. O. Dousse, F. Baccelli and P. Thiran, Impact of interference on connectivity in ad hoc networks, IEEE Infocom2003 (April 2003).

  4. P. Gupta and P.R. Kumar, The capacity of wireless networks. IEEE Transactions on Information Theory 46(2) (2000) 388–404.

    Article  MathSciNet  Google Scholar 

  5. M.E.J. Newman, S.H. Strogatz and D.J. Watts, Random graphs witharbitrary degree distributions and their applications, Physical Review E 64 (2001) 026118.

    Article  Google Scholar 

  6. G. Nemeth and G. Vattay, Giant clusters in random ad hoc networks, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 67 036110/1 036110/6 (March 2003).

    Google Scholar 

  7. I. Glauche, W. Krause, R. Sollacher and M. Greiner, Continuum percolation of wireless ad-hoc communication networks, cond-mat/0304579 (April 2003).

  8. B. Bollobas, Random Graphs (Academic Press, 1985).

  9. M.D. Penrose, On k-connectivity for a geometric random graph. Random Structures and Algorithms 15 (1999) 145–164.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Prasad, Universal Wireless Personal Communications (Artech House Publishers, 1998).

  11. T. Rappaport, Wireless Communications, Principles and Practice (Upper Saddle River Prentice-Hall PTR, 2002).

  12. C. Bettstetter, On the minimum node degree and connectivity of a wireless multihop network, in: Proc. 3rd ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc) (Lausanne, Switzerland, June 9–11 2002) pp. 80–91.

  13. H. Bertoni, Radio Propagation for Modern Wireless Systems (Prentice-Hall PTR, 2000).

  14. R. Hekmat and P. Van Mieghem, Degree distribution and hopcount in wireless ad-hoc networks, in: Proceeding of the 11th IEEE International Conference on Networks (ICON 2003) (Sydney, Australia, Sept. 28-Oct. 1 2003) pp. 603–609.

  15. C. Bettstetter and C. Hartmann, Connectivity of wireless multihop networks in a shadow fading environment, in Proceedings of the 6th ACM International Workshop on Modeling Analysis and Simulation of Wireless and Mobile Systems (MSWiM) (San Diego, CA, USA, September 2003) pp. 28–32.

  16. D.J. Watts, Small World, the Dynamics of Networks Between Order and Randomness (Princeton University Press, Princeton, New Jersey, 1999).

    Google Scholar 

  17. R. Albert and A.L. Barabasi, Statistical mechanics of complex networks, Review of Modern Physics 74 (2002) 47–97.

    Article  MathSciNet  Google Scholar 

  18. J. Diaz, J. Petit and M. Serna, Random geometric problems on [0,1]2, Randomization and Approximation Techniques in Computer Science vol. 1518 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1998) pp. 294–306.

    Google Scholar 

  19. P. Erdos and A. Renyi, On the evolution of random graphs, Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5 (1960) 17–61.

    MathSciNet  Google Scholar 

  20. B. Bollobas, Modern Graph Theory (Springer-Verlag, New York, 1998).

    Google Scholar 

  21. G. Hooghiemstra and P. Van Mieghem, On the mean distance in scale free graphs, Delft University of Technology, report20040605, http://www.nas.its.tudelft.nl/people/Piet/telconference.html 2004.

  22. S. Janson, D.E. Knuth, T. Luczak and B. Pitel, The birth of the giant component, Random Structures and Algorithms 4(3) (1993) 231–358.

    MathSciNet  Google Scholar 

  23. M. Molloy and B. Reed, The size of the giant component of a random graph with a given degree sequence, Combinatorics, Probability and Computing 7 (1998) 295–305.

    Article  MathSciNet  Google Scholar 

  24. P. Van Mieghem, The asymptotic behaviour of queueing systems: Large deviations theory and dominant pole approximation, Queueing Systems 23 (1996) 27–55.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Delft University of Technology, Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600, GA Delft, The Netherlands

    R. Hekmat & P. Van Mieghem

Authors
  1. R. Hekmat
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  2. P. Van Mieghem
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Correspondence to R. Hekmat.

Additional information

R. Hekmat Ramin Hekmat received M.Sc. degree in electrical engineering from Delft University of Technology (TU Delft) in the Netherlands in 1990. He worked since then for several telecommunication companies in the Netherlands and the United States in Research and Development as well as managerial positions. In September 2005 he obtained Ph.D degree for his work related to Ad-hoc Networks at TU Delft. Currently he is working as assistant professor in the faculty of Electrical Engineering, Mathematics and Computer Science of TU Delft. His prime research interest includes multi-user communication system, wireless communications and peer-to-peer networks.

P. Van Mieghem Piet Van Mieghem has obtained the Master and Ph. D. in Electrical Engineering from the K.U.Leuven (Belgium) in 1987 and 1991, respectively. He has joined the Interuniversity Micro Electronic Center (IMEC) from 1987-1991. He was a visiting scientist at MIT, department of electrical engineering from 1992-1993. From 1993 to 1998, he was working in Alcatel Corporate Research Center in Antwerp where he has gained experience in performance analysis of ATM systems and network architectural concepts of both ATM networks (PNNI) and the Internet. Currently, he is full professor at Delft University of Technology with a chair in telecommunication networks. The main theme of the research is evolution of the Internet architecture towards a broadband and QoS-aware network.

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Hekmat, R., Van Mieghem, P. Connectivity in Wireless Ad-hoc Networks with a Log-normal Radio Model. Mobile Netw Appl 11, 351–360 (2006). https://doi.org/10.1007/s11036-006-5188-7

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  • DOI: https://doi.org/10.1007/s11036-006-5188-7

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