Skip to main content
SpringerLink
Log in

Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

In this paper we analyze connectivity issues in one-dimensional ad hoc networks. Starting with a deterministic channel model, we show how an equivalent GI|D|∞ queueing model may be used to address network connectivity. In this way, we obtain exact results for the coverage probability, the node isolation probability and the connectivity distance for various node placement statistics. We then show how a GI|G|∞ model may be used to study broadcast percolation problems in ad hoc networks with general node placement in the presence of fading channels. In particular, we obtain explicit results for the case of nodes distributed according to a Poisson distribution operating in a fading/shadowing environment. In the latter case, heavy traffic theorems are applied to derive the critical transmission power for connectivity and broadcast percolation distance in highly dense networks. The impact of signal processing schemes able to exploit the diversity provided by small-scale fading by means of multiple antennas is considered. The analysis is then extended to the case of unreliable ad hoc networks, with an in-depth discussion of asymptotic results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Gupta and P. R. Kumar, “Critical power for asymptotic connectivity,” in Proc. of IEEE CDC, Tampa, USA, 1998.

  2. P. Santi and D. M. Blough, “The critical transmitting range for connectivity in sparse wireless ad hoc networks,” IEEE Trans. on Mob. Comp., vol. 2, no. 1, pp. 25–39, Jan—Mar 2003.

    Article  Google Scholar 

  3. O. Dousse, P. Thiran, and M. Hasler, “Connectivity in ad—hoc and hybrid networks,” in Proc. of IEEE INFOCOM, New York, USA, 2002.

  4. O. Dousse, F. Baccelli, and P. Thiran, “Impact of interferences on connectivity in ad—hoc networks,” in Proc. of IEEE INFOCOM, San Francisco, USA, 2003.

  5. P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Trans. on Inf. Th., vol. 46, no. 2, pp. 388–404, Mar. 2000.

    Article  MathSciNet  Google Scholar 

  6. A. E. Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Throughput-delay trade-off in wireless networks,” in Proc. of IEEE INFOCOM, Hong Kong, 2004.

  7. S. R. Kulkarni and P. Viswanath, “A deterministic approach to throughput scaling in wireless networks.” IEEE Trans. on Inf. Th., vol. 50, no. 6, pp. 1041–1049, Jun. 2004.

    Article  MathSciNet  Google Scholar 

  8. A. Rajeswaran and R. Negi, “Capacity of power constrained ad-hoc networks,” in Proc. of IEEE INFOCOM, Hong Kong, 2004.

  9. A. Jovicic, P. Viswanath, and S. R. Kulkarni, “Upper bounds to transport capacity of wireless networks,” IEEE Trans. on Inf. Th., vol. 50, no. 11, pp. 2555–2565, Nov. 2004.

    Article  MathSciNet  Google Scholar 

  10. M. Franceschetti, O. Dousse, D. Tse, and P. Thiran, “On the throughput capacity of random wireless networks,” 2004, subm. for publ.

  11. O. Dousse and P. Thiran, “Connectivity vs capacity in dense ad hoc networks,” in Proc. of IEEE INFOCOM, Hong Kong, 2004.

  12. M. Desai and D. Manjunath, “On the connectivity in finite ad hoc networks,” IEEE Comm. Lett., vol. 6, no. 10, pp. 437–439, Oct 2002.

    Article  Google Scholar 

  13. P. Panchapakesan and D. Manjunath, “On the transmission range in dense ad hoc radio networks,” in Proc. of SPCOM, Bangalore, India, 2001.

  14. R. Hekmat and P. Van Mieghem, “Study of connectivity in wireless ad—hoc networks with an improved radio model,” in Proc. of WiOpt, Cambridge, UK, 2004.

  15. M. Franceschetti, L. Booth, J. Bruck, M.Cook, and R. Meester, “Continuum percolation with unreliable and spread out connections,” Journal of Statistical Physics, vol. 118, no. 3/4, pp. 721–734, Feb. 2005.

    Article  MathSciNet  Google Scholar 

  16. D. Miorandi and E. Altman, “Coverage and connectivity of ad-hoc networks in presence of channel randomness,” INRIA, Tech. Rep. RR5377, 2004. [Online]. Available: http://www.inria.fr/rrrt/rr-5377.html

  17. P. Santi, “The critical transmitting range for connectivity in mobile ad hoc networks,” IEEE Trans. on Mob. Comp., vol. 4, no. 2, pp. 310–317, Mar. 2005.

    Article  Google Scholar 

  18. P. Hall, Introduction to the theory of coverage processes. New York: J. Wiley and sons, 1988.

    MATH  Google Scholar 

  19. S. Shakkottai, R. Srikant, and N. B. Shroff, “Unreliable sensor grids: coverage, connectivity and diameter,” in Proc. of IEEE INFOCOM, San Francisco, CA, 2003.

  20. L. Liu and D.-H. Shi, “Busy period in GIX|G|∟,” J. Appl. Prob., vol. 33, pp. 815–829, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. Abate, G. L. Choudhury, and W. Whitt, “An introduction to numerical transform inversion and its application to probability models,” in Computational Probability, W. Grassman, Ed. Boston: Kluwer, 1999, pp. 257–323.

    Google Scholar 

  22. W. Stadje, “The busy period of the queueing system M|G|∟,” J. Appl. Prob., vol. 22, pp. 697–704, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  23. P. Hall, “Heavy traffic approximations for busy period in an M|G|∟ queue,” Stochastic Processes and their Applications, vol. 19, pp. 259–269, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  24. Y.-C. Cheng and T. G. Robertazzi, “Critical connectivity phenomena in multihop radio models,” IEEE Trans.Comm., vol. 37, no. 7, pp. 770–777, Jul 1989.

    Article  Google Scholar 

  25. F. Baccelli and P. Bremaud, Elements of Queueing Theory. Berlin: Springer—Verlag, 1994.

    MATH  Google Scholar 

  26. L. Hanzo, C. H. Wong, and M. S. Yee, Adaptive Wireless Transceivers. New York: John Wiley and Sons, 2002.

    Google Scholar 

  27. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products. Orlando: Academic Press, 1983.

    Google Scholar 

  28. T. S. Rappaport, Wireless Communications. Upper Saddle River, New Jersey: Prentice Hall, 1999.

    Google Scholar 

  29. C. Bettstetter and C. Hartmann, “Connectivity of wireless multihop networks in a shadow fading environment,” in Proc. of ACM MSWiM, San Diego, CA, 2003.

  30. D. Stoyan, Comparison Methods for Queues and Other Stochasti Models. New York: John Wiley & Sons, 1983.

    Google Scholar 

  31. S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas on Comm., vol. 16, no. 8, pp. 1451–1458, Oct. 1998.

    Article  Google Scholar 

  32. E. Altman, “On stochastic recursive equations and infinite server queues,” in Proc. of IEEE INFOCOM, Miami, 2005.

Download references

Author information

Authors and Affiliations

  1. CREATE-NET, v. Solteri 38, 38100, Trento, Italy

    Daniele Miorandi

  2. INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Eitan Altman

Authors
  1. Daniele Miorandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eitan Altman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniele Miorandi.

Additional information

This work was partially supported by the EURO NGI Network of Excellence. The work of D. Miorandi was partially supported by Fond. A. Gini. This work has been done while D. Miorandi, at that time with University of Padova (Italy), was visiting the MAESTRO project at INRIA Sophia Antipolis.

Daniele Miorandi received his “Laurea” (summa cum laude) and Ph.D. degrees from Univ. of Padova (Italy) in 2001 and 2005, respectively. He currently holds a post-doc position at CREATE-NET, Trento (Italy). In 2003/04 he spent 12 months of his doctoral thesis visiting the MAESTRO team at INRIA Sophia Antipolis (France). His research interests include stochastic modelling, performance evaluation and protocols design for wireless networks.

Eitan Altman received the B.Sc. degree in electrical engineering (1984), the B.A. degree in physics (1984) and the Ph.D. degree in electrical engineering (1990), all from the Technion-Israel Institute, Haifa. In (1990) he further received his B.Mus. degree in music composition in Tel-Aviv university. Since 1990, he has been with INRIA (National research institute in informatics and control) in Sophia-Antipolis, France. His current research interests include performance evaluation and control of telecommunication networks and in particular congestion control, wireless communications and networking games. He is in the editorial board of several scientific journals: Stochastic Models, JEDC, COMNET, SIAM SICON and WINET. He has been the (co)chairman of the program committee of several international conferences and workshops (on game theory, networking games and mobile networks). More informaion can be found at http://www.inria.fr/mistral/personnel/Eitan.Altman/me.html

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miorandi, D., Altman, E. Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach. Wireless Netw 12, 573–587 (2006). https://doi.org/10.1007/s11276-006-6536-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-006-6536-z

Keywords

Search

Navigation