Advertisement

Self-stabilizing Consensus Average Algorithm in Distributed Sensor Networks

  • Jacques M. Bahi
  • Mohammed Haddad
  • Mourad Hakem
  • Hamamache Kheddouci
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7980)

Abstract

One important issue in sensor networks that has received renewed interest recently is average consensus, i.e., computing the average of n sensor measurements, where nodes iteratively exchange data with their neighbors and update their own data accordingly until reaching convergence to the right parameters estimate. In this paper, we introduce an efficient self-stabilizing algorithm to achieve/ensure the convergence of node states to the average of the initial measurements of the network. We prove that the convergence of the fusion process is finite and express an upper bound of the actual number of moves/iterations required by the algorithm. This means that our algorithm is guaranteed to reach a stable situation where no load will be sent from one sensor node to another. We also prove that the load difference between any two sensor nodes in the network is within \(\frac{\varepsilon}{D}\times\left\lfloor\frac{D+1}{2}\right\rfloor<\varepsilon,\) where ε is the prescribed global equilibrium threshold (this threshold is given by the system) and D is the diameter of the network.

Keywords

Sensor Network Sensor Node Wireless Sensor Network Link Failure Virtual Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akyildiz, I., Su, W., Sankarasubramniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Communications Magazine, 102–114 (2002)Google Scholar
  2. 2.
    Paradis, L., Han, Q.: A survey of fault management in wireless sensor networks. JNSM 15(2), 171–190 (2007)Google Scholar
  3. 3.
    Hai, L., Amiya, N., Ivan, S.: Fault-tolerant algorithms/protocols in wireless sensor networks. In: Handbook of Wireless Ad Hoc and Sensor Net., pp. 265–295 (2009)Google Scholar
  4. 4.
    Saleh, I., Eltoweissy, M., Agbaria, A., El-Sayed, H.: A fault tolerance management framework for wireless sensor networks. JCM 2(4), 38–48 (2007)Google Scholar
  5. 5.
    Ye, F., Zhang, H., Lu, S., Zhang, L., Hou, J.C.: A randomized energy-conservation protocol for resilient sensor networks. Wireless Networks 12(5), 637–652 (2006)CrossRefGoogle Scholar
  6. 6.
    de Souza, L.M.S., Vogt, H., Beigel, M.: A survey on fault tolerance in wireless sensor networks. Sap research, braunschweig, germanyGoogle Scholar
  7. 7.
    Lynch, N.: Distributed algorithms. Morgan Kaufmann Publishers, Inc. (1996)Google Scholar
  8. 8.
    Cedo, F., Cortés, A., Ripoll, A., Senar, M.A., Luque, E.: The convergence of realistic distributed load-balancing algorithms. Theory Comput. Syst. 41(4), 609–618 (2007)Google Scholar
  9. 9.
    Rabani, Y., Sinclair, A., Wanka, R.: Local divergence of markov chains and the analysis of iterative load-balancing schemes. In: Proceedings of the IEEE Symp. on Found. of Comp. Sci., Palo Alto (1998)Google Scholar
  10. 10.
    Bahi, J., Couturier, R., Vernier, F.: Synchronous distributed load balancing on dynamic networks. Journal of Parallel and Distributed Computing 65(11), 1397–1405 (2005)zbMATHCrossRefGoogle Scholar
  11. 11.
    Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transaction on Automatic Control 49(9), 1520–1533Google Scholar
  12. 12.
    Bliman, P., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. Journal of IFAC 44(8), 1985–1995 (2008)MathSciNetGoogle Scholar
  13. 13.
    Moallemi, C.C., Roy, B.V.: Consensus propagation. IEEE Trans. Inf. Theory 52(11), 4753–4766 (2006)CrossRefGoogle Scholar
  14. 14.
    Legg, J.A.: Tracking and sensor fusion issues in the tactical land environement. Technical Report TN.0605 (2005)Google Scholar
  15. 15.
    Olfati-Saber, R., Shamma, J.S.: Consensus filters for sensor networks and distributed sensor fusion. In: 44th IEEE Conf. on Dec. and Cont. CDC-ECC (2005)Google Scholar
  16. 16.
    Olfati-Saber, R.: Distributed kalman filter with embeded consensus filters. In: 44th IEEE Conf. on Dec. and Cont. (2005)Google Scholar
  17. 17.
    Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. In: Proc. of IEEE, pp. 215–233 (2007)Google Scholar
  18. 18.
    Xiao, L., Boyd, S., Lall, S.: A space-time diffusion scheme for peer-to-peer least-squares estimation. In: Proc. of Fifth International Conf. on Information Processing in Sensor Networks (IPSN 2006), pp. 168–176 (2006)Google Scholar
  19. 19.
    Talebi, M.S., Kefayati, M., Khalaj, B.H., Rabiee, H.R.: Adaptive consensus averaging for information fusion over sensor networks. In: IEEE International Conference on Mobile Adhoc and Sensor Systems (MASS), pp. 562–565 (2006)Google Scholar
  20. 20.
    Kar, S., Moura, J.M.F.: Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. IEEE Transactions on Signal Processing 57(1), 355–369 (2009)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Bahi, J.M., Giersch, A., Makhoul, A.: A scalable fault tolerant diffusion scheme for data fusion in sensor networks. In: InfoScale 2008, pp. 1–5. ICST press (2008)Google Scholar
  22. 22.
    Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Athena Scientific (1997)Google Scholar
  23. 23.
    Gupta, S.K.S., Srimani, P.K.: Self-stabilizing multicast protocols for ad hoc networks. Journal of Parallel and Distributed Computing 63(1), 87–96 (2003); Wireless and Mobile Ad Hoc Networking and ComputingGoogle Scholar
  24. 24.
    Beauquier, J., Clement, J., Messika, S., Rosaz, L., Rozoy, B.: Self-stabilizing counting in mobile sensor networks. In: PODC 2007: Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, pp. 396–397. ACM, New York (2007)CrossRefGoogle Scholar
  25. 25.
    Hoepman, J.-H., Larsson, A., Schiller, E.M., Tsigas, P.: Secure and self-stabilizing clock synchronization in sensor networks. In: Masuzawa, T., Tixeuil, S. (eds.) SSS 2007. LNCS, vol. 4838, pp. 340–356. Springer, Heidelberg (2007)Google Scholar
  26. 26.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)zbMATHCrossRefGoogle Scholar
  27. 27.
    Gradinariu, M., Tixeuil, S.: Conflict managers for self-stabilization without fairness assumption. In: International Conference on Distributed Computing Systems, p. 46 (2007)Google Scholar
  28. 28.
    Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In: Proceedings of the 17th International Symposium on Parallel and Distributed Processing, IPDPS 2003, pp. 162.2. IEEE Computer Society, Washington, DC (2003)Google Scholar
  29. 29.
    Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Trevisan, V.: Distance- k knowledge in self-stabilizing algorithms. Theoretical Computer Science 399(1-2), 118–127 (2008); Flocchini, P., Gąsieniec, L. (eds.): SIROCCO 2006. LNCS, vol. 4056. Springer, Heidelberg (2006)Google Scholar
  30. 30.
    Beauquier, J., Datta, A.K., Gradinariu, M., Magniette, F.: Self-stabilizing local mutual exclusion and daemon refinement. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 223–237. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  31. 31.
    Afek, Y., Dolev, S.: Local stabilizer. Journal of Parallel and Distributed Computing 62(5), 745–765 (2002)zbMATHCrossRefGoogle Scholar
  32. 32.
    Leal, W., Arora, A.: Scalable self-stabilization via composition. In: Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS 2004), pp. 12–21. IEEE Computer Society, Washington, DC (2004)Google Scholar
  33. 33.
    Jaworski, J., Ren, M., Rybarczyk, K.: Random key predistribution for wireless sensor networks using deployment knowledge. Computing 85(1-2) (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jacques M. Bahi
    • 1
  • Mohammed Haddad
    • 2
  • Mourad Hakem
    • 1
  • Hamamache Kheddouci
    • 2
  1. 1.DISC Laboratory, Femto-ST - UMR CNRSUniversité de Franche-ComtéFrance
  2. 2.LIRIS Laboratory, UMR CNRS 5205Université de Lyon 1France

Personalised recommendations