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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akyildiz, I., Su, W., Sankarasubramniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Communications Magazine, 102–114 (2002)
Paradis, L., Han, Q.: A survey of fault management in wireless sensor networks. JNSM 15(2), 171–190 (2007)
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)
Saleh, I., Eltoweissy, M., Agbaria, A., El-Sayed, H.: A fault tolerance management framework for wireless sensor networks. JCM 2(4), 38–48 (2007)
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)
de Souza, L.M.S., Vogt, H., Beigel, M.: A survey on fault tolerance in wireless sensor networks. Sap research, braunschweig, germany
Lynch, N.: Distributed algorithms. Morgan Kaufmann Publishers, Inc. (1996)
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)
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)
Bahi, J., Couturier, R., Vernier, F.: Synchronous distributed load balancing on dynamic networks. Journal of Parallel and Distributed Computing 65(11), 1397–1405 (2005)
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), 1520–1533
Bliman, P., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. Journal of IFAC 44(8), 1985–1995 (2008)
Moallemi, C.C., Roy, B.V.: Consensus propagation. IEEE Trans. Inf. Theory 52(11), 4753–4766 (2006)
Legg, J.A.: Tracking and sensor fusion issues in the tactical land environement. Technical Report TN.0605 (2005)
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)
Olfati-Saber, R.: Distributed kalman filter with embeded consensus filters. In: 44th IEEE Conf. on Dec. and Cont. (2005)
Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. In: Proc. of IEEE, pp. 215–233 (2007)
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)
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)
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)
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)
Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Athena Scientific (1997)
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 Computing
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)
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)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Gradinariu, M., Tixeuil, S.: Conflict managers for self-stabilization without fairness assumption. In: International Conference on Distributed Computing Systems, p. 46 (2007)
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)
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)
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)
Afek, Y., Dolev, S.: Local stabilizer. Journal of Parallel and Distributed Computing 62(5), 745–765 (2002)
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)
Jaworski, J., Ren, M., Rybarczyk, K.: Random key predistribution for wireless sensor networks using deployment knowledge. Computing 85(1-2) (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bahi, J.M., Haddad, M., Hakem, M., Kheddouci, H. (2013). Self-stabilizing Consensus Average Algorithm in Distributed Sensor Networks. In: Hameurlain, A., Küng, J., Wagner, R. (eds) Transactions on Large-Scale Data- and Knowledge-Centered Systems IX. Lecture Notes in Computer Science, vol 7980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40069-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-40069-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40068-1
Online ISBN: 978-3-642-40069-8
eBook Packages: Computer ScienceComputer Science (R0)