Near-Optimal Radio Use for Wireless Network Synchronization

  • Milan Bradonjić
  • Eddie Kohler
  • Rafail Ostrovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5804)

Abstract

In this paper we consider the model of communication where wireless devices can either switch their radios off to save energy (and hence, can neither send nor receive messages), or switch their radios on and engage in communication. The problem has been extensively studied in practice, in the setting such as deployment and clock synchronization of wireless sensor networks – see, for example, [31,41,33,29,40]. The goal in these papers is different from the classic problem of radio broadcast, i.e. avoiding interference. Here, the goal is instead to minimize the use of the radio for both transmitting and receiving, and for most of the time to shut the radio down completely, as the radio even in listening mode consumes a lot of energy.

We distill a clean theoretical formulation of minimizing radio use and present near-optimal solutions. Our base model ignores issues of communication interference, although we also extend the model to handle this requirement. We assume that nodes intend to communicate periodically, or according to some time-based schedule. Clearly, perfectly synchronized devices could switch their radios on for exactly the minimum periods required by their joint schedules. The main challenge in the deployment of wireless networks is to synchronize the devices’ schedules, given that their initial schedules may be offset relative to one another (even if their clocks run at the same speed). In this paper we study how frequently the devices must switch on their radios in order to both synchronize their clocks and communicate. In this setting, we significantly improve previous results, and show optimal use of the radio for two processors and near-optimal use of the radio for synchronization of an arbitrary number of processors. In particular, for two processors we prove deterministic matching \(\Theta\left(\sqrt{n}\right)\) upper and lower bounds on the number of times the radio has to be on, where n is the discretized uncertainty period of the clock shift between the two processors. (In contrast, all previous results for two processors are randomized, e.g.[33], [29]). For m = nβ processors (for any positive β< 1) we prove Ω(n(1 − β)/2) is the lower bound on the number of times the radio has to be switched on (per processor), and show a nearly matching (in terms of the radio use) Õ(n(1 − β)/2) randomized upper bound per processor, (where Õ notation hides poly-log(n) multiplicative term) with failure probability exponentially close to 0. For β ≥ 1 our algorithm runs with at most poly-log(n) radio invocations per processor. Our bounds also hold in a radio-broadcast model where interference must be taken into account.

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References

  1. 1.
    Aldous, D.: Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels. IEEE Transactions on Information Theory 33(2), 219–223 (1987)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. Journal of Computer and System Sciences 43, 290–298 (1991)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time complexity of broadcast in radio networks: an exponential gap between determinism and randomization. Journal of Computer and System Sciences 45, 104–126 (1992)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Blum, P., Meier, L., Thiele, L.: Improved interval-based clock synchronization in sensor networks. In: IPSN 2004: Proceedings of the third international symposium on Information processing in sensor networks, pp. 349–358 (2004)Google Scholar
  5. 5.
    Boulis, A., Srivastava, M.: Node-Level Energy Management for Sensor Networks in the Presence of Multiple Applications. Wireless Networks 10(6), 737–746 (2004)CrossRefGoogle Scholar
  6. 6.
    Boulis, A., Ganeriwal, S., Srivastava, M.: Aggregation in sensor networks: an energy-accuracy trade-off. Ad Hoc Networks 1(2-3), 317–331 (2003)CrossRefGoogle Scholar
  7. 7.
    Bollobas, B., de la Vega, W.F.: The diameter of random graphs. Combinatorica 2 (1982)Google Scholar
  8. 8.
    Bradonjić, M., Kohler, E., Ostrovsky, R.: Near-Optimal Radio Use For Wireless Network Synchronization (2008), http://arxiv.org/abs/0810.1756
  9. 9.
    Bush, S.F.: Low-energy sensor network time synchronization as an emergent property. In: Proc. 14th International Conference on Communications and Networks (ICCCN 2005), October 17-19, pp. 93–98 (2005)Google Scholar
  10. 10.
    Cali, F., Conti, M., Gregori, E.: IEEE 802.11 protocol: design and performance evaluation of an adaptive backoff mechanism. IEEE Journal on Selected Areas in Communications 18(9), 1774–1786 (2000)CrossRefGoogle Scholar
  11. 11.
    Chlebus, B., Gasieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in ad hoc radio networks. Distributed Computing 15(1), 27–38 (2002)CrossRefGoogle Scholar
  12. 12.
    Dutta, P., Culler, D.: Practical asynchronous neighbor discovery and rendezvous for mobile sensing applications. In: Proceedings of the 6th ACM conference on Embedded network sensor systems (SenSys 2008), pp. 71–84 (2008)Google Scholar
  13. 13.
    Elkin, M.L., Kortsarz, G.: Polylogarithmic Inapproximability of the Radio Broadcast Problem. In: Proc. of 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, Cambridge, MA, pp. 105–114 (2004)Google Scholar
  14. 14.
    Elson, J., Römer, K.: Wireless sensor networks: a new regime for time synchronization. SIGCOMM. Comput. Commun. Rev. 33(1), 149–154 (2003)CrossRefGoogle Scholar
  15. 15.
    Elson, J., Girod, L., Estrin, D.: Fine-Grained Network Time Synchronization using Reference Broadcasts. In: Proc. Fifth Symposium on Operating Systems Design and Implementation (OSDI 2002), vol. 36, pp. 147–163 (2002)Google Scholar
  16. 16.
    Fan, R., Chakraborty, I., Lynch, N.: Clock Synchronization for Wireless Networks. In: OPODIS 2004, pp. 400–414 (2004)Google Scholar
  17. 17.
    Gaber, I., Mansour, Y.: Centralized broadcast in multihop radio networks. Journal of Algorithms 46(1), 1–20 (2003)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Honda, N., Nishitani, Y.: The Firing Squad Synchronization Problem for Graphs. Theoretical Computer Sciences 14(1), 39–61 (1981)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kesselman, A., Kowalski, D.: Fast distributed algorithm for convergecast in ad hoc geometric radio networks. In: Conference on Wireless on demand Network Systems and Services (2005)Google Scholar
  20. 20.
    Knuth, D.: The Art of Computer Programming. Seminumerical Algorithms, 3rd edn., vol. 2. Addison-Wesley, Reading (1997)Google Scholar
  21. 21.
    Kobayashi, K.: The Firing squad synchronization problem for a class of polyautomata networks. Journal of Computer and System Science 17, 300–318 (1978)MATHCrossRefGoogle Scholar
  22. 22.
    Koo, C.: Broadcast in Radio Networks Tolerating Byzantine Adversarial Behavior. In: Proceedings of 23rd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), pp. 275–282 (2004)Google Scholar
  23. 23.
    Kamath, A.P., Motwani, R., Palem, K., Spirakis, P.: Tail bounds for occupancy and the satisfiability threshold conjecture. Random Structures and Algorithms 7, 59–80 (1995)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Kothapalli, K., Onus, M., Richa, A., Scheideler, C.: Efficient Broadcasting and Gathering in Wireless Ad Hoc Networks. In: IEEE International Symposium on Parallel Architectures, Algorithms and Networks, ISPAN (2005)Google Scholar
  25. 25.
    Kowalski, D., Pelc, A.: Broadcasting in undirected ad hoc radio networks. In: Proceedings of the twenty-second annual symposium on Principles of distributed computing, pp. 73–82. ACM Press, New York (2003)CrossRefGoogle Scholar
  26. 26.
    Kowalski, D., Pelc, A.: Faster deterministic broadcasting in ad hoc radio networks. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 109–120. Springer, Heidelberg (2003)Google Scholar
  27. 27.
    Kopetz, H., Ochsenreiter, w.: Global time in distributed real-time systems. Technical Report 15/89, Technische Universitat Wien, Wien Austria (1989)Google Scholar
  28. 28.
    Mills, D.L.: Internet time synchronization: the network time protocol. IEEE Transactions on Communications 39(10), 1482–1493 (1991)CrossRefGoogle Scholar
  29. 29.
    Moscibroda, T., von Rickenbach, P., Wattenhofer, R.: Analyzing the Energy-Latency Trade-Off During the Deployment of Sensor Networks. In: INFOCOM 2006. 25th IEEE International Conference on Computer Communications. Proceedings, April 2006, pp. 1–13 (2006)Google Scholar
  30. 30.
    Motwani, R., Raghavan, P.: Randomized algorithms. Cambridge University Press, New York (1995)MATHGoogle Scholar
  31. 31.
    McGlynn, M., Borbash, S.: Birthday protocols for low energy deployment and flexible neighbor discovery in ad hoc wireless networks. In: MobiHoc 2001: Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing, pp. 137–145 (2001)Google Scholar
  32. 32.
    Park, V., Corson, M.: A Highly Adaptive Distributed Routing Algorithm for Mobile Wireless Networks. In: INFOCOM 1997. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution (1997)Google Scholar
  33. 33.
    PalChaudhuri, S., Johnson, D.: Birthday paradox for energy conservation in sensor networks. In: Proceedings of the 5th Symposium of Operating Systems Design and Implementation (2002)Google Scholar
  34. 34.
    Polastre, J., Hill, J., Culler, D.: Versatile low power media access for wireless sensor networks. In: Proceedings of the 2nd international Conference on Embedded Networked Sensor Systems, SenSys 2004, Baltimore, MD, USA, November 03 - 05, pp. 95–107. ACM Press, New York (2004)CrossRefGoogle Scholar
  35. 35.
    Sichitiu, M.L., Veerarittiphan, C.: Simple, accurate time synchronization for wireless sensor networks. In: 2003 IEEE Wireless Communications and Networking, 2003. WCNC 2003, March 16-20, vol. 2, pp. 1266–1273 (2003)Google Scholar
  36. 36.
    Shnayder, V., Hempstead, M., Chen, B., Allen, G., Welsh, M.: Simulating the power consumption of large-scale sensor network applications. In: SenSys 2004: Proceedings of the 2nd international conference on Embedded networked sensor systems, pp. 188–200. ACM Press, New York (2004)CrossRefGoogle Scholar
  37. 37.
    Schurgers, C., Raghunathan, V., Srivastava, M.: Power management for energy-aware communication systems. ACM Trans. Embedded Comput. Syst. 2(3), 431–447 (2003)CrossRefGoogle Scholar
  38. 38.
    Sivrikaya, F., Yener, B.: Time synchronization in sensor networks: a survey. IEEE Network 18(4), 45–50 (2004)CrossRefGoogle Scholar
  39. 39.
    Sichitiu, M.L., Veerarittiphan, C.: Simple, Accurate Time Synchronization for Wireless Sensor Networks. In: Proc. IEEE Wireless Communications and Networking Conference (WCNC 2003), pp. 1266–1273 (2003)Google Scholar
  40. 40.
    Sundararaman, B., Buy, U., Kshemkalyani, A.D.: Clock synchronization for wireless sensor networks: a survey. Ad-hoc Networks 3(3), 281–323 (2005)CrossRefGoogle Scholar
  41. 41.
    Tseng, Y.-C., Hsu, C.-S., Hsieh, T.-Y.: Power-saving protocols for IEEE 802.11-based multi-hop ad hoc networks. Comput. Netw. 43(3), 317–337 (2003)MATHCrossRefGoogle Scholar
  42. 42.
    Zheng, R., Hou, J., Sha, L.: Asynchronous wakeup for ad hoc networks. In: Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing (MobiHoc 2003), pp. 35–45 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Milan Bradonjić
    • 1
  • Eddie Kohler
    • 2
  • Rafail Ostrovsky
    • 3
  1. 1.Theoretical Division, and Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Computer Science DepartmentUniversity of CaliforniaLos AngelesUSA
  3. 3.Computer Science Department and Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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