Computing Time Complexity of Population Protocols with Cover Times - The ZebraNet Example

  • Joffroy Beauquier
  • Peva Blanchard
  • Janna Burman
  • Sylvie Delaët
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6976)


Population protocols are a communication model for large sensor networks with resource-limited mobile agents. The agents move asynchronously and communicate via pair-wise interactions. The original fairness assumption of this model involves a high level of asynchrony and prevents an evaluation of the convergence time of a protocol (via deterministic means). The introduction of some “partial synchrony” in the model, under the form of cover times, is an extension that allows evaluating the time complexities.

In this paper, we take advantage of this extension and study a data collection protocol used in the ZebraNet project for the wild-life tracking of zebras in a reserve in central Kenya. In ZebraNet, sensors are attached to zebras and the sensed data is collected regularly by a mobile base station crossing the area. The data collection protocol of ZebraNet has been analyzed through simulations, but to our knowledge, this is the first time, that a purely analytical study is presented. Our first result is that, in the original protocol, some data may never be delivered to the base station. We then propose two slightly modified and correct protocols and we compute their worst case time complexities. Still, in both cases, the result is far from the optimal.


Mobile Agent Cover Time Decay Mechanism Variable Accumulation Data Collection Protocol 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angluin, D., Aspnes, J., Diamadi, Z., Fisher, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC, pp. 290–299 (2004)Google Scholar
  2. 2.
    Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. DC 21(3), 183–199 (2008)zbMATHGoogle Scholar
  3. 3.
    Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed Computing 20(4), 279–304 (2007)CrossRefzbMATHGoogle Scholar
  4. 4.
    Beauquier, J., Blanchard, P., Burman, J., Delaet, S.: Exact time complexity of zebranet with cover times. LRI Internal Report (2011)Google Scholar
  5. 5.
    Beauquier, J., Burman, J., Clément, J., Kutten, S.: On utilizing speed in networks of mobile agents. In: PODC, pp. 305–314 (2010)Google Scholar
  6. 6.
    Beauquier, J., Burman, J., Kutten, S.: A self-stabilizing transformer for population protocols with covering. Theor. Comput. Sci. 412(33), 4247–4259 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Beauquier, J., Clément, J., Messika, S., Rosaz, L., Rozoy, B.: Self-stabilizing counting in mobile sensor networks with a base station. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 63–76. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Cai, H., Eun, D.Y.: Crossing over the bounded domain: from exponential to power-law inter-meeting time in MANET. In: MOBICOM, pp. 159–170 (2007)Google Scholar
  9. 9.
    Chaintreau, A., Hui, P., Crowcroft, J., Diot, C., Gass, R., Scott, J.: Impact of human mobility on opportunistic forwarding algorithms. IEEE Transactions on Mobile Computing 6, 606–620 (2007)CrossRefGoogle Scholar
  10. 10.
    College, D.: The dartmouth wireless trace archive (2007)Google Scholar
  11. 11.
    Dwork, C., Lynch, N.A., Stockmeyer, L.J.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288–323 (1988)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fischer, M., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Guerraoui, R., Ruppert, E.: Even small birds are unique: Population protocols with identifiers. Technical Report CSE-2007-04. York University (2007)Google Scholar
  14. 14.
    Hong, S., Rhee, I., Kim, S.J., Lee, K., Chong, S.: Routing performance analysis of human-driven delay tolerant networks using the truncated levy walk model. In: MobilityModels, pp. 25–32 (2008)Google Scholar
  15. 15.
    Juang, P., Oki, H., Wang, Y., Martonosi, M., Peh, L.-S., Rubenstein, D.: Energy-efficient computing for wildlife tracking: design tradeoffs and early experiences with zebranet. In: ASPLOS, pp. 96–107 (2002)Google Scholar
  16. 16.
    Karagiannis, T., Boudec, J.L., Vojnovic, M.: Power law and exponential decay of inter contact times between mobile devices. In: MOBICOM, pp. 183–194 (2007)Google Scholar
  17. 17.
    Lindgren, A., Doria, A., Schelén, O.: Probabilistic routing in intermittently connected networks. SIGMOBILE Mob. Comput. Commun. Rev. 7, 19–20 (2003)CrossRefGoogle Scholar
  18. 18.
    Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Joffroy Beauquier
    • 1
    • 3
  • Peva Blanchard
    • 1
  • Janna Burman
    • 2
  • Sylvie Delaët
    • 1
  1. 1.LRIUniv. Paris-Sud 11OrsayFrance
  2. 2.MASCOTTEINRIA, I3S (CNRS/University of Nice Sophia-Antipolis)France
  3. 3.Grand Large projectINRIA SaclayFrance

Personalised recommendations