Computing time complexity of population protocols with cover times: the zebranet example

Authors:
Joffroy Beauquier;Peva Blanchard;Janna Burman;Sylvie Delaët1
Affiliations:
LRI, Univ. Paris-Sud 11, Orsay and Grand Large project, INRIA Saclay, France;LRI, Univ. Paris-Sud 11, Orsay, France;MASCOTTE, INRIA, I3S (CNRS/University of Nice Sophia-Antipolis), France;LRI, Univ. Paris-Sud 11, Orsay, France
Venue:
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Year:
2011

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Tight complexity analysis of population protocols with cover times - The ZebraNet example

Theoretical Computer Science

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Abstract

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.