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Queueing Systems

, Volume 76, Issue 2, pp 149–180 | Cite as

Clock synchronization in symmetric stochastic networks

  • Anatoly ManitaEmail author
Article

Abstract

We consider a stochastic model of clock synchronization in a wireless network of \(N\) sensors interacting with one dedicated accurate time server. For large \(N\) we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales \(t_{N}\rightarrow \infty \), \(N\rightarrow \infty \). We discuss the existence of phase transitions and find the exact timescales for which an effective clock synchronization of the system takes place.

Keywords

Stochastic networks Clock synchronization Wireless sensor networks Multi-dimensional Markov process Phase transitions 

Mathematics Subject Classification (2000)

60K35 60J27 90B15 60K20 

Notes

Acknowledgments

The work is supported by Russian Foundation for Basic Research (Grant No. 12-01-00897). The author is grateful to L.G. Afanasyeva for many interesting and useful discussions. The author also thanks the anonymous referee for a number of valuable comments and suggestions.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Probability, Faculty of Mathematics and MechanicsLomonosov Moscow State UniversityMoscow Russia

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