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Central Limit Theorem for Time to Broadcast in Radio Networks

Published online by Cambridge University Press:  27 July 2009

Krishnamurthi Ravishankar  and
Suresh Singh
Krishnamurthi Ravishankar
Affiliation:
Department of Math and Computer Science, SUNY at New Paltz, New Paltz, New York 12561
Suresh Singh
Affiliation:
Department of Computer Science, University of South Carolina, Columbia, South Carolina 29208
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Abstract

We study the problem of broadcasting in a system where nodes are equipped with radio transmitters with constant radius of transmission. A message originating at a node has to be transmitted to all the other nodes in the system. We prove the central limit theorem and the law of large numbers for the number of time steps required to complete a broadcast for the case when the nodes are placed on a line independently uniformly distributed. We show that the number of time steps required to broadcast is 3n/4 in probability.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 201 - 209
Copyright
Copyright © Cambridge University Press 1995

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