Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-18T14:28:46.539Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Battacharaya, R.N. & Waymire, E.C. (1990). Stochastic processes with applications. New York: Wiley.Google Scholar
2.Cheng, Y.-C. & Robartazzi, T.G. (1989). Critical connectivity phenomena in multihop radio models. IEEE Transactions on Communications 37(7): 770–777.CrossRefGoogle Scholar
3.Chlamtac, I. & Kutten, S. (1985). On broadcasting in radio networks-Problem analysis and protocol design. IEEE Transactions on Communications 33: 1240–1246.CrossRefGoogle Scholar
4.Deuschel, J. & Stroock, D.W. (1989). Large deviations. New York: Academic Press.Google Scholar
5.Hedetniemi, S.M., Hedetniemi, S.T., & Liestman, A.L. (1988). A survey of gossiping and broadcasting in communication networks. Networks 18: 319–349.CrossRefGoogle Scholar
6.Ravishankar, K. & Singh, S. (to appear). Broadcasting on [O, L]. Discrete applied math.Google Scholar
7.Weinstein, O. & Chlamtac, I. (1987). The wave expansion approach to broadcasting in multihop radio networks. IEEE INFOCOM 87. San Francisco, CA, pp. 874–881.Google Scholar