Title: On the power law relationship of the critical transmitting range and the number of nodes of ad hoc networks

Authors: Mun-Loong Kam, Gerard Leng

Addresses: Cooperative Systems Laboratory (Cosy-L), Department of Mechanical Engineering, National University of Singapore, Engineering Drive 117576, Singapore. ' Cooperative Systems Laboratory (Cosy-L), Department of Mechanical Engineering, National University of Singapore, Engineering Drive 117576, Singapore

Abstract: The relationship among connectivity probability, communication range and the number of nodes of an ad hoc network has been studied. A power law relationship of the form r = αN^−β is hypothesised to hold for the communication range (r) and the number of nodes (N), with α and β being functions of the connectivity probability of the network. Unlike the different forms of log relationships derived for different network settings, this power law relationship will be shown to hold for both static and mobile ad hoc network of various settings using extensive simulation data. The comparison between the commonly known log law and our power law will be made using the published simulation data for stationary network and network with random waypoint model mobility. We further hypothesise that the power law relationship between the communication range and the number of nodes holds across different network models. We propose to simplify and unify the research of this connectivity probability problem by focusing on the effect of different network models on the parameters (α and β) of the power law model.

Keywords: power law relationship; general property; critical transmitting range; static ad hoc networks; mobile ad hoc networks; MANETs; wireless networks; connectivity probability; communication range; nodes; mobile networks.

DOI: 10.1504/IJSNET.2010.033206

International Journal of Sensor Networks, 2010 Vol.7 No.4, pp.228 - 235

Published online: 13 May 2010 *

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