Title: Does the assumption of exponential arrival distributions in wireless sensor networks hold?

Authors: Krishna Doddapaneni; Ali Tasiran; Fredrick A. Omondi; Enver Ever; Purav Shah; Leonardo Mostarda; Orhan Gemikonakli

Addresses: Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA ' School of Science and Technology, Middlesex University, London NW44BT, UK; Economics Program, Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt, Mersin 10, Turkey ' School of Science and Technology, Middlesex University, London NW44BT, UK ' Computer Engineering Program, Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt, Mersin 10, Turkey ' School of Science and Technology, Middlesex University, London NW44BT, UK ' Computer Science Department, Camerino University, 62032 Camerino MC, Italy ' School of Science and Technology, Middlesex University, London NW44BT, UK

Abstract: Wireless sensor networks (WSNs) have seen a tremendous growth in various application areas despite prominent performance and availability challenges. Although researchers continue to address these challenges, the type of distributions for arrivals at the cluster head and intermediary routing nodes is still an interesting area of investigation. The general practice in published works is to compare an empirical exponential arrival distribution of WSNs with a theoretical exponential distribution in a Q-Q plot diagram. In this paper, we show that such comparisons based on simple eye checks are not sufficient since, in many cases, incorrect conclusions may be drawn from such plots. After estimating the maximum likelihood parameters of empirical distributions, we generate theoretical distributions based on the estimated parameters. By conducting Kolmogorov-Smirnov test statistics for each generated inter-arrival time distributions, we find out, if it is possible to represent the traffic into the cluster head by using theoretical distribution. Empirical exponential arrival distribution assumption of WSNs holds only for a few cases. The work is further extended to understand the effect of delay on inter-arrival time distributions based on the type of medium access control (MAC) used in WSNs.

Keywords: WSNs; wireless sensor networks; performance; maximum-likelihood estimates of empirical distributions; Q-Q plots; P-values; Kolmogorov-Smirnov test statistics; theoretical and empirical densities; cumulative distribution functions.

DOI: 10.1504/IJSNET.2018.089258

International Journal of Sensor Networks, 2018 Vol.26 No.2, pp.81 - 100

Received: 28 Nov 2015
Accepted: 15 Jul 2016
Published online: 11 Jan 2018 *

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