Does the Assumption of Exponential Arrival Distributions in Wireless Sensor Networks Hold?

Abstract

Wireless Sensor Networks have seen a tremendous growth in various application areas despite prominent performance and availability challenges. One of the common configurations to prolong the lifetime and deal with the path loss phenomena is having a multi-hop set-up with clusters and cluster heads to relay the information. 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 wireless sensor networks 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 wireless sensor networks holds only for a few cases. There are both theoretically known such as Gamma, Log-normal and Mixed Log-Normal of arrival distributions and theoretically unknown such as non-Exponential and Mixed cases of arrival in wireless sensor networks. The work is further extended to understand the effect of delay on inter-arrival time distributions based on the type of medium access control used in wireless sensor networks.