Packet Arrival Analysis in Wireless Sensor Networks

Wireless Sensor Networks have seen a tremendous growth in various application areas including health care, envi- ronmental monitoring, security, and military purposes despite prominent performance and availability challenges. In such applications, clustering plays an important role in enhancement of the life span and scalability of the network. 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, such plots may lead to incorrect conclusions. 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. Statistical analysis concluded that the general assumption of Empirical exponential arrival distribution in 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 net- works. 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.