Distributed sensor networks have been discussed for more than 30 years, but the vision of Wireless Sensor Networks (WSNs) has been brought into reality only by the rapid advancements in the areas of sensor design, information technologies, and wireless networks that have paved the way for the proliferation of WSNs. The unique characteristics of sensor networks introduce new challenges, amongst which prolonging the sensor lifetime is the most important. WSNs have seen a tremendous growth in various application areas including health care, environmental monitoring, security, and military purposes despite prominent performance and availability challenges. Clustering plays an important role in enhancement of the life span and scalability of the network, in such applications. Although researchers continue to address these grand challenges, the type of distributions for arrivals at the cluster head and intermediary routing nodes is still an interesting area of investigation. Modelling the behaviour of the networks becomes essential for estimating the performance metrics and further lead to decisions for improving the network performance, hence highlighting the importance of identifying the type of inter-arrival distributions at the cluster head. In this paper, we present extensive discussions on the assumptions of exponential distributions in WSNs, and present numerical results based on Q-Q plots for estimating the arrival distributions. The work is further extended to understand the impact of end-to-end delay and its effect on inter-arrival time distributions, based on the type of medium access control used in WSNs. Future work is also presented on the grounds that such comparisons based on simple eye checks are insufficient. Since in many cases such plots may lead to incorrect conclusions, demanding the necessity for validating the types of distributions. Statistical analysis is necessary to estimate and validate the empirical distributions of the arrivals in WSNs.