Normal Distribution on Energy Saving Problem for the Wireless Sensor Network Life on the Vacation Period

Based on math operations, we can do some analytic approaches for the energy saving for the WSN life. We will study the vacation period time using numerical methods for studding the energy saving mechanism in analytic models. Several research papers have reported that the normal distribution of a random variable has an enormous contribution in analyzing and comparing the data with each other, making the process easier according to methods used or observing the tendencies of numerous occurrences in life applications. This paper focuses on analyzing two problems: the first one is the normal distribution and its special cases by solving real problems of WSN node operations and the second one is the application of standard normal distribution relate to saving energy during vacation time in a certain time interval. The goal of our work is to obtain the appropriate algorithm to minimize the risk of data loss during the network vacation period, which is associated with the organization of network node structures after this period time, and to maximize the battery life of individual sensors. For that, we will use math methods and based on probability distribution theory, we derive some distributions of the processing period duration from an arbitrary fixed time up to a variable time t. The analytic approach based on the conception of Laplace transform and the Lagrange method performs better than the previous results. We continue by examining them through detailed calculations and graphs. We compare the predicted energy saving and the average real energy.