Accurate Modelling of IoT Data Traffic Based on Weighted Sum of Distributions

Abstract

This work proposes a novel mathematical approach to accurately model data traffic for the Internet of Things (IoT). Most of the conventional results on statistical data traffic models for IoT are based on the underlying assumption that the data generation follows standard Poisson or Exponential distribution which lacks experimental validation. However, in some of the use case applications a single statistical distribution is not adequate to provide the best fit for the inter-arrival time of the data packets generation. Based on the real data collected for over 10 weeks using our customized experimental IoT prototype for smart home application, in this paper we have established this very fact, citing barometric air pressure as an example. The statistical distribution of the inter-arrival time between the data packets for a specified barometric pressure fluctuation threshold is initially determined by approximating the best-fit with a set of standard classical distributions. The goodness-of-fit with the empirical data is numerically quantified using Kolmogorov-Smirnov (KS) Test. Furthermore, it is observed that any single standard distribution is unable to provide a good fit which is at least less than 10%. Therefore, a novel weighted distribution scheme is proposed that could provide an acceptable fit. The weighing factor including the location, scaling and weighing parameters of the best fitting distribution are estimated and analyzed. The distribution parameters are finally expressed as a function of the differential pressure value that can be used for different theoretical analysis and network optimization.