Modeling Energy for Wireless Sensor Networks with Heavy-Tailed Job Size Distributions
An important constraint in the wireless sensor network is the amount of energy available to each node. In an attempt to estimate the d energy consumption, an M / M / 1 queue model was proposed. In the M / M / 1 model, the packet length is assumed to have low variability and therefore service time is best modelled by the exponential distribution. However, recent studies have shown that computer system workloads follow heavy-tailed and highly variable packet sizes making the M / M / 1 queue model inaccurate. Therefore, we model energy consumption under heavy-tail distribution where packet sizes are highly variable as depicted in the Internet using M=G=1 queue model. The service time of packets in the M / G / 1 queue is modelled using Bounded Pareto, Lognormal, and Weibull distributions. The numerical results obtained from the derived models show that the energy consumption is higher under M / BoundedPareto / 1 than under M / M / 1 queue model. In addition, the energy consumption is higher under M / Weibull / 1 than under M / M / 1 queue model. However, the average energy consumption is lower under M / Lognormal / 1 than under M / M / 1 queue model. We also note that increase in the Coefficient of variability leads to increase in average energy consumption. Coefficient of variability is a standardized measure of dispersion of a probability distribution or frequency distribution. Coefficient of variability shows the extent of variability in relation to the mean of the population.