Abstract:
Background and Objective: Previous attempts to estimate the delay and energy consumption in wireless sensor networks employed an M/M/1 queue model. In the M/M/1 queue model, the packet length is assumed to have low variability in packet sizes and therefore,service time is best modeled by the exponential distribution. The objective of this study was to estimate the delay and energy consumption for wireless sensor networks with high coefficient of variability. Methodology: To overcome the weaknesses of M/M/1 queue model, this study proposed to model delay and energy consumption under heavy-tail distribution where packet sizes was highly variable as depicted in the Internet using M/G/1 queue model. The service time of packets in the M/G/1 queue was modeled using Bounded Pareto, Lognormal and Weibull distributions. Bounded Pareto, Lognormal and Weibull distributions that depict the heavy-tailed distributions. The coefficient of variation represents the ratio of the standard deviation to the mean and it is a useful statistic for comparing the degree of variation. Results: The numerical results obtained from the derived models show that the average waiting time and energy consumption is higher under the M/G/1 (where G represents Bounded Pareto and Weibull distributions) than under M/M/1 queue model.However, the average waiting time and energy consumption was lower under M/Lognormal/1 than under M/M/1 queue model. It was also observed that increase in the coefficient of variability leads to increase in average waiting time and energy consumption. Conclusion:The M/M/1 queue model under estimates delay and energy consumption for wireless sensor networks with high coefficient of variability.
