Quantile Approximation of the Erlang Distribution using Differential Evolution Algorithm

Erlang distribution is a particular case of the gamma distribution and is often used in modeling queues, traffic congestion in wireless sensor networks, cell residence duration and finding the optimal queueing model to reduce the probability of blocking. The application is limited because of the unavailability of closed-form expression for the quantile (inverse cumulative distribution) function of the distribution. The problem is primarily tackled using approximation since the inversion method cannot be applied. This paper extended a six parameter quantile model earlier proposed to the Nakagami distribution to the Erlang distributions. Consequently, the established relationship between the two distributions is now extended to their quantile functions. The quantile model was used to fit the machine (R software) values with their corresponding quartiles in two ways. Firstly, artificial neural network (ANN) was used to establish that a curve fitting can be achieved. Lastly, differential evolution (DE) algorithm was used to minimize the errors obtained from the curve fitting and hence estimate the values of the six parameters of the quantile model that will ensure the best possible fit, for different values of the parameters that characterize Erlang distribution. Hence, the problem is constrained optimization in nature and the DE algorithm was able to find the different values of the parameters of the quantile model. The simulation result corroborates theoretical findings. The work is a welcome result for the quest for a universal quantile model that can be applied to different distributions

A Monte Carlo localization method based on differential evolution optimization applied into economic forecasting in mobile wireless sensor networks

Abstract The localization of sensor node is an essential problem for many economic forecasting applications in wireless sensor networks. Considering that the mobile sensors change their locations frequently over time, Monte Carlo localization algorithm utilizes the moving characteristics of nodes and employs the probability distribution function (PDF) in the previous time slot to estimate the current location by using a weighted particle filter. However, it also has the problem of insufficient number of valid samples, which further affects the node’s localization accuracy. In this paper, differential evolution method is introduced into the Monte Carlo localization algorithm. The sample weight is taken as the objective function, and differential evolution algorithm is implemented in sample stage. Finally, the node position is estimated by making the sample close to the actual location of the node instead of being filtered out. The simulation results demonstrate that the proposed algorithm provides a better position estimation with less localization error