Approximating log-normally distributed secondary service time by hyper-exponential distribution for the analytical performance evaluation of cognitive radio networks

Abstract

In this paper, hyper-exponential distribution is proposed to approximate log-normally distributed secondary service time in a cognitive radio network (CRN). Hyper-exponential distributions of different orders (i.e., number of phases) are considered. Both moment matching and expectation maximization algorithm are employed and evaluated to determine the parameters of the hyper-exponential distributions that provides the best fit to the corresponding log-normal ones. A general teletraffic analysis is developed for the performance evaluation of the CRN considering an arbitrary order of the hyper-exponential distribution. The performance of the CRN is evaluated in terms of the new call blocking and forced termination probabilities of secondary users. Numerical results are obtained for both different ratios (acceleration factor) of the mean service times of PUs and SUs and different values of the number of phases of the hyper-exponential distribution. Numerical results show that, except for small values of the acceleration factor, the values of the different performance metrics obtained considering an n-th order hyper-exponential distribution become closer to those obtained by discrete event computer simulation (where the log-normal distribution is used to model the secondary service time) as n increases. For small values of the acceleration factor, the different performance metrics are insensitive to the probability distribution beyond the mean of the secondary service time.