Approximation of input distributions for queuing system with hyper-exponential arrival time

Here it is shown that using queuing system with hyper-exponential distributions of arrival time and service time both of them can be approximated at the level of first two and three moments. Hyper-exponential distribution with two terms has coefficient of variation more than 1, so using it for approximation of any arbitrary heavy-tailed distribution is possible. Our results show that increasing third moment leads to decreasing average waiting time in queue in queuing system with fixed two first moments of distributions of arrival time and service time and the same load on the system. It turns out a significant impact of the third moment.