Teletraffic models based on advanced queuing theory

In this paper, we present results on two classes of G/G/1 queuing systems (QS): system with delay and system with hyperexponential input distributions. The classes of these systems provide the interval variation coefficients between the arrival time and the service time which are both smaller and greater than 1 as a result, they cover the entire (0, ∞) interval. For obtaining the solution, the method of spectral solution expansion by Lindley integral equation is used. The choice of these probability distribution functions is justified by their simplicity and also by the fact that among the classes of distribution functions with coefficients of variation greater and smaller than 1, such as lognormal, Weibull, Gamma and the others, only hyperexponential and exponential distributions with delay allow to obtain an analytical solution. The exponential distribution with time delay gives the coefficient of variation c that is less than 1, and the hyperexponential distribution gives the coefficient that is greater than 1. Thus, a combination of the considered distributions allows to consider QS with coefficients of variation of input distributions in a wide range from 0 to ∞.