Optimizing H2/M/1 system characteristics calculation

Currently, there are no analytical methods for precisely determining the characteristics of queuing systems G/M/1 or G/M/m, and this lowers the degree of adequacy of stochastic network models to real computer and telecommunications networks and the quality of design decisions. This article shows the comparative results presented in various publications devoted to the calculation of the average waiting time in queuing systems G/M/1, in particular queuing system with hyper-exponential arrival rate. The results under consideration were obtained by completely different approaches, but the final calculated results are completely identical. These approaches have certain advantages to each other. Using of the analogues simplifies calculation of the characteristics for the system considered, and the author's approach expands the possibilities of calculating characteristics in terms of determining higher-order moments for the waiting time, which allows extracting information needed to calculate a jitter, for example. Considering the definition of jitter in telecommunications as the spread of the waiting time from its average value, knowledge of higher order moments for the waiting time makes it possible to obtain the jitter value via calculating the variance, i.e. second moment of random waiting time.