Features of application of hyperexponential and hypererlangian input distributions in queueing systems

It has been proposed to use two distribution laws of a fairly general form as input distributions for describing queuing systems: hyperexponential and hyperelangian with a wide range of variation coefficients. The main characteristic feature of these laws of distributions is revealed, showing that they can unambiguously be described both by the first two moments and by three moments. The mechanism for their approximation is proposed using the well-known method of moments using both the first two moments and the first three moments. The use of these laws of distributions in the queuing theory extends and complements the well-known incomplete formula for the average waiting time for queuing systems with arbitrary laws of intervals distribution of input requirements and service time. The results obtained are important for modern teletraffic theory.