Queueing system HE2/HE2/1

The article is devoted to the analysis of the queuing system HE2/HE2/1 type G/G/1 with hyper Erlangen input distributions of the second order. The goal is to obtain a solution for the average waiting time for requests in the queue. To achieve it, the classical method of spectral decomposition of the solution of Lindley integral equation is used. For the practical application of the results obtained, the method of moments is used. It turns out that the hyper Erlangen distribution law HE2, same as the hyperexponential law H2, which has three parameters, can be defined by both the first two moments and the first three moments. The article proposes an approximation mechanism for the hyper Erlangen law of arbitrary distributions using the well-known method of moments. The choice of such a law of probability distribution is due to the fact that its coefficient of variation is larger and covers a wider range than the hyperexponential distribution law, for which the coefficient of variation is greater than one. The method of spectral decomposition of the solution of the Lindley integral equation for the QS HE2/HE2/1 allows one to obtain a closed-form solution. Thus, the system under consideration allows working with coefficients of variations in the intake intervals and service time in the range ( , ∞), which expands the field of application of QS. The resulting formula for the average waiting time for the HE2/HE2/1 system complements and extends the well-known formula for the average waiting time in the G/G/1 system with arbitrary laws of the distribution of input flow intervals and service time.