Spectral decomposition for a QS based delay model with Erlang and hyperexponential distributions

This article is devoted to the study and obtaining a closed-form solution for the average delay of claims in a queue for a QS formed by two flows with Erlang and hyperexponential distributions of the second order for time intervals. As is known, the Erlang distribution ensures the coefficient of variation of the arrival intervals is less than one, and the hyperexponential distribution is greater than one. It is also known that the main characteristic of the QS, the average delay, is related to these coefficients of variations by a quadratic dependence. Studies of G/G/1 systems in queuing theory are topical due to the fact that they are used in modeling data transmission systems for teletraffic analysis. To solve the problem, the method of spectral decomposition of the solution of the Lindley integral equation was used. The spectral decomposition for the system under consideration made it possible to obtain a closed-form solution for the average delay of requests in the queue. For the practical application of the results obtained, the method of moments is used.