Delay model based on shifted hyperexponential and Erlang distributions

This article is devoted to the derivation of results for the average delay of requests in the queue for a queuing system formed by two flows with the laws of interval distributions in the form of second-order hyperexponential and Erlang distributions shifted to the right. In queuing theory, studies of G/G/1 systems are relevant due to the fact that there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In this case, the use of the hyperexponential distribution law ensures the coefficient of variation of the input flow intervals is large units, and the Erlang distribution is less than one. To solve the problem posed, the method of spectral decomposition of the solution of the integral Lindley equation was used, which plays an important role in the queueing theory. This method made it possible to obtain a solution for the average delay of requests in the queue for the system under consideration in a closed form. As is known, the remaining characteristics of the queuing system are derived from the average delay of requests.