Numerical-analytical delay model based on QS with operational shift of distribution principles

This article demonstrates results for a queuing system formed by right-shifting an Erlang distribution and a second-order hyperexponential distribution. As is known, the first distribution provides a coefficient of variation less than one, and the second one - more than one. From the general queuing theory, it is known that the average delay of requests in the queue in the QS G/G/1 is related to the coefficients of variation of arrival intervals and service times by a quadratic dependence, and the system we are considering belongs precisely to this type. An operational shift in the distribution laws leads to a multiple reduction in delay compared to a conventional system, and this value depends on the value of the shift parameter. To construct a mathematical model of the delay, the method of spectral solution of the Lindley integral equation for the system under consideration was applied. For the practical application of the obtained results, the standard method of oprobability theory moments is used. The obtained results of numerical and analytical modeling in Mathcad clearly confirm the adequacy of the proposed mathematical delay model.