Analysis of new queueing system E2/E2/1 with delay

In queuing theory, the G/G/1 systems are especially relevant in view of the fact that until now there is no solution in the final form for the general case. This article presents the results of queuing systems (QS) G/G/1: system E2/E2/1 with Erlang input distributions of the second order and the system with delay in time. We choose the second-order Erlang distributions as an input for the system considered, which are shifted to the right from the zero point. For such distribution laws, the method of spectral decomposition allows one to obtain a solution in closed form. It is shown that in such a system with delay, the average waiting time of calls in queue is less than in the usual system. Which is explained by the fact that the time shift operation reduces the value of variation coefficients of the intervals between the receipts and the service time, and as it is known from queuing theory, the average requirements waiting time is related to these variation coefficients by a quadratic dependence. The E2/E2/1 system works only for variation coefficients equal to , and the system c allows us to work with the variation coefficients of the arrival and service intervals from the interval (0, ), which extends the scope of these systems. To derive solutions, the classical method of spectral decomposition of the Lindley's integral equation solution is used.