Simulation of teletrafc based on E2/HE2/1 system

This article presents the results of deriving the formula for the average waiting time for the queuing system E2/HE2/1 with second-order Erlang and hyper-Erlang input distributions. By the definition of Kendall, this system belongs to the class G/G/1 with arbitrary laws of distribution of intervals of the input stream and service time. In queuing theory, studies of such systems are particularly relevant because it is impossible to find a solution for the average waiting time in the queue in the final form for the general case. For the system under consideration, such a solution can be obtained in closed form based on the classical method of spectral decomposition of the solution of the Lindley integral equation for systems of type G/G/1. Using higher-order Erlang and hyper-Erlang distributions is difficult to derive a solution for the average latency due to increasing computational complexity. The article presents the obtained spectral decomposition of the solution of the Lindley integral equation for the system under consideration and the calculation formula for the average waiting time in the queue. The adequacy of the results is confirmed by the correct use of the classical method of spectral decomposition and the results of numerical simulation. The E2/HE2/1 system is applicable when the coefficient of variation of the intervals of receipt is equal to 1/ 2 and the coefficient of variation of the service time is greater 1/ 2. For practical application of the results obtained, the probability method moments method is used. The results of numerical modeling in the Mathcad package unambiguously confirm the fact of the queuing theory that the average waiting time is related to the coefficients of variation of the intervals of arrival and service time by a quadratic dependence