Teletrafic models based on dual systems with hyperexponential and erlang distributions

This paper presents the results of studies on queuing systems (QS) H₂/E₂/1 and E₂/H₂/1 with second-order hyperexponential and Erlang input distributions. Considered QS are of type G/G/1. The use of these higher-order distribution laws is hindered by increasing computational complexity. For such second-order distribution laws, the classical method of spectral decomposition of the solution of the Lindley integral equation for G/G/1 systems makes it possible to obtain a solution in closed form. The article presents the obtained spectral decompositions of the solution of the Lindley integral equation for the considered systems and the 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. For practical application of the results obtained, the probability theory moments method is used. Systems of the G/G/1 type are widely used in the theory of teletraffic when modeling data transmission systems. For example, according to the average waiting time in the queue, packet delays in packet switching networks are estimated when they are modeled using QS.