Analysis of dual H2/M/1 and M/H2/1 systems

In this article we present the comparative results of authors' publications on dual H2/M/1 and M/H2/1 systems with hyperexponential input distributions of the second order. By Kendall's definition, these systems belong to the classes G/M/1 and M/G/1, respectively. The H2 distribution includes 3 unknown parameters and can therefore be approximated at the level of the first three moments. The solution for the average waiting time for the H2/M/1 system depends on the three moments of the H2 distribution. The average waiting time for the system M/H2/1 does not depend on the 3rd moment of the H2 distribution but depends only on the first two moments and completely coincides with the Pollaczek-Khinchine formula. This defines the qualitative difference between the dual systems in question: H2/M/1 and M/H2/1. These systems are compared by the average waiting time in the queue for the same system load. These data also vary. The solution for the average waiting time in the queue for both systems is based on the spectral decomposition method of the integral Lindley equation solution.