Computing non-Markovian queues using hyperexponential distributions

The purpose of the monograph is to analyze the peculiarities of applying hyperexponential distributions of order k (k=2,¿,6) with both real and paradoxical and complex-valued parameters for the approximate calculation of steady-state distributions of the number of customers in non-Markovian queueing systems by the fictitious phase method. We considered not only open, but also closed queueing systems, as well as single-channel systems with a threshold change of service times and with changes of service times depending on the number of customers in the system. We check the accuracy of the obtained approximate distributions of the number of customers in the queueing system using the potentials method (for single-channel systems) and the GPSS World simulation system. For systems with the gamma distributions and Weibull distributions, the conditions on the values of the variation coefficients are indicated, for which the best accuracy of calculating the steady-state probabilities is achieved compared with the results of simulation modeling. The book is intended for researchers and students engaged in simulation of queueing systems.