Algorithm for constructing a system of kolmogorov equations for studying the transition regime of two-phase queuing systems with a large number of requests

This work is devoted to the development of the Kolmogorov differential equations system constructing algorithm for a single-line queuing system with a Poisson input and phase service. The case of two phase system and an arbitrary finite number of customers in the system is considered. The new functions that significantly simplify the Kolmogorov differential equations system constructing algorithm and the system infinitesimal matrix are introduced. A comparative analysis of the complexity of previous algorithms and the algorithm presented by the authors is carried out too. The use of this algorithm will allow in the future to obtain analytical and numerical solutions of the main performance characteristics of the M/PH/1/n QS with a large number of applications in the transient operation mode.