Statistical integration of Erlang’s equations

Establishing analytical description of a queueing system is in the form of a system of first-order differential equations. That system can be very large, even unlimited. There are two commonly used methods of solving this system: analytical and numerical. Both are exact and reliable, but also very complicated. There is also the third solution method that can be realized by mathematical statistics. Statistical samples can be obtained by the Monte Carlo simulation, but well-known problems of accuracy and confidence of simulation results must be solved first. Motivation for this study comes from limitations of the classical queueing theory applied to military queueing systems.