A method of approximation of non-Markov controllable queueing processes

A Markov approximation method for non-Markov controllable queueing processes (NCQP) is put forward, the essence of which is that it involves developing a certain equivalent Markov controllable process with a finite number of states and controls, synthesizing numerically an optimal strategy of situation control of this process, and using this strategy for control of the desired NCQP. A class of NCQPs with limited aftereffects is described, the study of which can be made by the suggested approximation method. General properties of the Markov approximation are clarified and an example of this type of approximation is given for the investigation of a non-Markov controllable queueing system. Results of the experiment are offered, including results of the comparative analysis of the suggested Markov approximation method for NCQPs and the known method of timing.