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The rather simple method of calculation of electronic and gas temperature in the channel of arc of plasma generator is offered. This method is based on self-consistent two-temperature channel model of an electric arc. The method proposed enables to obtain radial allocation of gas and electronic temperatures in a non-conducting zone of an constant current arc, for prescribed parameters of discharge (current intensity and power of the discharge), with enough good precision. The results obtained can be used in model and engineering calculations to estimate gas and electronic temperatures in the channel of an arc plasma generator.

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The problem of various types of queues arising in queuing systems is considered in the paper. The concept of a physical queue is introduced; universal mathematical formulas of the first and second moments of main discrete and continuous random variables characterizing behavior of physical queues for various models of mixed type queuing systems are obtained.

The paper considers the formal theoretical bases of the analytical, simulation and optimization simulating of multi-channel queuing systems with waiting (with the unlimited and limited queue). The research is based on the use as an analytical platform of the simulation environment AnyLogic, which allows us to carry out simulation and optimization experiments, as well as perform parametric analysis of solutions and studies on sensitivity. Practical approbation of models is based on solving and researching a wide range of tasks on simulating queuing systems with an expectation from different subject areas. The basis of the methodology used for modeling and optimization is the provision of using as an optimization criterion (objective function) the total reduced costs in both service channels and queue losses. The research is aimed at reviewing and analyzing queuing systems with various event flows in the AnyLogic simulation environment.

The paper presents a mathematical model of an open multi-channel queuing system having m service facilities of identical efficiency with exponentially distributed service time. The input stream of Poisson character includes demands of different types arriving from an arbitrary quantity of sources h and having various size-limited queues, at the same time intervals between the nearest-neighbor limits are equal to the unit everywhere. General mathematical formulae for probabilistic characteristics, as well as for the first and second moments of numerical characteristics specifying the quality of service in a steady-state mode of work have been obtained.