Today, the practices for construction of mathematical models for service and methods for their study are based on classical works of Erlang, Khinchine, Palm, Pollaczek, Kendall, Gnedenko. In these works, initial characteristics and characteristics of interest are defined locally and refer to each single customer and to each instant of time. In this case the model doesn't take into account to the full extent control actions on an input flow, service times, a flow of refusals, a flow of serviced customers, and the queue discipline. In the this work a representation of real control processes in form of a Lyapunov – Yablonsky control system. A mathematical model of real queueing systems is determined with choice of strobing instants of time, choice of a nonlocal description of the input flows and saturation flows, choice of the set of the server states, control algorithm for conflicting flows of nonhomogeneous customers, a strategy of the mechanism for service and ques formation. This approach allows to solve nontraditional problems in analysis, synthesis, and optimization of concrete queueing control systems.

queuing theory, saturation flows, flows control algorithm, servicing mechanism strategy, quasi-regenerative flows, quasi-optimal control

Mathematical problems and theory of numerical methods