Bratiychuk A. Investigation of the queueing systems with finite waiting space

The thesis deals with queueing systems with Poisson input, general service time distribution and limited queue. Group arrival of the customers is allowed. A generalization of these systems by adding some resume level for the input stream are considered as well. To study these systems the modification of the Koroluyk's potential methods is proposed. The method proposed allowed not only to obtain the formulae for Laplace transforms functions of the functionals we are interested in by the standard approach but enables to write down the computational algorithms and programs for ergodic characteristics of the systems which have the essential advantages over known ones. These algorithms are used to study the optimization problems and to synthesize the queueing systems with characteristics given in advance. The original formulae for Laplace transform of the main functionals are obtained, and the asymptotic analysis of their distributions are performed as the queue length tends to infinity. For the systems with a resume level the limit theorems for busy period and the number of customers served during this period are obtained.