Queuing systems with limited waiting times

The paper deals with analytical and simulation study of queueing systems of mixed type - with reduced waiting times. The aim of the study is to develop a methodological framework for the modeling and analysis of the results of the simulation and optimization of functioning of the considered queueing systems. Presents the state graph of the system that describes processes in terms of the patterns of death and reproduction, the formal dependence to determine the performance and efficiency of systems. In the study based on the methodology of identifying patterns of modeling and comparison of systems with unlimited queue systems in which a possible withdrawal requests from the queue when exceeding a critical timeout. The considered systems are not the simplest, are characterized by the aftereffect, so in the article and studied the error estimate of the approximate formulas used to calculate the performance of systems with non-Poisson flows. Basic theoretical and methodological principles formulated in the work tested and researched on analytical platform AnyLogic. The practical significance of the obtained results lies in the possibility of a priori analysis of the effectiveness of service systems in their design and the optimization of existing ones. Given the a posteriori error estimate calculations of the performance of the system depending on the number of applications in it. Studied applied system, which is a marine cargo terminal with several quays in the conditions when a court can prematurely leave the place without maintenance in excess of the maximum permissible waiting time.