A compositional approach to the simulation of queuing systems with random parameters

A general approach to modeling random service processes under conditions of disturbances and uncertainty of the initial data is substantiated. A compositional approach to constructing simulation models of queuing with parametric uncertainty based on phase-type distributions and phase functions is proposed. The calculation and comparison of the characteristics of the developed simulation models with analytical solutions were carried out to confirm their effectiveness and accuracy. The problems of uncertainty of the initial data and their impact on the modeling of service systems are highlighted. The importance of taking into account parametric uncertainty in simulation models is emphasized in order to increase their adequacy and applicability in practice. The study includes a description of a general approach to modeling random service processes with uncertainty, as well as methodological foundations for the application of phase distributions and functions in compositional modeling. Four classes of service models are considered, differing in the type of integral core and phase function, which makes it possible to implement a variety of random service processes, taking into account their characteristics and conditions of their occurrence. The analysis of a model with an exponential integral core and various types of phase functions is carried out, which demonstrates the flexibility and wide possibilities of the proposed compositional approach to the study and modeling of service systems. The results of simulation modeling are presented, confirming analytical studies and showing the applicability and effectiveness of the developed approach in the construction and analysis of models of service systems with random parameters. The practical significance of the compositional method for the design and modernization of information and computing systems at various stages of their development, taking into account the uncertainty of the initial data, is noted. The work is focused on the development of simulation methods for queuing systems and opens up new prospects for their research and optimization in conditions of uncertainty of initial parameters.