Investigation of the Asymptotic Behavior of a Multichannel Queueing System with Different Types of Applications

In this paper, the object of the study is a multi-channel Queuing system with different types of applications and an unlimited number of waiting places. The incoming flow is Poisson and the service time is represented by a mixture of exponential distributions. The aim of the work is to study the asymptotic behavior of this Queuing system. In the process of work, the limiting behavior of the system was studied by describing and studying the analytical model and building a simulation model of the system. A computer program in Python that simulates the functioning of the system for the calculation of the stationary distribution was created. As a result of the work done, the values of limit probabilities for specific numerical values were found, and then comparative analysis of the obtained characteristics for each model was performed. The novelty of this work lies in the fact that the number of service devices and the number of types of applications are not fixed and a model is built that works for any set of incoming parameters. The constructed simulation model is of a general character and can be used in various industries and enterprises associated with Queuing systems.