student from 01.01.2024 until now
Kazan National Research Technological University (Computer Science and Applied Mathematics)
student from 01.01.2024 until now
Russian Federation
student from 01.01.2024 until now
Kazan, Russian Federation
This study presents the results of a comparative analysis of the accuracy of analytical and mathematical methods and simulation modeling in assessing the overall performance of queuing systems with a heterogeneous structure of service devices. Multi-channel fault management systems characterized by unequal service channels are considered, provided that applications are received in accordance with the Poisson process and the exponential law of service duration distribution. Special attention is paid to comparing the computational reliability, stability, and applicability of analytical and simulation approaches in the study of probabilistic and temporal characteristics of the studied systems. The article discusses the functioning processes of two-channel and three-channel systems with varying channel service rates. Systems of Kolmogorov equations are used to analytically describe the states of the systems. Simulation modeling is implemented using three different tools: AnyLogic and GPSS World specialized environments, as well as the Engee dynamic modeling environment. The paper examines ways of distributing incoming requests between service channels. An equally probable distribution of applications is considered, as well as a distribution that takes into account the intensity of channel maintenance and their throughput. In the course of the study, a series of computational experiments were conducted at different values of the intensity of the input flow of applications, which made it possible to assess the impact of the load on the performance of the systems. For two-channel and three-channel CFOs, the results of analytical calculations and simulation experiments were compared. The probability of a free system state (P0) and the probability of a denial of service (Potc) were selected as the key output characteristics for comparing methods. The results obtained showed a high degree of consistency between analytical calculations and simulation results in all considered programs. It is established that the largest deviations are observed at low values of the input flow intensity and are due to the statistical nature of the simulation, the finite time of the experiment and the peculiarities of the distribution of applications between the service channels. The analysis confirmed the effectiveness of using modern simulation tools to study complex CFR with heterogeneous channel characteristics. The results obtained demonstrate the possibility of using AnyLogic, GPSS World, and Engee in the design, analysis, and optimization of multichannel service systems of varying complexity.
QUEUING SYSTEMS (QMS), UNEQUAL CHANNELS, SIMULATION MODELING, KOLMOGOROV EQUATIONS, ANYLOGIC, GPSS WORLD, ENGEE
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