The paper proposes to study a mathematical model of a computing node in the form of an infinite queueing system with an input Markov modulated Poisson process. This correlated flow can model complex stochastic processes in a node, in which the rate of occurrence of arrivals depends on the state of the underlying process, which makes it useful taking into account the correlation between the moments of occurrence of tasks on the node. The service rate for each request depends on the number of requests in the system. The purpose of the study is to apply the asymptotic analysis method and obtain the Gaussian approximation of the probability distribution of the number of requests in the system.
Информационные технологии и математическое моделирование (ИТММ-2025) : материалы XXIV Международной конференции имени А. Ф. Терпугова, 20-25 октября 2025 г.. Томск, 2025. С. 304-309