Hysteresis strategy for a single-channel system with a queue and repeated calls
DOI:
https://doi.org/10.17721/1812-5409.2025/2.27Keywords:
stochastic system, repeated calls, variable rate of external flow, stationary distribution, migration processAbstract
A Markov-type service system with repeated calls is considered. The system consists of one service device, and one place in the queue is provided. A hysteresis strategy is used to optimize the system operation. The main idea of this type of control is related to the dependence of the intensity of the input flow on the number of sources of repeated calls in the system. The operation of such a system is modeled by a three-dimensional migration process. The conditions for the existence of a stationary regime are established for it, and the probabilistic characteristics of the process are investigated. The research method is based on the approximation of the initial process by a process with a limited state space. Explicit formulas of the scalar type are found for the probabilistic characteristics of the process in the stationary regime. With this aim, the method of equalizing probability flows through the boundaries of regions that are chosen in a special way is used. To illustrate the obtained results, an example of calculating stationary probabilities is given.
Pages of the article in the issue: 174 - 181
Language of the article: Ukrainian
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Copyright (c) 2025 Igor Makushenko, Iryna Usar, Hanna Livinska
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