stochastic system with repeated calls, service process, stationary probabilities, hysteresis strategy, stationary states, optimization
Abstract
The paper considers the problem of optimal control of the input flow intensity for multi-channel systems with a single retry attempt. This study is extremely relevant for modern telecommunication networks and cloud services, where dynamic load fluctuations require adaptive resource control mechanisms to ensure high-quality service. The focus is on the analysis and formalisation of the hysteresis control strategy, which is characterised by delay zones during mode switching. This approach stabilises system operation under heavy load conditions and avoiding frequent switching between operating modes. With this strategy, the service process is simulated using a three-dimensional continuous-time Markov chain. The complexity of choosing a research method depends significantly on the number of service devices, the number of repeated attempts, and the control strategy. The situation is complicated by the fact that the phase space of the multi-dimensional service process is unlimited, and special approaches should be developed for its analysis. Therefore, to find stationary probabilities, the method of approximation of the system by the corresponding system with a finite phase space was used, and stationary probabilities were constructed in vector-matrix form. It is assumed that the stationary probabilities of the truncated model approximate those of the model with an unlimited phase space, since the corresponding service processes are migration processes. An optimisation problem aimed at maximising the system's quality is formulated and solved. The simulation results confirm the effectiveness and economic feasibility of hysteresis strategies compared to conventional approaches, making them a promising tool for controlling input flows.
Author Biography
O.V. Pryshchepa, National University of Water and Environmental Engineering, Rivne
