Queueing Systems with Unstable Service Units as Mathematical Models of Hybrid Energy Systems

The growing number of electronic devices and the development of distributed computing systems make the problem of energy shortages relevant. At the same time, there is a global trend towards a transition to renewable energy, which, although it contributes to the environmental stability of the world, such systems are less reliable and productive than fuel systems. In this way, hybrid energy systems combining two or more types of energy resources are becoming widespread. In the paper, the queueing theory approach is applied for the modelling of hybrid energy systems and evaluating their efficiency. As a model of hybrid systems combining two energy sources, we propose a queueing system with an unlimited number of servers and an additional unstable service unit. The two cases of the model are considered—a system with switching between two service units and a system with its joint operation. A non-stationary Poisson arrival process is proposed to model the flow of electricity requests that reflects the dynamics of electricity consumption over time. The multi-dimensional Markov process of the system states is studied, and some analytical expressions for the probability characteristics are presented. In addition, the simulation framework is developed. Numerical examples of generating electricity consumption volumes for different input parameters are presented.