Imitation modeling of semi-markov processesin systems with discrete states and continuous time

Abstract

The problem of constructing a simulation model for the operation of complex systems, built on a block-modular principle, in which two-dimensional semi-Markov processes take place, has been solved. These processes determine the sequence of change of discrete states that characterize partial or complete loss of the functionality of the systems. The state changing process is nested with respect to the process that forms the time the system is in the states. The flows of events that provide for the change of states and determine the time the system is in the states have arbitrary probability distributions. The simulation results are estimates of stationary probabilities of states. Improving the accuracy of probability estimates is provided by their recurrent averaging over an increasing number of model realizations. This allows the use of simulation models to determine the characteristics of systems when their parameters change. The correctness of the simulation model is confirmed by comparing the results of simulation with the results of calculations using analytical formulas. The example shows that the simulation model allows you to get results with the same accuracy is much easier than using calculations using analytical formulas. Possible ways of using probability estimates are help in making decisions about the compliance of systems with their requirements, checking the correctness of analytical models.