Recursive Approach for Evaluation of Time Intervals between Transactions in Polling Procedure

An ergodic semi-Markov process with the structure represented by the full graph with loops, which simulates a digital control algorithm that generated transactions onto an object, is investigated. Elementary simplifications for reduction of semi-Markov processes are defined. Recursive procedure for reduction of initial semi-Markov process structure till the model, which includes selected states with its links only, is proposed. Formulae for recalculation of probabilities, weighted densities and expectations of time of switching to linked states are obtained. It is shown that recursive procedure may be used also for calculation of time expectation of return the process to one of selected states that simplified the task of evaluation of time intervals between transactions in polling procedure.