Simplified calculation of first-arrival time probability density function value in Markov chain
Yan Hua · Computer-aided engineering · 2006
To simplify the calculation of the first-arrival time probability density function value in the Markov chain, a matrix portrayal of graph is constructed to show the oriented graph produced which vividly obtain all paths from one condition to another at first time. The question is transformed to accumulate all probability values which satisfy the situation from one condition to another at first time. The first-arrival time probability density function value from one condition to another at first time is calculated through one-step stationary transition probability which is provided by the question. This method not only calculates the first-arrival time probability density function value from one condition to another with direct-viewing, thus omits memorizing complex general formula, but also omits the computation work about calculating n-step stationary transition probability again on the basis of one-step stationary transition probability for calculating the function value. Particularly, in the case of n being relatively small, the manual calculation by this method is faster and easier to be understood than by formula method, therefore reflects an obvious advantage.