A Markov chain model for system forecast and evaluation

Abstract

In order to forecast and evaluate a system more reasonably, this paper establishes a mathematical model, based on the theory that the finite irreducible aperiodic homogeneous Markov chain has one and only stationary distribution. At first, calculates the proportions of every sort of members in a system, as the initial distribution. After one unit of time, ciphers the system's state distribution again. According to the two different state distributions, the transition probability matrix can be got through cyphering. Then we can compute the final state distribution of the system when it becomes stable, using the properties of homogeneous Markov chain. So the system can be predicted. In addition we illustrate the application of this model through an example. After verification, the model is more objective and appropriate than the traditional methods.