A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns

A system consisting of supply and demand is considered in this paper. Both the supply patterns and demand patterns are random. Thus, both the supply and the demand are modeled by Markov processes. The performance measure considered here is the probability that the demand is met by the supply during given time interval image. A close form expression for the performance measure is obtained by using aggregated stochastic process theory and Kronecker matrix operations. In the meanwhile, the performance measures in a general interval image and multiple intervals image have also been given. Finally, a numerical example is given to illustrate the results obtained in this paper.