Several new performance measures 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. Both the state space of the supply and the demand are not binary (on/off), and they are partitioned into several ‘levels’ of functionality. The performance measure considered here is the probability that the demand is met by the corresponding ‘level’ supply. A closed form expression for the performance measure is obtained by using aggregated stochastic process theory and Kronecker matrix operations. In the meanwhile, the probability density function of a cycle time and the customer's demand can be met in this cycle has also been given. Finally, a numerical example is given to illustrate the results obtained in this paper.