Ergodicity of hedging control policies in single-part multiple-state manufacturing systems

The Markov renewal viewpoint of single-part/multiple-state manufacturing systems under hedging control policies, subjected to a constant rate of demand for parts, is used to derive sufficient criteria to guarantee the ergodicity of the resulting parts surplus process. The criteria are simple and directly verifiable from an analysis of the Markov chain characterizing the dynamics of the discrete manufacturing system production state. A key intermediate result in reaching these criteria is a potentially very useful system of linear differential equations with boundary conditions which can be generalized to permit computation of moments of arbitrary order for sojourn times in the regions between successive hedging points in the parts surplus space