Service facilities with Markovian demand and deterministic supply with an application in repair modelling

Recent research by the author was concerned with systems modelled by two processes, the ‘supply’ process and the ‘demand’ process. The systems modelled thereby were such that the goods produced were not storable and were lost if not consumed immediately. In the present paper, we continue this earlier research, now assuming that supply is deterministic and demand is modelled by an irreducible Markov process with a finite, partitioned state space. Combining an earlier result with ‘propositional calculus’, a closed-form expression is obtained for the probability that demand will be met by supply during the first k supply periods. As an application, two repair disciplines for a small computer network will be examined. The computational tool used is SCILAB, a free numerical package run on LINUX.