SPECIFIED DEMAND PATTERNS FOR FINITE MARKOV SYSTEMS IN DISCRETE AND CONTINUOUS TIME WITH ILLUSTRATIVE EXAMPLES

摘要

We consider systems whose time-dependent behaviour can be described by a Markov chain with a finite state space. There is a finite set of subsets of the state space given and every point in the time interval under consideration is associated with one of these subsets, thereby definig a demand (or usage) pattern. Closed form expressions are derived for the probability of a demand pattern being satisfied, in both, discrete and continuous time. Known reliability measures are identified as special cases. We illustrate the theory on two examples: the first is a system comprising three power transmission lines, the second is a small computer system consisting of four units, each in one of the states up or down. The demand patterns cover a four-week period.