Expected reachability for piecewise deterministic linear Markov processes

In this paper, we define expected reachability and reachable set for the class of piecewise linear deterministic systems. We develop formulas for calculating the reachable set and analyze its variance and discuss how to implement these formulas numerically. We also discuss a sufficient condition for the system to be completely reachable. Our definition is motivated by problems in the field of manufacturing production control and examples are given to show the usefulness of these concepts.