In practice, systems always operate in environments which are constantly plagued by uncertainty. This is especially true in dealing with DES, which, by their nature, often involve unpredictable human actions and machine failures. The process of resource sharing (which provides an important motivation for studying DES) is inherently characterized by such unpredictability: changing user demand, computer breakdowns, inconsistencies in human decision making, etc. While the untimed (or logical) models considered in Chaps. 2–4 do account for “all possible behaviors” of the system, their use is limited to logical (or qualitative) performance objectives.