Stochastic Timed Automata
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 Chapters 2 to 4 do account for “all possible behaviors” of the system, their use is limited to logical (or qualitative) performance objectives. Deterministic timed models of the type considered in Chapter 5 certainly contribute to our basic understanding of some quantitative properties of the dynamic behavior of a system (for instance, the periodic behavior of systems that can be modeled as marked graphs). But their use is limited since models with deterministic clock structures only capture a single timed string of events (or states), or, in other words, a single sample path of the system. If we are to develop either descriptive or prescriptive techniques for evaluating performance and for “optimally” controlling timed DES with respect to quantitative performance measures and in the presence of uncertainty, more refined models that incorporate stochastic elements are required.
KeywordsService Time Poisson Process Queue Length Sample Path Interarrival Time
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