Stochastic Timed Automata

One of the simplest model classes of stochastic discrete event systems are stochastic timed automata, which are explained in this chapter. The states and state transitions of a discrete event system are explicitly modeled in an automaton. Their level of abstraction is thus identical to the actual set of reachable states and state transitions, which makes them easy to understand and use for simple systems. More complex behavior is however better expressed with one of the model classes that are covered later in this text. The only abstraction of an automaton is in the notion of events, which correspond to actions that may happen in several states. One event can thus lead to many state transitions in the full model.

An automaton is said to be deterministic or nondeterministic depending on whether there are events for which more than one associated state transition starts at one state. Standard automata describe states and state transitions without a notion of time. Delays of actions (interevent times) are associated to events and their associated state transitions in timed automata, for which the performance can then be evaluated. In a stochastic timed automaton, the interevent times are allowed to be random, and given by a probability distribution function.