On Concurrent Events and Correctness in Stochastic Models

In performance / dependability modeling, it sometimes happens that two events are scheduled to occur at the same time. In this case, the modeler has two alternatives: specify an ordering, (perhaps deterministically or probabilistically), or leave the order unspecified. If the order is unspecified, it is assumed that the order does not matter, or that the events can happen concurrently (simultaneously). It is important to be able to express concurrency, but the ability to express concurrency may also lead to the specification of ambiguous models. There are a number of checks to determine whether models are or may be ambiguous (usually implying an incorrectly specified model) with different thresholds of ambiguity. We give a survey of a number of techniques, describing their relative usefulness and characteristics, and then provide the theoretical foundation for an efficient implementation of a particularly useful check called the well-specified check.