Towards testing stochastic timed systems

In this paper we present a first approach to the definition of conformance testing relations for systems presenting stochastic timed behavior. By stochastic time we mean that the probability of performing an event may vary according to the elapsed time. In particular, we will consider delays specified by means of random variables. In order to define our formal model, we will provide a stochastic extension of the notion of finite state machine. We will give a first implementation relation and we will discuss its practical drawbacks. That is, we will show that this relation cannot be appropriately checked under a black/grey-box testing methodology. We will also present other alternative implementation relations that can be checked up to a certain degree of confidence. We will define test cases and how they are applied to implementations. Finally, we will give a test generation algorithm providing complete, up to a degree of confidence, test suites.