Model-Based Testing for General Stochastic Time

Many systems are inherently stochastic: they interact with unpredictable environments or use randomised algorithms. Then classical model-based testing is insufficient: it only covers functional correctness. In this paper, we present a new model-based testing framework that additionally covers the stochastic aspects in hard and soft real-time systems. Using the theory of stochastic automata for specifications, test cases and a formal notion of conformance, it provides clean mechanisms to represent underspecification, randomisation, and stochastic timing. Supporting arbitrary continuous and discrete probability distributions, the framework generalises previous work based on purely Markovian models. We cleanly define its theoretical foundations, and then outline a practical algorithm for statistical conformance testing based on the Kolmogorov-Smirnov test. We exemplify the framework’s capabilities and tradeoffs by testing timing aspects of the Bluetooth device discovery protocol.