Further steps towards efficient runtime verification: Handling probabilistic cost models

Abstract

We consider high-level models that specify system behaviors probabilistically and support the specification of cost attributes. Specifically, we focus on Discrete Time Markov Reward Models (D-MRMs), i.e. state machines where probabilities can be associated with transitions and rewards (costs) can be associated with states and transitions. Through probabilities we model assumptions on the behavior of environment in which an application is embedded. Rewards can instead model the cost assumptions involved in the system's operations. A system is designed to satisfy the requirements, under the given assumptions. Design-time assumptions, however, can turn out to be invalid at runtime, and therefore it is necessary to verify whether changes may lead to requirements violations. If they do, it is necessary to adapt the behavior in a self-healing manner to continue to satisfy the requirements. We have previously presented an approach to support efficient runtime probabilistic model checking of DTMCs for properties expressed in PCTL. In this paper we extend the approach to D-MRMs and reward properties. The benefits of the approach are justified both theoretically and empirically on significant test cases.