Probabilistic Models Toward Controlling Smart-* Environments

Today, a growing number of physical objects in our surroundings are connected to the Internet and provide the digital world with an interface to the physical world through sensors and actuators. At the heart of this trend, smart-* systems and applications leverage this interface to smartly and seamlessly assist individuals in their everyday lives. However, when interacting with the physical world by means of actuators, these applications introduce a methodological disruption. Indeed, in comparison to the classical distributed software applications that operate in the bounded and predictable digital world, these applications operate in and through the physical world, open and subject to uncertainties that cannot be modeled accurately. These uncertainties lead the behavior of the applications to potentially drift at runtime, compromising their intrinsic functionality. In this paper, we propose a framework to estimate the behavioral drift of smart-* systems and applications at runtime. To this end, we first rely on the Moore finite state machine (FSM) modeling framework. This framework is used for specifying the ideal behavior of a smart-* application in terms of the effects, and it is expected to produce within the physical environment as it executes. We then appeal on the control theory and propose a framework for projecting the Moore FSM to its associated continuous density Input/Output hidden Markov model (CD-IOHMM) state observer. By accounting for uncertainties through probabilities, it extends Moore FSM with viability zones, i.e., zones where the effects of a smart-* application within the physical environment are satisfactory without necessarily being perfect. At runtime, the CD-IOHMM state observer can compute the probability of the observed effects, i.e., it gives direct insight into the behavioral drift of the concrete application. We validate our approach on a real data set. The results demonstrate the soundness and efficiency of the proposed approach at estimating the behavioral drift of smart-* applications at runtime. In view of these results, one can envision using this estimation for supporting a decision-making algorithm (e.g., within a self-adaptive system).