In many real-time embedded systems, the choice of values for the timing delays can crucially affect the safety or quantitative characteristics of their execution. We propose a parameter synthesis algorithm that finds optimal timing delays guaranteeing that the system satisfies a given quantitative property. As a modelling framework we consider networks of Timed Input/Output Automata (TIOA) with priorities and parametric guards. To express system properties we extend Metric Temporal Logic (MTL) with counting formulas. We implement the algorithm using constraint solving and Monte Carlo sampling, and demonstrate the feasibility of our approach on a simplified model of a pacemaker. We are able to synthesise timing delays that ensure with high probability that energy usage is minimised, while maintaining the basic safety property of the pacemaker.

We develop a novel hybrid heart model in Simulink that is suitable for quantitative verification of implantable cardiac pacemakers. The heart model is formulated at the level of cardiac cells, can be adapted to patient data, and incorporates stochasticity. It is inspired by the timed and hybrid automata network models of Jiang et al and Ye et al, where probabilistic behaviour is not considered. In contrast to our earlier work, we work directly with action potential signals that the pacemaker sensor inputs from a specific cell, rather than ECG signals. We validate the model by demonstrating that its composition with a pacemaker model can be used to check safety properties by means of approximate probabilistic verification.

Stochastic modelling and algorithmic verification techniques have been proved useful in analysing and detecting unusual trends in performance and energy usage of systems such as power management controllers and wireless sensor devices. Many important properties are dependent on the cumulated time that the device spends in certain states, possibly intermittently. We study the problem of verifying continuous-time Markov Chains (CTMCs) against Linear Duration Properties (LDP), that is, properties stated as conjunctions of linear constraints over the total duration of time spent in states that satisfy a given property. We identify two classes of LDP properties, Eventuality Duration Properties (EDP) and Invariance Duration Properties (IDP), respectively referring to the reachability of a set of goal states, within a time bound; and the continuous satisfaction of a duration property over an execution path. The central question that we address is how to compute the probability of the set of infinite timed paths of the CTMC that satisfy a given LDP. We present algorithms to approximate these probabilities up to a given precision, stating their complexity and error bounds. The algorithms mainly employ an adaptation of uniformisation and the computation of volumes of multidimensional integrals under systems of linear constraints, together with different mechanisms to bound the errors.

Stochastic modeling and algorithmic verification techniques have been proved useful in analyzing and detecting unusual trends in performance and energy usage of systems such as power management controllers and wireless sensor devices. Many important properties are dependent on the cumulated time that the device spends in certain states, possibly intermittently. We study the problem of verifying continuous-time Markov chains (CTMCs) against linear duration properties (LDP), i.e. properties stated as conjunctions of linear constraints over the total duration of time spent in states that satisfy a given property. We identify two classes of LDP properties, eventuality duration properties (EDP) and invariance duration properties (IDP), respectively referring to the reachability of a set of goal states, within a time bound; and the continuous satisfaction of a duration property over an execution path. The central question that we address is how to compute the probability of the set of infinite timed paths of the CTMC that satisfy a given LDP. We present algorithms to approximate these probabilities up to a given precision, stating their complexity and error bounds. The algorithms mainly employ an adaptation of uniformization and the computation of volumes of multi-dimensional integrals under systems of linear constraints, together with different mechanisms to bound the errors.

Implantable medical devices, such as cardiac pacemakers, must be designed and programmed to the highest levels of safety and reliability. Recently, errors in embedded software have led to a substantial increase in safety alerts, costly device recalls or even patient death. To address such issues, we propose a model-based framework for quantitative, automated verification of pacemaker software. We adapt the electrocardiogram model of Clifford et al, which generates realistic normal and abnormal heart beat behaviours, with probabilistic transitions between them, to produce a timed sequence of action potential signals that serve as pacemaker input. Working with the timed automata model of the pacemaker by Jiang et al, we develop a methodology for deriving the composition of the heart and the pacemaker, based on discretisation. The main correctness properties we consider include checking that the pacemaker corrects Bradycardia (slow heart beat) and does not induce Tachycardia (fast heart beat), for a range of realistic heart behaviours. We also analyse under sensing, through considering noise on sensor readings, and energy usage. We implement the framework using the probabilistic model checker PRISM and MATLAB and demonstrate encouraging experimental results. Our approach can be adapted to individual patients and is applicable to other pacemaker models.