Bounded Model Checking of GSMP Models of Stochastic Real-Time Systems

Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMP). While GSMPs is a rich model for stochastic systems widely used in performance evaluation, existing model checking algorithms are applicable only to subclasses such as discrete-time or continuous-time Markov chains. The main contribution of the paper is an algorithm to compute the probability that a given GSMP satisfies a property of the form “can the system reach a target before time T within k discrete events, while staying within a set of safe states”. For this, we show that the probability density function for the remaining firing times of different events in a GSMP after k discrete events can be effectively partitioned into finitely many regions and represented by exponentials and polynomials. We report on illustrative examples and their analysis using our techniques

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

Frequencies in Forgetful Timed Automata

International audienceA quantitative semantics for infinite timed words in timed automata based on the frequency of a run is introduced in [6]. Unfortunately, most of the results are obtained only for one-clock timed automata because the techniques do not allow to deal with some phenomenon of convergence between clocks. On the other hand, the notion of forgetful cycle is introduced in [4], in the context of entropy of timed languages, and seems to detect exactly these convergences. In this paper, we investigate how the notion of forgetfulness can help to extend the computation of the set of frequencies to n-clock timed automata

Modelling Clock Synchronization in the Chess gMAC WSN Protocol

We present a detailled timed automata model of the clock synchronization algorithm that is currently being used in a wireless sensor network (WSN) that has been developed by the Dutch company Chess. Using the Uppaal model checker, we establish that in certain cases a static, fully synchronized network may eventually become unsynchronized if the current algorithm is used, even in a setting with infinitesimal clock drifts

Towards reduction of Paradigm coordination models

The coordination modelling language Paradigm addresses collaboration between components in terms of dynamic constraints. Within a Paradigm model, component dynamics are consistently specified at a detailed and a global level of abstraction. To enable automated verification of Paradigm models, a translation of Paradigm into process algebra has been defined in previous work. In this paper we investigate, guided by a client-server example, reduction of Paradigm models based on a notion of global inertness. Representation of Paradigm models as process algebraic specifications helps to establish a property-preserving equivalence relation between the original and the reduced Paradigm model. Experiments indicate that in this way larger Paradigm models can be analyzed.Comment: In Proceedings PACO 2011, arXiv:1108.145

From Coordination to Stochastic Models of QoS

Reo is a channel-based coordination model whose operational semantics is given by Constraint Automata (CA). Quantitative Constraint Automata extend CA (and hence, Reo) with qua

Probabilistic Reachability for Parametric Markov Models

Abstract. Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (nΘ(logn)). We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.

A Probabilistic Quantitative Analysis of Probabilistic-Write/Copy-Select

Probabilistic-Write/Copy-Select (PWCS) is a novel synchronization scheme suggested by Nicholas Mc Guire which avoids expensive atomic operations for synchronizing access to shared objects. Instead, PWCS makes inconsistencies detectable and recoverable. It builds on the assumption that, for typical workloads, the probability for data races is very small. Mc Guire describes PWCS for multiple readers but only one writer of a shared data structure. In this paper, we report on the formal analysis of the PWCS protocol using a continuous-time Markov chain model and probabilistic model checking techniques. Besides the original PWCS protocol, we also considered a variant with multiple writers. The results were obtained by the model checker PRISM and served to identify scenarios in which the use of the PWCS protocol is justified by guarantees on the probability of data races. Moreover, the analysis showed several other quantitative properties of the PWCS protocol