3,507 research outputs found
A Hierarchy of Scheduler Classes for Stochastic Automata
Stochastic automata are a formal compositional model for concurrent
stochastic timed systems, with general distributions and non-deterministic
choices. Measures of interest are defined over schedulers that resolve the
nondeterminism. In this paper we investigate the power of various theoretically
and practically motivated classes of schedulers, considering the classic
complete-information view and a restriction to non-prophetic schedulers. We
prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic
reachability. We find that, unlike Markovian formalisms, stochastic automata
distinguish most classes even in this basic setting. Verification and strategy
synthesis methods thus face a tradeoff between powerful and efficient classes.
Using lightweight scheduler sampling, we explore this tradeoff and demonstrate
the concept of a useful approximative verification technique for stochastic
automata
Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events
that can be non-exponentially distributed. Within parametric ACTMCs, the
parameters of alarm-event distributions are not given explicitly and can be
subject of parameter synthesis. An algorithm solving the -optimal
parameter synthesis problem for parametric ACTMCs with long-run average
optimization objectives is presented. Our approach is based on reduction of the
problem to finding long-run average optimal strategies in semi-Markov decision
processes (semi-MDPs) and sufficient discretization of parameter (i.e., action)
space. Since the set of actions in the discretized semi-MDP can be very large,
a straightforward approach based on explicit action-space construction fails to
solve even simple instances of the problem. The presented algorithm uses an
enhanced policy iteration on symbolic representations of the action space. The
soundness of the algorithm is established for parametric ACTMCs with
alarm-event distributions satisfying four mild assumptions that are shown to
hold for uniform, Dirac and Weibull distributions in particular, but are
satisfied for many other distributions as well. An experimental implementation
shows that the symbolic technique substantially improves the efficiency of the
synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
Analysing Decisive Stochastic Processes
In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems and probabilistic vector addition systems with states. In this paper, we extend the concept of decisiveness to more general stochastic processes. This extension is non trivial as we consider stochastic processes with a potentially continuous set of states and uncountable branching (common features of real-time stochastic processes). This allows us to obtain decidability results for both qualitative and quantitative verification problems on some classes of real-time stochastic processes, including generalized semi-Markov processes and stochastic timed
automat
Consistency Analysis of Sensor Data Distribution
In this paper we analyze the probability of consistency of sensor data
distribution systems (SDDS), and determine suitable evaluation models. This
problem is typically difficult, since a reliable model taking into account all
parameters and processes which affect the system consistency is unavoidably
very complex. The simplest candidate approach consists of modeling the state
sojourn time, or holding time, as memoryless, and resorting to the well known
solutions of Markovian processes. Nevertheless, it may happen that this
approach does not fit with some working conditions. In particular, the correct
modeling of the SDDS dynamics requires the introduction of a number of
parameters, such as the packet transfer time or the packet loss probability,
the value of which may determine the suitability of unsuitability of the
Markovian model. Candidate alternative solutions include the Erlang phase-type
approximation of nearly constant state holding time and a more refined model to
account for overlapping events in semi-Markov processes.Comment: IEEE IWCMC 2013, Cagliari, Italy, June 201
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
Transport in finite size systems: an exit time approach
In the framework of chaotic scattering we analyze passive tracer transport in
finite systems. In particular, we study models with open streamlines and a
finite number of recirculation zones. In the non trivial case with a small
number of recirculation zones a description by mean of asymptotic quantities
(such as the eddy diffusivity) is not appropriate. The non asymptotic
properties of dispersion are characterized by means of the exit time
statistics, which shows strong sensitivity on initial conditions. This yields a
probability distribution function with long tails, making impossible a
characterization in terms of a unique typical exit time.Comment: 16 RevTeX pages + 6 eps-figures include
Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis
We consider parametric version of fixed-delay continuous-time Markov chains
(or equivalently deterministic and stochastic Petri nets, DSPN) where
fixed-delay transitions are specified by parameters, rather than concrete
values. Our goal is to synthesize values of these parameters that, for a given
cost function, minimise expected total cost incurred before reaching a given
set of target states. We show that under mild assumptions, optimal values of
parameters can be effectively approximated using translation to a Markov
decision process (MDP) whose actions correspond to discretized values of these
parameters
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