919 research outputs found
Distributed Semi-Markov Processes in Stochastic T-Timed Petri Nets
The heaps of pieces modelling approach (see Gaubert/Mairesse, PNPM'99) admits a (max,+)-linear model for the time consumption, under earliest firing and a given trace, of safe T-timed nets. The present paper shows that this type of model can be extended, using an appropriate partial order semantics under cluster view, to include stochastic choice and timing; we give the algorithmic construction of that semantics and obtain a semi-Markov property in multi-dimensional real time
CSL model checking of Deterministic and Stochastic Petri Nets
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described
Process algebra for performance evaluation
This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions
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
On Zone-Based Analysis of Duration Probabilistic Automata
We propose an extension of the zone-based algorithmics for analyzing timed
automata to handle systems where timing uncertainty is considered as
probabilistic rather than set-theoretic. We study duration probabilistic
automata (DPA), expressing multiple parallel processes admitting memoryfull
continuously-distributed durations. For this model we develop an extension of
the zone-based forward reachability algorithm whose successor operator is a
density transformer, thus providing a solution to verification and performance
evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of
cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Performance queries on Semi-Markov Stochastic Petri nets with an extended continuous Stochastic logic
Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to ¢¤£¦ ¥ states.
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
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
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