383 research outputs found
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
TRANSIENT ANALYSIS OF A PREEMPTIVE RESUME M/D/l/2/2 THROUGH PETRI NETS
Stochastic Petri Nets (SPN) are usually designed to support exponential distributions
only, with the consequence that their modelling power is restricted to Markovian systems.
In recent years, some attempts have appeared in the literature aimed to define SPN
models with generally distributed firing times. A particular subclass, called Deterministic
and Stochastic Petri Nets (DSPN), combines into a single model both exponential and
deterministic transitions. The available DSPN implementations require simplifying assumptions
which limit the applicability of the model to preemptive repeat different service
mechanisms only. The present paper discusses a semantical generalization of the DSPNs
by including preemptive mechanisms of resume type. This generalization is crucial in
connection with fault tolerant systems, where the work performed before the interruption
should not be lost. By means of this new approach, the transient analysis of a M/D/1/2/2
queue (with 2 customers, 1 server, exponential thinking and deterministic service time) is
fully examined under different preemptive resume policies
Stochastic simulation of event structures
Currently the semantics of stochastic process algebras are defined using (an extension) of labelled transition systems. This usually results in a semantics based on the interleaving of causally independent actions. The advantage is that the structure of transition systems closely resembles that of Markov chains, enabling the use of standard solution techniques for analytical and numerical performance assessment of formal specifications. The main drawback is that distributions are restricted to be exponential. In [2] we proposed to use a partial-order semantics for stochastic process algebras. This allows the support of non-exponential distributions in the process algebra in a perspicuous way, but the direct resemblance with Markov chains is lost. This paper proposes to exploit discrete-event simulation techniques for analyzing our partial-order model, called stochastic event structures. The key idea is to obtain from event structures so-called (time-homogeneous) generalized semiMarkov ..
An Evaluation Framework for Comparative Analysis of Generalized Stochastic Petri Net Simulation Techniques
Availability of a common, shared benchmark to provide repeatable, quantifiable, and comparable results is an added value for any scientific community. International consortia provide benchmarks in a wide range of domains, being normally used by industry, vendors, and researchers for evaluating their software products. In this regard, a benchmark of untimed Petri net models was developed to be used in a yearly software competition driven by the Petri net community. However, to the best of our knowledge there is not a similar benchmark to evaluate solution techniques for Petri nets with timing extensions. In this paper, we propose an evaluation framework for the comparative analysis of generalized stochastic Petri nets (GSPNs) simulation techniques. Although we focus on simulation techniques, our framework provides a baseline for a comparative analysis of different GSPN solvers (e.g., simulators, numerical solvers, or other techniques). The evaluation framework encompasses a set of 50 GSPN models including test cases and case studies from the literature, and a set of evaluation guidelines for the comparative analysis. In order to show the applicability of the proposed framework, we carry out a comparative analysis of steady-state simulators implemented in three academic software tools, namely, GreatSPN, PeabraiN, and TimeNET. The results allow us to validate the trustfulness of these academic software tools, as well as to point out potential problems and algorithmic optimization opportunities
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