Lorenzo Ridi

Transient analysis of non-Markovian models using stochastic state classes

The method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMPs) through the symbolic derivation of probability density functions over supports described by Difference Bounds Matrix (DBM) zones. This makes steady state analysis viable, provided that at least one regeneration point is visited by every cyclic behaviour of the model. We extend the approach providing a way to derive transient probabilities. To this end, stochastic state classes are extended with a supplementary timer that enables the symbolic derivation of the distribution of time at which a class can be entered. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can be applied to perform transient analysis of GSMPs within any given time bound. In the special case of models underlying a Markov Regenerative Process (MRGP), the method can also be applied to the symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalised renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.

Oris: a tool for modeling, verification and evaluation of real-time systems

Oris is a tool for qualitative verification and quantitative evaluation of reactive timed systems, which supports modeling and analysis of various classes of timed extensions of Petri Nets. As most characterizing features, Oris implements symbolic state space analysis of preemptive Time Petri Nets, which enable schedulability analysis of real-time systems running under priority preemptive scheduling; and stochastic Time Petri Nets, which enable an integrated approach to qualitative verification and quantitative evaluation. In this paper, we present the current version of the tool and we illustrate its application to two different case studies in the areas of qualitative verification and quantitative evaluation, respectively.

Sirio: A Framework for Simulation and Symbolic State Space Analysis of non-Markovian Models

Sirio is a framework for simulation and symbolic analysis of preemptive and stochastic extensions of Time Petri Nets (TPNs), enabling an integrated approach to correctness verification and quantitative evaluation of timed concurrent systems. In particular, it supports evaluation of transient and steady-state reward measures, both through simulation and analysis. As a characterizing trait, Sirio manages models with multiple concurrently enabled generally distributed (GEN) timers that underlie a Generalized Semi-Markov Process (GSMP). We describe here the SW architecture of the framework, highlighting design choices oriented towards reusability and extensibility, and we illustrate its application to a case study in the area of quantitative evaluation.

A framework for simulation and symbolic state space analysis of non-markovian models

Formal methods supporting development of safety-critical systems require tools that can be integrated within composed environments. Sirio is a framework for simulation and analysis of various timed extensions of Petri Nets, supporting correctness verification and quantitative evaluation of timed concurrent systems. As a characterizing trait, Sirio is expressly designed to support reuse and to facilitate extensions such as the definition of new reward measures, new variants of the analysis, and new models with a different semantics. We describe here the functional responsibilities and the SW architecture of the framework.

Putting Preemptive Time Petri Nets to Work in a V-Model SW Life Cycle

Preemptive Time Petri Nets (pTPNs) support modeling and analysis of concurrent timed SW components running under fixed priority preemptive scheduling. The model is supported by a well-established theory based on symbolic state space analysis through Difference Bounds Matrix (DBM) zones, with specific contributions on compositional modularization, trace analysis, and efficient overapproximation and cleanup in the management of suspension deriving from preemptive behavior. In this paper, we devise and implement a framework that brings the theory to application. To this end, we cast the theory into an organic tailoring of design, coding, and testing activities within a V-Model SW life cycle in respect of the principles of regulatory standards applied to the construction of safety-critical SW components. To implement the toolchain subtended by the overall approach into a Model Driven Development (MDD) framework, we complement the theory of state space analysis with methods and techniques supporting semiformal specification and automated compilation into pTPN models and real-time code, measurement-based Execution Time estimation, test case selection and execution, coverage evaluation.

Developing a Scheduler with Difference-Bound Matrices and the Floyd-Warshall Algorithm

A study of difference-bound matrices and the Floyd-Warshall algorithm in the development of an online scheduler provides the backdrop for a comparison of software practice and algorithmic theory.

Transient Analysis of Generalised Semi-Markov Processes Using Transient Stochastic State Classes

The method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMP) through symbolic derivation of probability density functions over Difference Bounds Matrix (DBM) zones. This makes viable steady state analysis in both discrete and continuous time, provided that each cyclic behavior that changes the enabling status of generally distributed transitions visits at least one regeneration point. However, transient analysis is supported only in discrete time. We extend the approach providing a way to derive continuous time transient probabilities. To this end, stochastic state classes are extended with a supplementary age clock that enables symbolic derivation of the distribution of times at which the states of a zone can be reached. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can in principle be applied to transient analysis with any given time bound for any GSMP. In the special case of models underlying a Markov Regenerative Process (MRP), the method can also be applied to symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalized renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.This paper analyzes the status quo about the application of Enterprise Resource Planning (abbreviated as ERP) of Chinese service industry, Studying and discussing about the implementation of the theory for the service industry ERP system. Whats more, it proposes the implementation methods of the service industry ERP system. Finally, a case of domestic implementation of ERP systems about beauty chain is also provided.

Automatic Code Generation from Real-Time Systems Specifications

We address the problem of rapid development of complex real-timetask-sets through a Model Driven Development (MDD) approach.%The task-set is specified according to the graphic formalism of timelineschemas and it is translated into C-code that implements the dynamic architecture of the task-set on top of Linux-RTAI operating system.%The transformation is performed through an engine obtained as an instance of a new model-transformation framework based on Java and eXtensible Stylesheet Language Transformations (XSLT) called JComposer. This is designed according to a flexible architecture that enables agile evolution of specification formalisms and target artifacts employed along the development process.

Stochastic Fault Trees for cross-layer power management of WSN monitoring systems

Critical systems require supervising infrastructures to keep their unreliability under control. We propose safety-critical systems to be modeled through a fault-tolerant architecture based on Stochastic Fault Trees (SFTs) and we refer to a scenario where the monitoring infrastructure is a Wireless Sensor Network (WSN). SFTs associate the failure time of leaf events with a non-Markovian (GEN) cumulative distribution function (CDF) and support the evaluation of system unreliability over time. In the reference scenario, the SFT model dynamically updates system unreliability according to samples delivered by the WSN, it maintains a dynamic measure of the safe time-horizon within which the system is expected to operate under a given threshold of unreliability, and it also provides the WSN with a measure of the contribution of each basic event to system unreliability.

Probabilistic Model Checking of Non-Markovian Models with Concurrent Generally Distributed Timers

In the analysis of stochastic concurrent timed models, probabilistic model checking combines qualitative identification of feasible behaviors with quantitative evaluation of their probability. If the stochastic process underlying the model is a Continuous Time Markov Chain (CTMC), the problem can be solved by leveraging on the memoryless property of exponential distributions. However, when multiple generally distributed timers can be concurrently enabled, the underlying process may become a Generalized Semi Markov Process (GSMP) for which simulation is often advocated as the only viable approach to evaluation. The method of stochastic state classes provides a means for the analysis of models belonging to this class, that relies on the derivation of multivariate joint distributions of times to fire supported over Difference Bounds Matrix (DBM) zones. Transient stochastic state classes extend the approach with an additional age clock associating each state with the distribution of the time at which it can be reached. We show how transient stochastic state classes can be used to perform bounded probabilistic model checking also for models with underlying GSMPs, and we characterize the conditions for termination of the resulting algorithm, both in exact and approximate evaluation. We also show how the number of classes enumerated to complete the analysis can be largely reduced through a look-ahead in the non-deterministic state class graph of reachable DBM zones. As notable traits, the proposed technique accepts efficient implementation based on DBM zones without requiring the split of domains in regions, and it expresses the bound in terms of a bilateral constraint on the elapsed time without requiring assumptions on the discrete number of executed transitions. Experimental results based on a preliminary implementation in the Oris tool are reported.