Peps2007-Stochastic Automata Networks Software Tool

2016

This presentation introduces a process-algebraic framework with data for modelling and generating Markov automata. We show how an existing linearisation procedure for process-algebraic representa-tions of probabilistic automata can be reused to transform systems in our new framework to a special format. This format enables easy state space generation and facilitates the definition of syntactic re-duction techniques. We introduce several such techniques, which treat data as well as Markovian and interactive behaviour in a fully symbolic manner. In this way, reductions are obtained on the specifi-cation level instead of the model level, reducing state spaces prior to their construction. 1

2010

The Stochastic Automata Networks (SAN) formalism provides a compact and modular description for Markovian models. Moreover, SAN is suitable to derive performance indices for systems analysis and interpretation using iterative numerical solutions based on a descriptor and a state space sized probability vector. Depending on the size of the model this operation is computationally onerous and sometimes impracticable. An alternative method to compute indices from a model is simulation, mainly because it simply requires the definition of a pseudorandom generator and transition functions for states that enable the creation of a trajectory. The sampling process can be different for each technique, establishing some rules to collect samples for further statistical analysis. Simulation techniques often demand lots of samples in order to calculate statistically relevant performance indices. We focus our attention on the parallelization of sampling techniques to enhance the generation of more samples in less time, drawing considerations about the impact on results accuracy.

2004

We present techniques for computing the solution of large Markov chain models whose generators can be represented in the form of a generalized tensor algebra, such as Stochastic Automata Networks (SAN). Many large systems include a number of replications of identical components. This paper exploits replication by aggregating similar components. This leads to a state space reduction, based on lumpability. We define SAN with replicas, and we show how such SAN models can be strongly aggregated, taking functional rates into account. A tensor representation of the matrix of the aggregated Markov chain is proposed, allowing to store this chain in a compact manner and to handle larger models with replicas more efficiently. Examples and numerical results are presented to illustrate the reduction in state space and, consequently, the memory and processing time gains.

2010

In this paper we develop a copula based approximation framework for scalable analysis of Stochastic Automata Networks (SAN) arising in reliability analysis, and can be described by CTMCs. Copulas provide a general approach to model joint distributions in terms of their marginals. Using copulas functions, the dependencies between the interacting automata in the SAN can be captured in terms of local state probabilities associated with the automata involved, avoiding the need of reachability analysis, which is cursed with state space explosion. We prove results related to invariance of copula with system parameters, and consistency of the approximation. We also outline an empirical procedure for determining copulas that can best represent the underlying dependence in a given SAN. We illustrate this approach through various examples of increasing complexity.

The use of stochastic formalisms, such as Stochastic Automata Networks (SAN), can be very useful for statistical prediction and behavior analysis. Once well fitted, such formalisms can generate probabilities about a target reality. These probabilities can be seen as a statistical approach of knowledge discovery. However, the building process of models for real world problems is time consuming even for experienced modelers. Furthermore, it is often necessary to be a domain specialist to create a model. This work illustrates a new method to automatically learn simple SAN models directly from a data source. This method is encapsulated in a tool called SAN GEnerator (SANGE). This new model fitting method is powerful and relatively easy to use; therefore this can grant access to a much broader community to such powerful modeling formalisms.

2005

This paper presents the theoretical underpinning of a model for symbolically representing probabilistic transition systems, an extension of labelled transition systems for the modelling of general (discrete as well as continuous or singular) probability spaces. These transition systems are particularly suited for modelling softly timed systems, real-time systems in which the time constraints are of random nature. For continuous probability spaces these transition systems are infinite by nature.

2006

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Lecture Notes in Computer Science, 2000

Stp, 1997

We discuss a new model for the analysis and simulation of stochastic systems which we call stochastic automata. Basically, they are a combination of the timed automata model and generalised semi-Markov processes (GSMPs for short). We discuss their behaviour and we compare them to the GSMPs model. In addition, we de ne a stochastic process algebra that supports general distribution (both continuous and discrete). Its semantics is given in terms of stochastic automata. We show that stochastic automata can be expressed in terms of the process algebra. We discuss a concrete example and we nish by discussing our current work on this topic and possible future directions.

2011