Leonardo Brenner

The Peps Software Tool

Peps is a software package for solving very large Markov models expressed as Stochastic Automata Networks (San). The San formalism defines a compact storage scheme for the transition matrix of the Markov chain and it uses tensor algebra to handle the basic vector matrix multiplications. Among the diverse application areas to which Peps may be applied, we cite the areas of computer and communication performance modeling, distributed and parallel systems and finite capacity queueing networks. This paper presents the numerical techniques included in version 2003 of the Peps software, the basics of its interface and three practical examples.

PEPS2007 - Stochastic Automata Networks Software Tool

We give an overview of GRIP, a symmetry reduction tool for the probabilistic model checker PRISM, together with experimental results for a selection of example specifications.This work presents the new version of PEPS software tool, designed for solving models expressed using Stochastic Automata Networks (SAN). The SAN formalism is historically the first Markovian structured formalism employing Tensor Algebra. PEPS tool was first launched in the late 80’s and it’s still a live project, therefore a short timeline of its previous versions, as well as the new features included in version 2015, are presented, such as an efficient and powerful just-in-time function evaluation.

Performance Models For Master/Slave Parallel Programs

This paper proposes the use of Stochastic Automata Networks (SAN) to develop models that can be efficiently applied to a large class of parallel implementations: master/slave (m/s) programs. We focus our technique in the description of the communication between master and slave nodes considering two standard behaviors: synchronous and asynchronous interactions. Although the SAN models may help the pre-analysis of implementations, the main contribution of this paper is to point out advantages and problems of the proposed modeling technique.

Phase-type distributions in stochastic automata networks

Abstract Stochastic automata networks (S ans ) are high-level formalisms for modeling very large and complex Markov chains in a compact and structured manner. To date, the exponential distribution has been the only distribution used to model the passage of time in the evolution of the different S an components. In this paper we show how phase-type distributions may be incorporated into S ans thereby providing the wherewithal by which arbitrary distributions can be used which in turn leads to an improved ability for more accurately modeling numerous real phenomena. The approach we develop is to take a S an model containing phase-type distributions and to translate it into another, stochastically equivalent, S an model having only exponential distributions. In the S an formalism, it is the events that are responsible for firing transitions and our procedure is to associate a stochastic automaton with each event having a phase-type distribution. This automaton models the distribution of time until the event occurs. In this way, the size of the elementary matrices remain small, because the size of the automata are small: the automata are either those of the original S an , or are those associated with the phase-type events and are of size k , the number of phases in the representation of the distribution.

MQNA - Markovian queueing networks analyser

This paper describes the MQNA - Markovian queueing networks analyser, a software tool to model and obtain the stationary solution of a large class of queueing networks. MQNA can directly solve open and closed product-form queueing networks using classical algorithms. For finite capacity queueing models, MQNA generates Markovian description in the stochastic automata networks (SAN) and stochastic petri nets (SPN) formalisms. Such descriptions can be exported to the PEPS - performance evaluation of parallel systems and SMART - stochastic model checking analyzer for reliability and timing software tools that can solve SAN and SPN models respectively.

A framework to decompose GSPN models

This paper presents a framework to decompose a single GSPN model into a set of small interacting models. This decomposition technique can be applied to any GSPN model with a finite set of tangible markings and a generalized tensor algebra (Kronecker) representation can be produced automatically. The numerical impact of all the possible decompositions obtained by our technique is discussed. To do so we draw the comparison of the results for some practical examples. Finally, we present all the computational gains achieved by our technique, as well as the future extensions of this concept for other structured formalisms.

Performance analysis issues for parallel implementations of propagation algorithm

We present a theoretical study to evaluate the performance of a family of parallel implementations of the propagation algorithm. The propagation algorithm is used to an image interpolation application. The theoretical performance analysis is based on the construction of generic models using stochastic automata networks (SAN) formalism to describe each implementation scheme. The prediction results can be compared to the achieved performance in some real test cases to verify the accuracy of our modeling technique. The main contribution is to point out the advantages and problems of our approach to the development of generic models of parallel implementations.