Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.Comment: The 12th International Conference on Learning Representations (ICLR 2024

Dependability modeling and evaluation – From AADL to stochastic Petri nets

Conduire des analyses de sûreté de fonctionnement conjointement avec d'autres analyses au niveau architectural permet à la fois de prédire les effets des décisions architecturales sur la sûreté de fonctionnement du système et de faire des compromis. Par conséquent, les industriels et les universitaires se concentrent sur la définition d'approches d'ingénierie guidées par des modèles (MDE) et sur l'intégration de diverses analyses dans le processus de développement. AADL (Architecture Analysis and Design Language) a prouvé son aptitude pour la modélisation d'architectures et ce langage est actuellement jugé efficace par les industriels dans de telles approches. Notre contribution est un cadre de modélisation permettant la génération de modèles analytiques de sûreté de fonctionnement à partir de modèles AADL dans l‘objectif de faciliter l'évaluation de mesures de sûreté de fonctionnement comme la fiabilité et la disponibilité. Nous proposons une approche itérative de modélisation. Dans ce contexte, nous fournissons un ensemble de sous-modèles génériques réutilisables pour des architectures tolérantes aux fautes. Le modèle AADL de sûreté de fonctionnement est transformé en un RdPSG (Réseau de Petri Stochastique Généralisé) en appliquant des règles de transformation de modèle. Nous avons implémenté un outil de transformation automatique. Le RdPSG résultant peut être traité par des outils existants pour obtenir des mesures de sûreté de fonctionnement. L'approche est illustrée sur un ensemble du Système Informatique Français de Contrôle de Trafic Aérien. ABSTRACT : Performing dependability evaluation along with other analyses at architectural level allows both predicting the effects of architectural decisions on the dependability of a system and making tradeoffs. Thus, both industry and academia focus on defining model driven engineering (MDE) approaches and on integrating several analyses in the development process. AADL (Architecture Analysis and Design Language) has proved to be efficient for architectural modeling and is considered by industry in the context presented above. Our contribution is a modeling framework allowing the generation of dependability-oriented analytical models from AADL models, to facilitate the evaluation of dependability measures, such as reliability or availability. We propose an iterative approach for system dependability modeling using AADL. In this context, we also provide a set of reusable modeling patterns for fault tolerant architectures. The AADL dependability model is transformed into a GSPN (Generalized Stochastic Petri Net) by applying model transformation rules. We have implemented an automatic model transformation tool. The resulting GSPN can be processed by existing tools to obtain dependability measures. The modeling approach is illustrated on a subsystem of the French Air trafic Control System

Availability modeling and evaluation of web-based services - A pragmatic approach

Cette thèse porte sur le développement d’une approche de modélisation pragmatique permettant aux concepteurs d’applications et systèmes mis en oeuvre sur le web d’évaluer la disponibilité du service fourni aux utilisateurs. Plusieurs sources d’indisponibilité du service sont prises en compte, en particulier i) les défaillances matérielles ou logicielles affectant les serveurs et ii) des dégradations de performance (surcharge des serveurs, temps de réponse trop long, etc.). Une approche hiérarchique multi-niveau basée sur une modélisation de type performabilité est proposée, combinant des chaînes de Markov et des modèles de files d’attente. Les principaux concepts et la faisabilité de cette approche sont illustrés à travers l’exemple d’une agence de voyage. Plusieurs modèles analytiques et études de sensibilité sont présentés en considérant différentes hypothèses concernant l’architecture, les stratégies de recouvrement, les fautes, les profils d’utilisateurs, et les caractéristiques du trafic. ABSTRACT : This thesis presents a pragmatic modeling approach allowing designers of web-based applications and systems to evaluate the service availability provided to the users. Multiple sources of service unavailability are taken into account, in particular i) hardware and software failures affecting the servers, and ii) performance degradation (overload of servers, very long response time, etc.). An hierarchical multi-level approach is proposed based on performability modeling, combining Markov chains and queueing models. The main concepts and the feasibility of this approach are illustrated using a web-based travel agency. Various analytical models and sensitivity studies are presented considering different assumptions with respect to the architectures, recovery strategies, faults, users profile and traffic characteristics

First IJCAI International Workshop on Graph Structures for Knowledge Representation and Reasoning (GKR@IJCAI'09)

International audienceThe development of effective techniques for knowledge representation and reasoning (KRR) is a crucial aspect of successful intelligent systems. Different representation paradigms, as well as their use in dedicated reasoning systems, have been extensively studied in the past. Nevertheless, new challenges, problems, and issues have emerged in the context of knowledge representation in Artificial Intelligence (AI), involving the logical manipulation of increasingly large information sets (see for example Semantic Web, BioInformatics and so on). Improvements in storage capacity and performance of computing infrastructure have also affected the nature of KRR systems, shifting their focus towards representational power and execution performance. Therefore, KRR research is faced with a challenge of developing knowledge representation structures optimized for large scale reasoning. This new generation of KRR systems includes graph-based knowledge representation formalisms such as Bayesian Networks (BNs), Semantic Networks (SNs), Conceptual Graphs (CGs), Formal Concept Analysis (FCA), CPnets, GAI-nets, all of which have been successfully used in a number of applications. The goal of this workshop is to bring together the researchers involved in the development and application of graph-based knowledge representation formalisms and reasoning techniques

Second Workshop on Modelling of Objects, Components and Agents

This report contains the proceedings of the workshop Modelling of Objects, Components, and Agents (MOCA'02), August 26-27, 2002.The workshop is organized by the 'Coloured Petri Net' Group at the University of Aarhus, Denmark and the 'Theoretical Foundations of Computer Science' Group at the University of Hamburg, Germany. The homepage of the workshop is: http://www.daimi.au.dk/CPnets/workshop02

Process algebra approach to parallel DBMS performance modelling

Abstract unavailable please refer to PD