Heap Models, Composition and Control

International audienc

Max-plus algebra in the history of discrete event systems

This paper is a survey of the history of max-plus algebra and its role in the field of discrete event systems during the last three decades. It is based on the perspective of the authors but it covers a large variety of topics, where max-plus algebra plays a key role

Modeling and Performance Analysis of Manufacturing Systems Using Max-Plus Algebra

In response to increased competition, manufacturing systems are becoming more complex in order to provide the flexibility and responsiveness required by the market. The increased complexity requires decision support tools that can provide insight into the effect of system changes on performance in an efficient and timely manner. Max-Plus algebra is a mathematical tool that can model manufacturing systems in linear equations similar to state-space equations used to model physical systems. These equations can be used in providing insight into the performance of systems that would otherwise require numerous time consuming simulations. This research tackles two challenges that currently hinder the applicability of the use of max-plus algebra in industry. The first problem is the difficulty of deriving the max-plus equations that model complex manufacturing systems. That challenge was overcome through developing a method for automatically generating the max-plus equations for manufacturing systems and presenting them in a form that allows analyzing and comparing any number of possible line configurations in an efficient manner; as well as giving insights into the effects of changing system parameters such as the effects of adding buffers to the system or changing buffers sizes on various system performance measures. The developed equations can also be used in the operation phase to analyze possible line improvements and line reconfigurations due to product changes. The second challenge is the absence of max-plus models for special types of manufacturing systems. For this, max-plus models were developed for the first time for modeling mixed model assembly lines (MMALs) and re-entrant manufacturing systems. The developed methods and tools are applied to case studies of actual manufacturing systems to demonstrate the effectiveness of the developed tools in providing important insight and analysis of manufacturing systems performance. While not covering all types of manufacturing systems, the models presented in this thesis represent a wide variety of systems that are structurally different and thus prove that max-plus algebra is a practical tool that can be used by engineers and managers in modeling and decision support both in the design and operation phases of manufacturing systems

Dynamic analysis of repetitive decision-free discreteevent processes: The algebra of timed marked graphs and algorithmic issues

A model to analyze certain classes of discrete event dynamic systems is presented. Previous research on timed marked graphs is reviewed and extended. This model is useful to analyze asynchronous and repetitive production processes. In particular, applications to certain classes of flexible manufacturing systems are provided in a companion paper. Here, an algebraic representation of timed marked graphs in terms of reccurrence equations is provided. These equations are linear in a nonconventional algebra, that is described. Also, an algorithm to properly characterize the periodic behavior of repetitive production processes is descrbed. This model extends the concepts from PERT/CPM analysis to repetitive production processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44155/1/10479_2005_Article_BF02248590.pd

Analyse pire cas exact du réseau AFDX

L'objectif principal de cette thèse est de proposer les méthodes permettant d'obtenir le délai de transmission de bout en bout pire cas exact d'un réseau AFDX. Actuellement, seules des bornes supérieures pessimistes peuvent être calculées en utilisant les approches de type Calcul Réseau ou par Trajectoires. Pour cet objectif, différentes approches et outils existent et ont été analysées dans le contexte de cette thèse. Cette analyse a mis en évidence le besoin de nouvelles approches. Dans un premier temps, la vérification de modèle a été explorée. Les automates temporisés et les outils de verification ayant fait leur preuve dans le domaine temps réel ont été utilisés. Ensuite, une technique de simulation exhaustive a été utilisée pour obtenir les délais de communication pire cas exacts. Pour ce faire, des méthodes de réduction de séquences ont été définies et un outil a été développé. Ces méthodes ont été appliquées à une configuration réelle du réseau AFDX, nous permettant ainsi de valider notre travail sur une configuration de taille industrielle du réseau AFDX telle que celle embarquée à bord des avions Airbus A380. The main objective of this thesis is to provide methodologies for finding exact worst case end to end communication delays of AFDX network. Presently, only pessimistic upper bounds of these delays can be calculated by using Network Calculus and Trajectory approach. To achieve this goal, different existing tools and approaches have been analyzed in the context of this thesis. Based on this analysis, it is deemed necessary to develop new approaches and algorithms. First, Model checking with existing well established real time model checking tools are explored, using timed automata. Then, exhaustive simulation technique is used with newly developed algorithms and their software implementation in order to find exact worst case communication delays of AFDX network. All this research work has been applied on real life implementation of AFDX network, allowing us to validate our research work on industrial scale configuration of AFDX network such as used on Airbus A380 aircraft. ABSTRACT : The main objective of this thesis is to provide methodologies for finding exact worst case end to end communication delays of AFDX network. Presently, only pessimistic upper bounds of these delays can be calculated by using Network Calculus and Trajectory approach. To achieve this goal, different existing tools and approaches have been analyzed in the context of this thesis. Based on this analysis, it is deemed necessary to develop new approaches and algorithms. First, Model checking with existing well established real time model checking tools are explored, using timed automata. Then, exhaustive simulation technique is used with newly developed algorithms and their software implementation in order to find exact worst case communication delays of AFDX network. All this research work has been applied on real life implementation of AFDX network, allowing us to validate our research work on industrial scale configuration of AFDX network such as used on Airbus A380 aircraft

Non-stationary service curves : model and estimation method with application to cellular sleep scheduling

In today’s computer networks, short-lived flows are predominant. Consequently, transient start-up effects such as the connection establishment in cellular networks have a significant impact on the performance. Although various solutions are derived in the fields of queuing theory, available bandwidths, and network calculus, the focus is, e.g., about the mean wake-up times, estimates of the available bandwidth, which consist either out of a single value or a stationary function and steady-state solutions for backlog and delay. Contrary, the analysis during transient phases presents fundamental challenges that have only been partially solved and is therefore understood to a much lesser extent. To better comprehend systems with transient characteristics and to explain their behavior, this thesis contributes a concept of non-stationary service curves that belong to the framework of stochastic network calculus. Thereby, we derive models of sleep scheduling including time-variant performance bounds for backlog and delay. We investigate the impact of arrival rates and different duration of wake-up times, where the metrics of interest are the transient overshoot and relaxation time. We compare a time-variant and a time-invariant description of the service with an exact solution. To avoid probabilistic and maybe unpredictable effects from random services, we first choose a deterministic description of the service and present results that illustrate that only the time-variant service curve can follow the progression of the exact solution. In contrast, the time-invariant service curve remains in the worst-case value. Since in real cellular networks, it is well known that the service and sleep scheduling procedure is random, we extend the theory to the stochastic case and derive a model with a non-stationary service curve based on regenerative processes. Further, the estimation of cellular network’s capacity/ available bandwidth from measurements is an important topic that attracts research, and several works exist that obtain an estimate from measurements. Assuming a system without any knowledge about its internals, we investigate existing measurement methods such as the prevalent rate scanning and the burst response method. We find fundamental limitations to estimate the service accurately in a time-variant way, which can be explained by the non-convexity of transient services and their super-additive network processes. In order to overcome these limitations, we derive a novel two-phase probing technique. In the first step, the shape of a minimal probe is identified, which we then use to obtain an accurate estimate of the unknown service. To demonstrate the minimal probing method’s applicability, we perform a comprehensive measurement campaign in cellular networks with sleep scheduling (2G, 3G, and 4G). Here, we observe significant transient backlogs and delay overshoots that persist for long relaxation times by sending constant-bit-rate traffic, which matches the findings from our theoretical model. Contrary, the minimal probing method shows another strength: sending the minimal probe eliminates the transient overshoots and relaxation times

Proceedings of the Conference on Production Systems and Logistics: CPSL 2022

[no abstract available

Exact worst-case communication delay analysis of AFDX network

The main objective of this thesis is to provide methodologies for finding exact worst case end to end communication delays of AFDX network. Presently, only pessimistic upper bounds of these delays can be calculated by using Network Calculus and Trajectory approach. To achieve this goal, different existing tools and approaches have been analyzed in the context of this thesis. Based on this analysis, it is deemed necessary to develop new approaches and algorithms. First, Model checking with existing well established real time model checking tools are explored, using timed automata. Then, exhaustive simulation technique is used with newly developed algorithms and their software implementation in order to find exact worst case communication delays of AFDX network. All this research work has been applied on real life implementation of AFDX network, allowing us to validate our research work on industrial scale configuration of AFDX network such as used on Airbus A380 aircraft