Compositions of (max, +) automata

This paper presents a compositional modeling approach by means of (max, +) automata. The motivation is to be able to model a complex discrete event system by composing sub-models representing its elementary parts. A direct modeling of safe timed Petri nets using (max, +) automata is first introduced. Based on this result, two types of synchronous product of (max, +) automata are proposed to model safe timed Petri nets obtained by merging places and/or transitions in subnets. An asynchronous product is finally proposed to represent particular bounded timed Petri nets

Performance analysis using timed Petri Nets

Petri Nets have been successfully used to model and evaluate the performance of distributed systems. Several researchers have extended the basic Petri Net model to include time, and have demonstrated that restricted classes of Petri Nets can be analyzed efficiently. Unfortunately, the restrictions prohibit the techniques from being applied to many interesting systems, e.g. communication protocols. This paper proposes a version of timed Petri Nets which accurately models communication protocols, and which can be analyzed using Timed Reachability Graphs. Procedures for constructing and analyzing these graphs are presented. The analysis is shown to be applicable to a larger class of Timed Petri Nets than previously thought. The model and the analysis technique are demonstrated using a simple communication protocol

Compositional specification of timed systems

We present timed automata and timed Petri nets and argue that timed automata and their associated parallel composition operator are not well adapted for the compositional description of timed Petri nets. Timed automata with deadlines are presented. We present a compositional translation method from 1-safe timed Petri nets to this model. We also present basic ideas for a general compositional specification framewor

Séquentialisation du comportement de réseaux de Petri temporisés

In this paper we are interested in sequentialization of formal power series with coefficients in the semiring (R ∪ {−∞}, max, +) which represent the behavior of timed Petri nets. Several approaches make it possible to derive nondeterministic (max,+) automata modeling safe timed Petri nets. Their nondeterminism is a serious drawback since determinism is a crucial property for numerous results on (max,+) automata (in particular, for applications to performance evaluation and control) and existing procedures for determinization succeed only for restrictive classes of (max,+) automata. We present a natural semi-algorithm for determinization of behaviors based on the semantics of timed Petri nets. The resulting deterministic (max,+)-automata are often infinite, but a sufficient condition is proposed to ensure that the semi-algorithm terminates and leads to a finite state deterministic (max,+)-automaton. Moreover, if the net cannot be sequentialized we propose a restriction of its logical behavior so that the sufficient condition becomes satisfied for the restricted net

Performance Analysis of Stochastic Timed Petri Nets using Linear

Stochastic timed Petri nets are a useful tool in performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for problems of practical sizes. In this paper, we provide a method to compute efficiently upper and lower bounds for the throughputs and mean token numbers in general Markovian timed Petri nets. Our approach is based on uniformization technique and linear programmin

Computing Optimal Coverability Costs in Priced Timed Petri Nets

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However, we show that the infimum of the costs is computable.Comment: 26 pages. Contribution to LICS 201

COSMIC: A Model for Multiprocessor Performance Analysis

COSMIC, the Combined Ordering Scheme Model with Isolated Components, describes the execution of specific algorithms on multiprocessors and facilitates analysis of their performance. Building upon previous modeling efforts such as Petri nets, COSMIC structures the modeling of a system along several issues including computational and overhead costs due to sequencing of operations, synchronization between operations, and contention for limited resources. This structuring allows us to isolate the performance impact associated with each issue. Finally, studying the performance of a system while executing a specific algorithm gives insight into its performance under realistic operating conditions. The model also allows us to study realistically sized algorithms with ease, especially when they are regularly structured. During the analysis of a system modeled by COSMIC, a set timed Petri nets is produced. These Petri nets are then analyzed to determine measures of the systems performance. To facilitate the specification, manipulation, and analysis of large timed Petri nets, a set of tools has been developed. These tools take advantage of several special properties of the timed Petri nets that greatly reduce the computational resources required to calculate the required measures. From this analysis, performance measures show not only total performance, but also present a breakdown of these results into several specific categories

Algebraic Approach to Timed Petri Nets

One aspect often needed when modelling systems of any kind is time-based analysis, especially for real-time or in general time-critical systems. Algebraic place/transition (P/T) nets do not inherently provide a way to model the passing of time or to restrict the firing behaviour with regards to passing time. In this paper, we present an extension of algebraic P/T nets by adding time durations to transitions and timestamps to tokens. We define categories for different timed net classes and functorial relations between them. Our first result is the definition of morphisms preserving firing behaviour for all timed net classes. As second result, we define structuring techniques for timed P/T nets in a way that our category fulfills the properties of M-adhesive systems, a general categorical framework for structuring and transforming high-level algebraic structures. We demonstrate our approach by applying it to model a real-time communication network