Analysis Of Concurrent Systems Research Articles

Modelling, simulation and performance evaluation of the IEEE 802.11e protocol with station mobility.

In this article, we present a parameterized Colored Petri Net (CPN) model of the IEEE 802.11e protocol for wireless communications with mobile stations. CPNs provide a graphical model for the modeling and analysis of concurrent systems, which can be parameterized by the use of constants, and thus they allow us to create more flexible models. Our CPN model captures the protocol's behavior, and the specific parameters used for the 802.11e protocol and the scenarios to be evaluated are captured by the CPN parameters. The model presented is flexible enough to cover full customization of traffic types, user mobility and collision avoidance protocols. In this model, there is an access point (AP) which is visible to all the stations, and we assume that due to physical restrictions, there are two range groups. All the stations in the same range group are visible to each other. The impact of mobility is then analyzed by studying a situation in which the stations move in a controlled way to the same range group. The simulation results demonstrate the impact on network performance for sensitive and insensitive traffic types, as well as the role of the RTS/CTS protocol in collision avoidance, especially when users are located in different regions. Specifically, we show how the performance improves in the different scenarios when the stations move to the same area, where they can see each other, and we also study the impact on the performance for each type of traffic.

On Hierarchical Construction of the State Space of an Automated Manufacturing System Modeled With Petri Nets

State space techniques are one of the main approaches deployed for the analysis of concurrent systems. However, state space construction is stalled by a common phenomenon called the state explosion problem which makes it a tough task or even impossible when the state space computation demands prohibitive cost (time and memory). We limit general resource allocation systems (RASs) to a certain class whose state space can be hierarchically constructed, yet it comprises various enough types of real-world discrete event systems, such as automated manufacturing systems. This paper focuses on a class of RASs modeled with Petri nets (PNs), where, through pure algebraic operations, a novel method to compute the state spaces is proposed, which is motivated by the superposition property. Given a PN model of a system and a target resource configuration, we first propose a special initial marking called the initial basis marking and compute the corresponding reachability graph. Then, we increase the capacity of the resource places in an incremental way and generate the reachability graphs by taking advantage of the PN structure and the previously computed reachability graph until the capacity function of resources reaches the target resource configuration. A complete enumeration of reachable states can be obtained by a recursive scheme. Experimental studies also demonstrate the efficiency of the proposed approach in terms of computational cost and its high-potential to cope with the state-explosion problem.

Programming and symbolic computation in Maude

Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite theories. Maude has also a formal environment of verification tools. Symbolic computation is a powerful technique for reasoning about the correctness of concurrent systems and for increasing the power of formal tools. We present several new symbolic features of Maude that enhance formal reasoning about Maude programs and the effectiveness of formal tools. They include: (i) very general unification modulo user-definable equational theories, and (ii) symbolic reachability analysis of concurrent systems using narrowing. The paper does not focus just on symbolic features: it also describes several other new Maude features, including: (iii) Maude's strategy language for controlling rewriting, and (iv) external objects that allow flexible interaction of Maude object-based concurrent systems with the external world. In particular, meta-interpreters are external objects encapsulating Maude interpreters that can interact with many other objects. To make the paper self-contained and give a reasonably complete language overview, we also review the basic Maude features for equational rewriting and rewriting with rules, Maude programming of concurrent object systems, and reflection. Furthermore, we include many examples illustrating all the Maude notions and features described in the paper.

Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

We propose an extension with immediate multiactions of discrete time stochastic Petri box calculus (dtsPBC), pre- sented by I.V. Tarasyuk. The resulting algebra dtsiPBC is a discrete time analogue of stochastic Petri box calculus (sPBC) with immediate multiactions, proposed by H. MaciV. Valero and others within a continuous time domain. The step operational semantics is constructed via labeled probabilistic transition systems. The denotational seman- tics is defined on the basis of a subclass of labeled discrete time stochastic Petri nets with immediate transitions. A consistency of the both semantics is demonstrated. In order to evaluate performance, the corresponding semi-Markov chains and (reduced) discrete time Markov chains are analyzed. We define step stochastic bisimulation equivalence of expressions and prove that it can be applied to reduce their transition systems and underlying semi-Markov chains while preserving the functionality and performance characteristics. We explain how this equivalence may help to sim- plify performance analysis of the algebraic processes. In a case study, a method of modeling, performance evaluation and behaviour preserving reduction of concurrent systems is outlined and applied to the shared memory system.

On-the-fly model checking for extended action-based probabilistic operators

The quantitative analysis of concurrent systems requires expressive and user-friendly property languages combining temporal, data handling, and quantitative aspects. In this paper, we aim at facilitating the quantitative analysis of systems modeled as PTSs (Probabilistic Transition Systems) labeled by actions containing data values and probabilities. We propose a new regular probabilistic operator that specifies the probability measure of a path described by a generalized regular formula involving arbitrary computations on data values. This operator, which subsumes the Until operators of PCTL and their action-based counterparts, can provide useful quantitative information about paths having certain (e.g., peak) cost values. We integrated the regular probabilistic operator into MCL (Model Checking Language) and we devised an associated on-the-fly model checking method, based on a combined local resolution of linear and Boolean equation systems. We implemented the method in the EVALUATOR model checker of the CADP toolbox and experimented it on realistic PTSs modeling concurrent systems.

Performance analysis of concurrent systems in algebra dtsiPBC

Petri box calculus PBC is a well-known algebra of concurrent processes with a Petri net semantics. In the paper, an extension of PBC with discrete stochastic time and immediate multiactions, which is referred to as discrete time stochastic and immediate PBC (dtsiPBC), is considered. Performance analysis methods for concurrent and distributed systems with random time delays are investigated in the framework of the new stochastic process algebra. It is demonstrated that the performance evaluation is possible not only via the underlying semi-Markov chains of the dtsiPBC expressions but also with the use of the underlying discrete time Markov chains, and the latter analysis technique is more optimal.

A Rough Set Approach to Information Systems Decomposition

The aim of this paper is to present the methods and algorithms of information systems decomposition. In the paper, decomposition with respect to reducts and the so-called global decomposition are considered. Moreover, coverings of information systems by components are discussed. An essential difference between two kinds of decomposition can be observed. In general, global decomposition can deliver more components of a given information system. This fact can be treated as some kind of additional knowledge about the system. The proposed approach is based on rough set theory. To demonstrate the usefulness of this approach, we present an illustrative example coming from the economy domain. The discussed decomposition methods can be applied e.g. for design and analysis of concurrent systems specified by information systems, for automatic feature extraction, as well as for control design of systems represented by experimental data tables.

ITL semantics of composite Petri nets

interval temporal logic (itl) and Petri nets are two well developed formalisms for the specification and analysis of concurrent systems. itl allows one to specify both the system design and correctness requirements within the same logic based on intervals (sequences of states). As a result, verification of system properties can be carried out by checking that the formula describing a system implies the formula describing a requirement. Petri nets, on the other hand, have action and local state based semantics which allows for a direct expression of causality aspects in system behaviour. As a result, verification of system properties can be carried out using partial order reductions or invariant based techniques. In this paper, we investigate a basic semantical link between temporal logics and compositionally defined Petri nets. In particular, we aim at providing a support for the verification of behavioural properties of Petri nets using methods and techniques developed for itl.

Structured performance analysis for component-based systems

The component-based system (CBS) paradigm is now largely used to design software systems. In addition, performance and behavioural analysis remains a required step for the design and the construction of efficient systems. This is especially the case of CBS, which involve interconnected components running concurrent processes. This paper proposes a compositional method for modelling and structured performance analysis of CBS. Modelling is based on stochastic well-formed nets (SWNs), a high level model of stochastic Petri nets, widely used for dependability analysis of concurrent systems. Starting from the definition of the system given in a suitable architecture description language, and from the definition of the elementary components, we build an SWN of the global system together with a set of SWNs modelling the components of the CBS and their connections. From these models, we derive performances of the system thanks to a structured analysis induced by the structure of the CBS. We describe the application of our method through an example designed in the framework of the CORBA component model.

A state/event-based model-checking approach for the analysis of abstract system properties

We present the UMC framework for the formal analysis of concurrent systems specified by collections of UML state machines. The formal model of a system is given by a doubly labelled transition system, and the logic used to specify its properties is the state-based and event-based logic UCTL. UMC is an on-the-fly analysis framework which allows the user to interactively explore a UML model, to visualize abstract behavioural slices of it and to perform local model checking of UCTL formulae. An automotive scenario from the service-oriented computing (SOC) domain is used as case study to illustrate our approach.

Variant Narrowing and Equational Unification

Narrowing is a well-known complete procedure for equational E-unification when E can be decomposed as a union E=@D@?B with B a set of axioms for which a finitary unification algorithm exists, and @D a set of confluent, terminating, and B-coherent rewrite rules. However, when B @A, effective narrowing strategies such as basic narrowing easily fail to be complete and cannot be used. This poses two challenges to narrowing-based equational unification: (i) finding effective narrowing strategies that are complete modulo B under mild assumptions on B, and (ii) finding sufficient conditions under which such narrowing strategies yield finitary E-unification algorithms. Inspired by Comon and Delaune's notion of E-variant for a term, we propose a new narrowing strategy called variant narrowing that has a search space potentially much smaller than full narrowing, is complete, and yields a finitary E-unification algorithm when E has the finite variant property. We also discuss applications to symbolic reachability analysis of concurrent systems specified as rewrite theories, and in particular to the formal analysis of cryptographic protocols modulo the algebraic properties of the underlying cryptographic functions.

State space analysis of Petri nets with relation-algebraic methods

A large variety of systems can be modelled by Petri nets. Their formal semantics are based on linear algebra which in particular allows the calculation of a Petri net’s state space. Since state space explosion is still a serious problem, efficiently calculating, representing, and analysing the state space is mandatory. We propose a formal semantics of Petri nets based on executable relation-algebraic specifications. Thereupon, we suggest how to calculate the markings reachable from a given one simultaneously. We provide an efficient representation of reachability graphs and show in a correct-by-construction approach how to efficiently analyse their properties. Therewith we cover two aspects: modelling and model checking systems by means of one and the same logic-based approach. On a practical side, we explore the power and limits of relation-algebraic concepts for concurrent system analysis.

Implementing Coloured Petri Nets Using a Functional Programming Language

Coloured Petri Nets (CPNs) are a graphically oriented modelling language for concurrent systems based on Petri Nets and the functional programming language Standard ML. Petri Nets provide the primitives for modelling concurrency and synchronisation. Standard ML provides the primitives for modelling data manipulation and for creating compact and parameterisable CPN models. Functional programming and Standard ML have played a major role in the development of CPNs and the CPN computer tools supporting modelling, simulation, verification, and performance analysis of concurrent systems. At the modelling language level, Standard ML has extended Petri Nets with the practical expressiveness required for modelling systems of the size and complexity found in typical industrial projects. At the implementation level, Standard ML has been used to implement the formal semantics of CPNs that provide the theoretical foundation of the CPN computer tools. This paper provides an overview of how functional programming and Standard ML are applied in the CPN modelling language and the supporting computer tools. We give a detailed presentation of the key algorithms and techniques used for implementing the formal semantics of CPNs, and we survey a number of case studies where CPNs have been used for the design and analysis of systems. We also demonstrate how the use of a Standard ML programming environment has allowed Petri Nets to be used for the implementation of systems.

An Integrated Approach for the Specification and Analysis of Stochastic Real-Time Systems

A formal approach for the specification and analysis of concurrent systems is proposed which integrates two different orthogonal aspects of time: (i) real-time, concerning the expression of time constraints and the verification of exact time properties, and (ii) probabilistic-time, concerning the probabilistic quantification of durations of system activities via exponential probability distributions and the evaluation of system performance. We show that these two aspects, that led to different specification paradigms called timed automata and Markovian process algebras, respectively, can be expressed in an integrated way by a single language: a process algebra capable of expressing activities with generally distributed durations. In particular, we consider the calculus of Interactive Generalized Semi-Markov Processes (IGSMPs) and we present formal techniques for compositionally deriving, from an IGSMP specification, (i) a pure real-time model (called Interactive Timed Automaton), by considering the support of general distributions, and (ii) a pure probabilistic-time model (called Interactive Weighted Markov Chain), by approximating general distributions with phase-type distributions.

Specification and Analysis of the MPEG-2 Video Encoder with Timed-Arc Petri Nets

Petri nets are a very suitable model for the description and analysis of concurrent systems. Several timed extensions of Petri nets have been defined to capture some additional aspects, concerning with the behaviour in time of the described systems. In this paper we illustrate the use of timed-arc Petri nets for the modelling of timed concurrent systems, using the MPEG-2 video encoder as an example. From the analysis of the model we conclude that the performance of the encoding process could be improved by introducing some minor changes on the encoder.

Hypergraph construction and its application to the static analysis of concurrent systems

We define a construction operation on hypergraphs based on a colimit and show that its expressiveness is equal to the graph expressions of Bauderon and Courcelle. We also demonstrate that by closing a set of rewrite rules under graph construction we obtain a notion of rewriting equivalent to the double-pushout approach of Ehrig. The usefulness of our approach for the compositional modelling of concurrent systems is then demonstrated by giving a semantics of process graphs (corresponding to a process calculus with mobility) and of Petri nets. We introduce on the basis if a hypergraph construction, a method for the static analysis of process graphs, related to type systems.

Introduction

This special issue of Mathematical Structures in Computer Science is devoted to the theory and applications of graph transformations. This research area dates back to the early seventies and is based on mathematical techniques from graph theory, algebra, logic and category theory. The theory of graph transformations has become attractive as a modelling and programming paradigm for complex graphical structures in a large variety of areas in computer science and for applications to other fields. During the Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems (GRATRA 2000) – a satellite of ETAPS 2000 in Berlin – 35 lectures were presented by participants from all over the world. The authors of presentations that stressed the theoretical point of view were invited to submit a full version of their presentation to Mathematical Structures in Computer Science. After a careful refereeing process nine papers have been accepted, seven of which are included in this special issue.The paper by Ehrenfeucht, Petre, Prescott and Rozenberg connects the important new area of DNA computing in vivo to our area of graph transformation. An application of hypergraph constructions to the static analysis of concurrent systems is presented by König, and normal forms for context-free node rewriting hypergraph grammars by Klempien-Hinrichs. The construction of pushout complements for ‘partly total algebras’ generalising attributed graphs is presented by Burmeister, Llabrés and Roselló. Finally, Courcelle and Makowsky present operations on relational structures (generalising different kinds of graphs and hypergraphs) that are compatible with monadic second order logic. Four other accepted papers could not be included in this special issue because of space limitations.They will appear in regular issues of MSCS:— R. Heckel, M. Llabrés, H. Ehrig and F. Orejas: Concurrency and loose semantics of open graph transformation systems.— L. Helouet, C. Jard and B. Caillaud: An event structure based semantics for high-level message sequence charts.— J. Larossa and G. Valiente: Constraint satisfaction algorithms for graph pattern matching.— N. Verlinden and D. Janssens: Algebraic properties for Local Action Systems.We are most grateful to all the referees of these papers, to Olga Runge and Claudia Ermel for technical support, and to Giuseppe Longo and Cambridge University Press for fruitful cooperation in editing this special issue.

Deadlock prevention using Petri nets and their unfoldings

Unfoldings of Petri nets (PN) provide a method for the analysis of concurrent systems without restoring the state space of a system. This allows one to overcome the “state explosion” problem. Many properties of the initial PN (boundedness, safety, persistency and hazards) can be checked by constructing the unfolding. A deadlock prevention procedure first detects deadlocks using an unfolding. Then, the first method reduces the unfolding to a set of deadlock-free subunfoldings that cover all live behaviours. The second method uses a direct transformation at the level of the original PN. The methods are implemented as subroutines in the Berkeley program SIS. Although the deadlock detection problem is known to be NP-complete, experimental results show that for highly parallel specifications deadlock prevention by unfoldings is typically more efficient than deadlock prevention based on symbolic BDD (binary decision diagrams) traversal of the corresponding reachability graph.

Efficient analysis of concurrent systems by Petri nets

Efficient analysis of concurrent systems by Petri nets

Efficient analysis of concurrent systems by Petri nets

Efficient analysis of concurrent systems by Petri nets