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Petri Nets and Performance Models, 1993. Proceedings., 5th International Workshop on

Date 19-22 Oct. 1993

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  • Proceedings of 5th International Workshop on Petri Nets and Performance Models

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  • Computational algorithms for product form solution stochastic Petri nets

    Page(s): 98 - 107
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    It is shown that the steady-state probability distribution of stochastic Petri nets (SPNs) with product form solution can be efficiently computed using an algorithm whose space and time complexities are polynomial in the number of places and in the number of tokens in the initial marking of the SPN. Basic to the derivation of such an algorithm is a product form solution criterion proposed by J. L. Coleman et al. (1992). The algorithm relies on the derivation of a recursive expression of the normalization constant that is a generalization of that derived by J. P. Buzen (1973) for multiple class product form queuing networks with load independent service centers View full abstract»

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  • A general iterative technique for approximate throughput computation of stochastic marked graphs

    Page(s): 138 - 147
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    A general iterative technique for approximate throughput computation of stochastic strongly connected marked graphs is presented. It generalizes a previous technique based on net decomposition through a single input-single output cut, allowing the split the model through any cut. The approach has two basic foundations. First, a deep understanding of the qualitative behavior of marked graphs leads to a general decomposition technique. Second, after the decomposition phase, an iterative response time approximation method is applied for the computation of the throughput. Experimental results on several examples generally have an error of less than 3%. The state space is usually reduced by more than one order of magnitude; therefore, the analysis of otherwise intractable systems is possible View full abstract»

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  • Constructive modelling and design basic research within the European QMIPS-project

    Page(s): 88 - 95
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    The main objectives of the Quantitative Modelling in Parallel Systems (QMIPS) project, a research activity on quantitative modeling of parallel and distributed systems, are summarized. Elements of a constructive modeling and design methodology are discussed, and stochastic process algebras are emphasized as an interesting base for it View full abstract»

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  • Operational analysis of timed Petri nets and application to the computation of performance bounds

    Page(s): 128 - 137
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    Operational analysis techniques are used to partially characterize the behavior of timed Petri nets under very weak assumptions on their timing semantics. New operational inequalities are derived that are typical of the presence of synchronization and that were therefore not considered in queuing network models. An interesting application of the operational laws to the statement and the efficient solution of problems related to the estimation of performance bounds insensitive to the timing probability distributions is shown. The results obtained generalize and improve in a clear setting results that were derived in the last few years for several different subclasses of timed Petri nets. In particular, the extension to well-formed colored nets appears straightforward and allows an efficient exploitation of model symmetries View full abstract»

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  • Synthesis of GSPN models for workload mapping on concurrent architectures

    Page(s): 204 - 215
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    Construction of GSPN models of complex systems is a difficult task that often demands significant expertise. Faithful representation of detailed behavioral semantics and overall correctness usually require a significant number of iterations and refinements. This modeling effort is substantially hindering widespread application of Petri net based techniques to ever complex systems. One of the many application areas where this modeling problem arises is distribution of computation workload onto concurrent MIMD architectures. An approach based on the automatic generation of GSPN models for workload mapping on concurrent architectures is described. The methodology is based on the synthesis of a net starting from a precedence graph of the computation. The construction of a complete net modeling the MIMD architecture under a specified workload is possible for a given set of architectures. Nets generated by the synthesis process exhibit higher complexity than manually generated ones, but this is not a serious drawback since net solutions and performance estimates can be derived using standard analysis tools (GreatSPN) View full abstract»

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  • Conflict sets in colored Petri nets

    Page(s): 76 - 85
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    Generalized stochastic Petri nets provide the modeller with immediate transitions, but a model will be correct only if the modeller can specify how to solve the firing conflicts between these transitions. This task is usually cumbersome and may be impossible for large nets. In confusion-free nets, these conflict sets are subsets of equivalence classes of a structural conflict relation, which greatly simplifies the previous task. The authors solve the problem of detecting confusion in colored stochastic Petri nets and computing the equivalence classes of the structural conflict relation. The approach relies on two techniques: the symbolic representation of structural relations and the definition of operations on these symbolic relations. Combined with the lumping method presented by G. Chiola et al. (1991), the algorithm could be the basis of an efficient tool for the analysis of colored generalized stochastic Petri nets View full abstract»

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  • Queueing Petri Nets-A formalism for the combined qualitative and quantitative analysis of systems

    Page(s): 14 - 23
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    System analysis is often needed with respect to both qualitative and quantitative aspects. In recent decades, several formalisms have been developed that attempt to combine these aspects in one description. Present emphasis is on stochastic Petri nets. One disadvantage of these formalisms is the difficulties when describing scheduling strategies with Petri net elements. A new version of queuing Petri nets (QPNs), which combines queuing networks and Petri nets, aiming at eliminating these disadvantages is described. The new version also exhibits the modeling of timed transitions and timeless queues for describing pure scheduling mechanisms. QPNs are a superset of queueing networks and (generalized stochastic) Petri nets. The analysis of QPNs is discussed, and it is shown that efficient analysis techniques from Petri net theory can be exploited for analysis of QPNs, thus supporting the general objective of combining Petri net and queueing network formalisms View full abstract»

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  • Aggregation and reduction techniques for hierarchical GCSPNs

    Page(s): 216 - 225
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    The classes of stochastic well-formed colored nets (SWNs) and hierarchical generalized colored stochastic Petri nets (HGCSPNs) have been recently introduced for the specification and analysis of complex systems. SWNs allow the specification of models including symmetries in a very compact way and additionally can be used to generate a reduced Markov chain (MC) from the net specification by exploiting symmetries in the model. HGCSPNs allow a modular specification of a net using several smaller parts. This decomposition of the net specification can also be used to handle the state explosion of the underlying MC by describing the generator matrix using only much smaller subnet matrices. The author combines SWNs and HGCSPNs, allowing the automatic generation of a reduced MC from the hierarchical net specification. Approximative aggregation techniques for hierarchical nets are introduced View full abstract»

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  • Automated time scale decomposition and analysis of stochastic Petri nets

    Page(s): 248 - 257
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    The automated application of time-scale decomposition to stochastic Petri nets is studied. Time-scale decomposition exploits the tendency of a system to approach a short-term equilibrium between relatively rare events and has been extensively studied in the context of Markov chains and queuing networks. Previous approaches for applying time-scale decomposition to SPN models relied heavily upon human insight in ways what hampered algorithmic implementation. A simple and effective method for specifying the time-scale decomposition of a SPN is presented, and solution techniques that take advantage of structural information from the SPN are described View full abstract»

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  • GSPN modelling methods for performance and dependability evaluation of a real-life flexible manufacturing system

    Page(s): 290 - 299
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    Generalized stochastic Petri nets (GSPNs) are used to model and analyze a real flexible manufacturing system (FMS). First, performance and dependability evaluation are applied to a real-life system. A global system is decomposed to reduce the complexity evaluation. Temporal analysis is used to derive performance measures such as the average production per day. Second, a solution is proposed to increase the production rate by introducing buffers with finite capacity and a reorganization of jobs on different production lines View full abstract»

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  • On the structural and behavioural characterization of P/T nets

    Page(s): 66 - 75
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    Deadlocks and traps are well-known net structures that may be identified to characterize the behavior of nets. These structures have been defined on ordinary nets (with arc multiplicity 1). Although they can be computed on generalized nets (with arc multiplicity ⩾ 1), their relation with behavioral properties becomes less clear in this case. Similar problems may be found in the definition of conflicts: the structural concept is defined in terms of sharing of input places, while the behavioral definition of conflict is usually introduced in the framework of safe nets. A redefinition of some behavioral properties for P/T nets in their general case is attempted in order to have a better correspondence between behavioral and structural properties View full abstract»

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  • A reactive real-time systems modelling and programming aid tool based on the synchronous Petri nets formalism

    Page(s): 34 - 43
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    The design and the implementation of a reactive real-time system modeling and programming tool based on the synchronous Petri nets formalism (SynPN) are presented. This formalism combines the advantages of two existing formalisms: the synchronous languages (SL) and the Petri nets (PN). The SynPN basic assumptions and the synchronous interpretation principles are explained, illustrated with examples. The SynPN formal definition is given as well as the interpretation algorithm. The SynPN based tool, which aids in reactive real-time system modeling and programming is introduced. The modeling and the programming of a chronometer using the SynPN formalism are addressed View full abstract»

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  • On scalable net modeling of OLTP

    Page(s): 270 - 279
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    Practical experiments with the net modeling of OLTP (online transaction processing) applications are discussed. The goal was to propose a convenient and flexible model that would be easy to modify with respect to different scheduling algorithms, number of processors, and disks. The parameters of the model may be varied depending on the size of available memory and timing in a model in order to provide the necessary information to analyze the functioning of the system under different transaction rates and conditions, to identify bottlenecks and potential inefficiencies in the system design. The main effort was focused on speeding up the simulation through combining nets with code, using refinement techniques, and exploiting the scalability of colored Petri nets View full abstract»

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  • A characterization of independence for competing Markov chains with applications to stochastic Petri nets

    Page(s): 117 - 126
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    It is shown that recently obtained product form results for stochastic Petri nets can immediately be obtained as a special case of a simple exclusion mechanism for the product process of a collection of Markov chains. The model is described, and several examples of exclusion/competition mechanisms that can be modeled in the framework of this paper are given View full abstract»

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  • Quantitative evaluation of discrete event systems: Models, performances and techniques

    Page(s): 2 - 11
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    Assuming that with the increasing complexity of new architectures, modeling and performance evaluation of discrete event systems are more and more necessary, the authors present some general remarks on the modeling concept. Queuing networks, whose theory has been stimulated by needs in the computing field, are presented, together with the main ideas of their general solution. A more recent formalism, that of extended Petri nets, is presented. This formalism allows more sophisticated Markovian models to be solved mathematically View full abstract»

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  • Fast simulation of rare events in stochastic Petri nets

    Page(s): 238 - 247
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    It is shown how variance reduction techniques can be used simulating rare events in stochastic Petri nets. The application of fast simulation methods is illustrated for several classes of stochastic Petri nets: GSPNs, deterministic and stochastic Petri nets, and Petri nets with generally distributed firing times are studied. For the latter case, different state change policies such as resampling and age memory are distinguished. Some experiments show the usefulness of this approach View full abstract»

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  • Definition of the model-"Stochastic timed well formed coloured nets"

    Page(s): 24 - 33
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    A model able to deal with the main characteristics of the real-time distributed systems (complex systems with a big number of components; systems with a lot of different time characteristics and, in particular, time constraints) is defined. The stochastic timed well-formed colored nets (STWN model) are based on two underlying models: the well-formed colored nets (WN) which provide both a concise and a structured representation and are well adapted for representing big systems composed of sets of components with a common behavior, and the stochastic timed Petri nets (STPN model) which have the ability to deal with combinations of arbitrary distribution (exponential, deterministic (time 0 and ± 0), uniform and mixed) and are well adapted for representing systems with time constraints (time critical systems). The analysis of the dynamic behavior of an STWN model is based on an object called the randomized symbolic state graph, which is an aggregated semi-Markov process which allows a lot of performance evaluations. Simple and illustrative examples showing the advantage of the STWN model are presented View full abstract»

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  • A methodology for formal expression of hierarchy in model solution

    Page(s): 258 - 267
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    A methodology for formal specification of hierarchy both in model specification and model solution is presented. Hierarchy is allowed to exist among different model types used in performance and dependability modeling. This offers a lot of flexibility and power to the modeler. The methodology presents a unified view of a variety of modeling techniques such as hierarchical composition, behavioral decomposition, iterative hierarchical modeling, reward-based performability modeling, aggregation, etc. This methodology brings the hierarchical modeling technique(s), based on which the model is constructed, to the fore. The results in a better understanding of the model by the user and it can simplify model validation if need be. Such a methodology would also make the design of modeling toolkits, which allow these modeling techniques, much simpler by presenting a conceptually simpler and unified view of a variety of modeling techniques. The formal expression is also expected to assist the modeler in construction of large, complex models View full abstract»

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  • Validation and performance analysis of network algorithms by coloured Petri nets

    Page(s): 280 - 289
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    Different usage parameter control (UPC) algorithms for high-speed asynchronous transfer mode (ATM) networks are studied. The purpose of the UPC algorithms is to prevent congestion in the network by monitoring input traffic and marking the excess traffic. Four UPC algorithms are modeled by means of hierarchical colored Petri nets with time. The purpose of the model is validation and performance analysis of the algorithms. The behavior of each algorithm is investigated when confronted with different kinds of traffic sources, e.g., video or videophony. The investigations determine the triggered jumping window algorithm to be the most suitable for a majority of traffic types. The use of colored Petri nets as a modeling and simulation language is discussed View full abstract»

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  • Computing bounds for the performance indices of quasi-lumpable stochastic well-formed nets

    Page(s): 148 - 157
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    The stochastic well-formed colored Petri net (SWN) formalism and the associated reachability graph (RG). The method for computing bounds of quasi-lumpable Markov chains is summarized. A structural analysis algorithm to check whether a given SWN is quasi-lumpable, and a modified symbolic RG (SRG) generation algorithm for the generation of the aggregate MC used for the bounds computation are described. Two application examples are shown View full abstract»

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  • Algorithms for product-form stochastic Petri nets-A new approach

    Page(s): 108 - 116
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    A general relationship between utilizations in product-form stochastic Petri nets (PF-SPNs) is used to derive a method for calculating the normalizing constant. The method collects the contributions of many states together as geometric sums and in general provides a recursive algorithm with numerical complexity independent of the size of the initial marking. The technique is applied to some simple examples, and closed-form solutions are obtained for the normalizing constant View full abstract»

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  • Parallel architectures with regular structure: A case study in modelling using stochastic well-formed coloured Petri nets

    Page(s): 226 - 235
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    It is shown how to study the latency of packets exchanged by MIMD distributed memory architectures with regular structures. To reach this goal, the single node, the architecture topology, the routing algorithm, and the flow control algorithm are modeled. Models have been built with the formalism of stochastic well-formed coloured Petri nets (SWNs) having in mind modularity. Different types of nodes, topology, routing, and flow control are modeled in isolation and are then intermixed to study different architectures. To achieved simplicity and modularity, SWNs are used to their full power, so that this work constitutes quite a complete example of modeling with SWNs View full abstract»

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  • A characterization of the stochastic process underlying a stochastic Petri net

    Page(s): 170 - 179
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    Stochastic Petri nets (SPNs) with generally distributed firing times are isomorphic to generalized semi-Markov processes (GSMPs), but simulation is the only feasible approach for their solution. The authors explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPNs), deterministic and stochastic Petri nets (DSPNs), semi-Markovian stochastic Petri nets (SM-SPNs), timed Petri nets (TPNs), and generalized timed Petri nets (GTPNs) are particular entries in the hierarchy. Additional classes of SPNs for which it is shown how to compute an analytical solution are obtained by the method of the embedded Markov chain (DSPNs are just one example in this class) and state discretization, which the authors apply not only to the continuous-time case (PH-type distributions), but also to the discrete case View full abstract»

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  • Towards a simplified building of time Petri Nets reachability graph

    Page(s): 46 - 47
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    An enumerative approach for time Petri nets (or Melin's model) analysis is presented. In this model, if a transition t is enabled at time τ, it can be fired at any time in the interval [τ+tmax(t)]. It is shown that the firing condition at the nth firing can be expressed by the means of the marking, the enabling point of enabled transitions, and the minimal and maximal elapsed time between to firings. This result leads to an attractive definition of state classes and allows a simple computation of reachable state classes. The approach presented has two main advantages. First, the computation of reachable state classes is more simple and does not require any solution of a system. Second, the graph obtained is a subgraph of that given by M. Menasche (1982) View full abstract»

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