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Throughput analysis of synchronous data flow graphs
 In ACSD’06, Proc. (2006), IEEE
, 2006
"... Synchronous Data Flow Graphs (SDFGs) are a useful tool for modeling and analyzing embedded data flow applications, both in a single processor and a multiprocessing context or for application mapping on platforms. Throughput analysis of these SDFGs is an important step for verifying throughput requir ..."
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Cited by 41 (16 self)
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Synchronous Data Flow Graphs (SDFGs) are a useful tool for modeling and analyzing embedded data flow applications, both in a single processor and a multiprocessing context or for application mapping on platforms. Throughput analysis of these SDFGs is an important step for verifying throughput requirements of concurrent realtime applications, for instance within designspace exploration activities. Analysis of SDFGs can be hard, since the worstcase complexity of analysis algorithms is often high. This is also true for throughput analysis. In particular, many algorithms involve a conversion to another kind of data flow graph, the size of which can be exponentially larger than the size of the original graph. In this paper, we present a method for throughput analysis of SDFGs, based on explicit statespace exploration and we show that the method, despite its worstcase complexity, works well in practice, while existing methods often fail. We demonstrate this by comparing the method with stateoftheart cycle mean computation algorithms. Moreover, since the statespace exploration method is essentially the same as simulation of the graph, the results of this paper can be easily obtained as a byproduct in existing simulation tools. 1
A Comparison of Performance Evaluation Process Algebra and Generalized Stochastic Petri Nets
 In Proc. 6th International Workshop on Petri Nets and Performance Models
, 1995
"... Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the mo ..."
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Cited by 34 (8 self)
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Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the modeller, considering both the definition and the analysis of the performance model. Our goal is to provide a better understanding of both formalisms, and to prepare a fertile ground for exchanging ideas and techniques between the two. To illustrate similarities and differences, we make the different issues more concrete by means of an example modelling resource contention. 1 Introduction In this paper we present a comparison of two formalisms which may be used to develop performance models as continuous time Markov chains (CTMC). Generalized stochastic Petri nets (GSPN) is a wellestablished high level modelling paradigm which has been widely applied in performance analysis. In contrast, Per...
Properties and Performance Bounds for Closed Free Choice Synchronized Monoclass Queueing Networks
 IEEE Transactions on Automatic Control
, 1991
"... Several proposals exist for the introduction of synchronization constraints into Queueing Networks (QN). We show that many monoclass QN with synchronizations can naturally be modelled with a subclass of Petri Nets (PN) called Free Choice nets (FC), for which a wide gamut of qualitative behavioural a ..."
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Cited by 32 (21 self)
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Several proposals exist for the introduction of synchronization constraints into Queueing Networks (QN). We show that many monoclass QN with synchronizations can naturally be modelled with a subclass of Petri Nets (PN) called Free Choice nets (FC), for which a wide gamut of qualitative behavioural and structural results have been derived. We use some of these net theoretic results to characterize the ergodicity, boundedness and liveness of closed Free Choice Synchronized Queueing Networks (FCSQN). Moreover we define upper and lower throughput bounds based on the mean value of the service times, without any assumption on the probability distributions (thus including both the deterministic and the stochastic cases). We show that monotonicity properties exist between the throughput bounds and the parameters of the model in terms of population and service times. We propose (theoretically polynomial and practically linear complexity) algorithms for the computation of these bounds, based on ...
Properties and Performance Bounds for Timed Marked Graphs
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS  I: FUNDAMENTAL THEORY AND APPLICATIONS
, 1992
"... A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performan ..."
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Cited by 22 (8 self)
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A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performance models. In particular, ergodicity is derived from boundedness and liveness of the underlying Petri net representation, which can be efficiently computed in polynomial time on the net structure. In case of unbounded (i.e., nonstronglyconnected) marked graphs, ergodicity is computed as a function of the average transition firing delays. Then the problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic marked graphs is studied. In particular, linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., attainable) bounds for the throughput of transitions for marked graphs with dete...
Operational Analysis of Timed Petri Nets and Application to the Computation of Performance Bounds
 In Proceedings 5th International Workshop on Petri Nets and Performance Models  PNPM93
, 1993
"... We use operational analysis techniques to partially characterize the behaviour 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 queueing ne ..."
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Cited by 21 (8 self)
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We use operational analysis techniques to partially characterize the behaviour 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 queueing network models. We show 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. 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 WellFormed Coloured nets appears straightforward and allows an efficient exploitation of models symmetries. 1 Introduction Operational analysis is a conceptually very simple way of deriving mathematical equations relating observable quantities in queueing systems [11]. In...
Structural Techniques and Performance Bounds of Stochastic Petri Net Models
 Advances in Petri Nets 1992, volume 609 of Lecture Notes in Computer Science
, 1992
"... In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an "autonomou ..."
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Cited by 21 (10 self)
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In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an "autonomous" Petri net or as a generalization of classical queueing networks with the addendum of a general synchronization primitive. It constitutes an adequate tool for both the validation of logical properties and the evaluation of performance measures of concurrent and distributed systems. Qualitative and quantitative understandings of Petri net models are stressed here making special emphasis on structural techniques for the analysis of logical and performance properties. Important aspects from the performance point of view, such as relative throughput of stations (transitions), and number of servers present at them, are related to Petri net concepts like P or Tsemiflows or liveness bounds...
Recent Developments in NonMarkovian Stochastic Petri Nets
, 1998
"... Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in ..."
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Cited by 21 (4 self)
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Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This paper reviews recent developments by providing the theoretical background and the possible areas of application. Markovian Petri nets are first considered together with very well established extensions known as Generalized Stochastic Petri nets and Stochastic Reward Nets. Key ideas for coping with large state spaces are then discussed. The challenging area of nonMarkovian Petri nets is considered, and the related analysis techniques are surveyed together with the detailed elaboration of an example. Finally new models based on Continuous or Fluid Stochastic Petri Nets are briefly discussed.
Performance Analysis of Stochastic Timed Petri Nets using Linear Programming Approach
 IEEE Transactions on Software Engineering
, 1995
"... 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. ..."
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Cited by 16 (0 self)
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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 programming.
Performance analysis of concurrent systems with early evaluation
 In Proceedings International Conference on ComputerAided Design
, 2006
"... Early evaluation allows to execute operations when enough information at the inputs has been received to determine the value at the outputs. Systems that can tolerate variablelatency units, such as latencyinsensitive or asynchronous systems, can enhance their performance by using early evaluation. ..."
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Cited by 10 (6 self)
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Early evaluation allows to execute operations when enough information at the inputs has been received to determine the value at the outputs. Systems that can tolerate variablelatency units, such as latencyinsensitive or asynchronous systems, can enhance their performance by using early evaluation. The most relevant example of a unit with early evaluation is the multiplexor: the output can be determined as soon as the information of the selected channel arrives, without waiting for the other channels. This paper analyzes the potential impact of early evaluation in concurrent systems. An analytical model, based on a Petri net extension with early firing is proposed to estimate the performance. The reduction of the analytical model to a linear programming formulation for an efficient estimation of the upper bound for the system throughput is proposed. The results show the accuracy of the model and the benefits of early evaluation. 1.
Improving Throughput Upper Bounds for Net Based Models of Manufacturing Systems
, 1992
"... This paper addresses the improvement of throughput upper bounds for live and bounded stochastic Petri nets, presented by the authors in previous works. The introduction of a greater amount of structural information, traps and implicit places, allows to improve the bounds using linear programming pro ..."
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Cited by 8 (8 self)
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This paper addresses the improvement of throughput upper bounds for live and bounded stochastic Petri nets, presented by the authors in previous works. The introduction of a greater amount of structural information, traps and implicit places, allows to improve the bounds using linear programming problems defined on the net structure, on the routing probabilities, and on the mean service time of transitions. The obtained bounds can be applied for the analysis of manufacturing systems modelled by means of stochastic Petri nets. An example is presented and evaluated using the introduced techniques. 1 INTRODUCTION Timed and stochastic Petri nets constitute an adequate model for the evaluation of performance measures of concurrent and distributed systems (see, e.g., [1, 2, 3, 4]). Nevertheless, one of the main problems in the actual use of these models for the evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. The computation of upper ...