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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 30 (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 ...
Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector
 IEEE Transactions on Software Engineering
, 1991
"... This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, defined as having a unique consistent ..."
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Cited by 25 (13 self)
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This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, defined as having a unique consistent firing count vector, independently of the stochastic interpretation of the net model. In particular, persistent and monoTsemiflow nets subclasses are considered. Upper and lower throughput bounds are computed using linear programming problems defined on the incidence matrix of the underlying net. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). From a different perspective, the considered subclasses of stochastic nets can be viewed as special classes of synchronized queueing networks, thus the proposed bounds can be applied to these networks. ...
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 16 (7 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...
Concurrent Execution Of Timed Petri Nets
 Proceedings of the 1994 Winter Simulation Conference
, 1994
"... The dynamics of discrete event systems can be effectively described and analyized using the timed Petri net formalism. The aim of this paper is to comprehensively present the achievements attained in accelerating Petri net executions by using parallel or distributed multiprocessing environments. The ..."
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Cited by 15 (7 self)
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The dynamics of discrete event systems can be effectively described and analyized using the timed Petri net formalism. The aim of this paper is to comprehensively present the achievements attained in accelerating Petri net executions by using parallel or distributed multiprocessing environments. The basic problem is to generate concurrent Petri net executions insuring correctness in the sense that the partial ordering of transition firings produced is consistent with the total event ordering that would be produced by a (hypothetical) sequential execution. Two lines of thought have been followed: in parallel simulations transition firings evolve as governed by a SIMD iteration mechanism. Distributed simulations aim at a proper synchronization of firings in spatially different net parts to avoid timing inconsistencies and alterations of the execution behavior. In both cases, structural properties of the underlying Petri net can be efficiently used to simplify and/or accelerate concurrent...
Tight Polynomial Bounds for SteadyState Performance of Marked Graphs
, 1989
"... 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., reachable) bounds for the t ..."
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Cited by 14 (11 self)
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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., reachable) bounds for the throughput of transitions for live and bounded Marked Graphs with time associated with transitions. These bounds depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed. 1 Introduction One of the main problems in the actual use of timed and stochastic Petri net models for the performance evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. Exact performance results are usually obtained from the numerical solu...
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 14 (9 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...
Latency and Throughput Tradeoffs in SelfTimed SpeedIndependent Pipelines and Rings
, 1990
"... Asynchronous pipelines control the flow of tokens through a sequence of logical stages based on the status of local completion detectors. As in a synchronously clocked circuit, the design of selftimed pipelines can trade off between achieving low latency and high throughput. However, there are m ..."
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Cited by 12 (1 self)
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Asynchronous pipelines control the flow of tokens through a sequence of logical stages based on the status of local completion detectors. As in a synchronously clocked circuit, the design of selftimed pipelines can trade off between achieving low latency and high throughput. However, there are more degrees of freedom because of the variances in specific latch and function block styles, and the possibility of varying both the number of latches between function blocks and their connections to the completion detectors. This report demonstrates the utility of a graphbased methodology for analyzing the timing dependencies and uses it to make comparisons of different configurations. It is shown that the extremes for high throughput and low latency differ significantly, the placement of the completion detectors influences timing as much as adding an additional latch, and the choice as to whether or static logic is best is dependent on the cost in complexity of the completion detectors.
EventBased Modelling of Ecological Systems With Asynchronous Cellular Automata
 Gale Research
, 1997
"... In this article, we give an example for the modelling of ecological systems with cellular automata based on the description of cell's behaviour by Petri nets. Petri nets offer a formal modelling technique with eventbased, concurrent, asynchronous state changes where graphical symbols are used ..."
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Cited by 10 (0 self)
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In this article, we give an example for the modelling of ecological systems with cellular automata based on the description of cell's behaviour by Petri nets. Petri nets offer a formal modelling technique with eventbased, concurrent, asynchronous state changes where graphical symbols are used for the description of states resp. state changes. This allows the formal description of cellular automata with asynchronous cells' behaviour within one synchronous time phase of the automaton; i. e., within one time phase of the whole automaton, many asynchronous `ministeps' of cells can appear. This can be used e. g. to model moving individuals that cross an arbitrary number of cells within one time phase. By this attempt, a large class of individualoriented models can be defined in a more abstract and formal manner than it can be done by computer simulation programs. Since Petri nets allow a graphical representation of the modelled cells' behaviour, interactions, dependencies or causeeff...
Accepting Zeno words: a way towards timed refinements
, 2000
"... . Timed models were introduced to describe the behaviors of realtime systems and they were usually required to produce only executions with divergent sequences of times. However, when some physical phenomena are represented by convergent executions, Zeno words appear in a natural way. Moreover, ..."
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Cited by 7 (2 self)
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. Timed models were introduced to describe the behaviors of realtime systems and they were usually required to produce only executions with divergent sequences of times. However, when some physical phenomena are represented by convergent executions, Zeno words appear in a natural way. Moreover, time can progress if such an infinite execution can be followed by other ones. Therefore, in a first part, we extend the definition of timed automata, allowing to generate sequences of infinite convergent executions, while keeping good properties for the verification of systems: emptiness is still decidable. In a second part, we define a new notion of refinement for timed systems, in which actions are replaced by recognizable Zeno (timed) languages. We study the properties of these timed refinements and we prove that the class of transfinite timed languages is the closure of the usual one (languages accepted by Muller or Buchi timed automata) under refinement. 1 Introduction The...
A Reachable Throughput Upper Bound for Live and Safe Free Choice Nets
, 1991
"... This paper addresses the computation of upper bounds for the throughput of transitions of live and safe deterministically or stochastically timed free choice nets. The obtained results are extensions of the marked graph case, presented by the authors in previous works. Polynomial complexity algor ..."
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Cited by 6 (5 self)
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This paper addresses the computation of upper bounds for the throughput of transitions of live and safe deterministically or stochastically timed free choice nets. The obtained results are extensions of the marked graph case, presented by the authors in previous works. Polynomial complexity algorithms are derived using linear programming techniques. The obtained values are tight in the sense that, with the only knowledge of the net topology, the mean service times of transitions, and the routing rates at conflicts, is not possible to improve the bounds. Topics: Timed and stochastic nets. Analysis and synthesis, structure, and behaviour of nets. 1 Introduction One of the main problems in the actual use of timed and stochastic Petri net models for the performance evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain ...