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The Möbius Modeling Tool
 IN PROCEEDINGS OF THE 9TH INTERNATIONAL WORKSHOP ON PETRI NETS AND PERFORMANCE MODELS
"... Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usef ..."
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Cited by 73 (12 self)
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Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usefulness of such tools to practitioners, and hampers new and existing formalisms and solvers. This paper describes the method that a new modeling tool, cal led Mobius, uses to eliminate these limitations. Mobius provides an infrastructure to support multiple interacting formalisms and solvers, and is extensible in that new formalisms and solvers can be added to the tool without changing those already implemented. Mobius provides this capability through the use of an abstract functional interface, which provides a formalismindependent interface to models. This allows models expressed in multiple formalisms to interact with each other, and with multiple solvers.
Modeling and Analysis of Timed Petri Nets Using Heaps of Pieces
, 1997
"... We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. Fo ..."
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Cited by 55 (18 self)
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We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. For a subclass including all safe Free Choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components). We illustrate the heapbased modeling by the typical case of safe jobshops. For a periodic schedule, we obtain a heapbased throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules. Keywords Timed Petri nets, automata with multiplicities, heaps of pieces, (max,+) semiring, scheduling. I. Introduction The purpose of this paper 1 is to prove the following result: Timed safe Pe...
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 36 (16 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 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 ...
A Formal Approach to the Integration of Performance Aspects in the Modeling and Analysis of Concurrent Systems
 Information and Computation
, 1998
"... A formal approach for modeling and analyzing concurrent systems is proposed which integrates performance characteristics in the early stages of the design process. The approach relies on both stochastically timed process algebras and stochastically timed Petri nets in order to exploit their compleme ..."
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Cited by 29 (13 self)
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A formal approach for modeling and analyzing concurrent systems is proposed which integrates performance characteristics in the early stages of the design process. The approach relies on both stochastically timed process algebras and stochastically timed Petri nets in order to exploit their complementary advantages. The approach is instantiated to the case of EMPA (Extended Markovian Process Algebra), introduced together with the collection of its four semantics and the notion of equivalence that are required in order to implement the approach. Finally, the case study of the alternating bit protocol is presented to illustrate the adequacy of the approach. 1
A Modeling Framework to Implement Preemption Policies in NonMarkovian SPNs
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2000
"... ... this paper, we consider, in particular, the class of stochastic Petri nets whose marking process can be mapped into a Markov regenerative process. An adequate mathematical framework is developed to deal with the considered class of Markov Regenerative Stochastic Petri Nets (#####). An unified ..."
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Cited by 23 (4 self)
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... this paper, we consider, in particular, the class of stochastic Petri nets whose marking process can be mapped into a Markov regenerative process. An adequate mathematical framework is developed to deal with the considered class of Markov Regenerative Stochastic Petri Nets (#####). An unified approach for the solution of #####s where different preemption policies can be defined in the same model is presented. The solution is provided both in steadystate and in transient condition. An example concludes the paper.
State Space Construction and SteadyState Solution of GSPNs on a SharedMemory Multiprocessor
, 1997
"... A common approach for the quantitative analysis of a generalized stochastic Petri net (GSPN) is to generate its entire state space and then solve the corresponding continuoustime Markov chain (CTMC) numerically. This analysis often suffers from two major problems: the state space explosion and the ..."
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Cited by 23 (4 self)
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A common approach for the quantitative analysis of a generalized stochastic Petri net (GSPN) is to generate its entire state space and then solve the corresponding continuoustime Markov chain (CTMC) numerically. This analysis often suffers from two major problems: the state space explosion and the stiffness of the CTMC. In this paper we present parallel algorithms for sharedmemory machines that attempt to alleviate both of these difficulties: the large main memory capacity of a multiprocessor can be utilized and long computation times are reduced by efficient parallelization. The algorithms comprise both CTMC construction and numerical steadystate solution. We give experimental results obtained with a Convex SPP16 sharedmemory multiprocessor that show the behavior of the algorithms and the parallel speedups obtained.
Preemptive Repeat Identical Transitions in Markov Regenerative Stochastic Petri Nets
 In 6th International Conference on Petri Nets and Performance Models  PNPM95
, 1995
"... The recent literature on Markov Regenerative Stochastic Petri Nets (MRSPN) assumes that the random firing time associated to each transition is resampled each time the transition fires or is disabled by the firing of a competitive transition. This modeling assumption does not cover the case of preem ..."
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Cited by 22 (14 self)
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The recent literature on Markov Regenerative Stochastic Petri Nets (MRSPN) assumes that the random firing time associated to each transition is resampled each time the transition fires or is disabled by the firing of a competitive transition. This modeling assumption does not cover the case of preemption mechanisms of repeat identical nature (pri). In this policy, an interrupted job must be repeated with an identical requirement so that its associated random variable must not be resampled. The paper investigates the implication of a pri policy into a MRSPN and describes an analytical procedure for the derivation of expressions for the transient probabilities. Key words: Stochastic Petri Nets, SemiMarkov Reward Models, Markov regenerative processes, preemptive repeat identical policy. 1 Introduction The analysis of stochastic systems with nonexponential timing is of increasing interest in the literature and requires the development of suitable modeling tools. Choi et al. have shown ...
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 22 (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.