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An Algorithm for Exact Bounds on the Time Separation of Events in Concurrent Systems
 IEEE Trans. on Comp
, 1995
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Maxplus algebra and system theory: Where we are and where to go now
 Annu. Rev. Control
, 1999
"... Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison ..."
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Cited by 42 (18 self)
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Abstract: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which maxplus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison with classical linear system theory, there are areas which are practically untouched, mostly because the corresponding mathematical tools are yet to be fabricated. This is the case of the geometric approach of systems which is known, in the classical theory, to provide another important insight to systemtheoretic and controlsynthesis problems, beside the algebraic machinery. A preliminary discussion of geometric aspects in the maxplus algebra and their use for system theory is proposed in the last part of the paper. Résumé: Plus de seize ans après le début d’une théorie linéaire de certains systèmes à événements discrets dans laquelle l’algèbre maxplus et autres outils algébriques assimilés jouent un rôle central, ce papier cherche àdécrire quelques uns des principaux résultats obtenus de façon informelle, en s’appuyant sur des exemples. Par comparaison avec la théorie classique des systèmes linéaires, il existe des domaines pratiquement vierges, surtout en raison du fait que les outils mathématiques correspondants restent à forger. C’est en particulier le cas de l’approche géométrique des systèmes qui, dans la théorie classique, est connue pour apporter un autre regard important sur les questions de théorie des systèmes et de synthèse de lois de commandes àcôté de la machinerie purement algébrique. Une discussion préliminaire sur les aspects géométriques de l’algèbre maxplus et leur utilité pour la théorie des systèmes est proposée dans la dernière partie du papier.
Performance Evaluation of (max,+) Automata
 IEEE Trans. on Automatic Control
, 1993
"... Automata with multiplicities over the (max,+) semiring can be used to represent the behavior of timed discrete event systems. This formalism which extends both conventional automata and (max,+) linear representations covers a class of systems with synchronization phenomena and variable schedules. Pe ..."
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Cited by 35 (8 self)
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Automata with multiplicities over the (max,+) semiring can be used to represent the behavior of timed discrete event systems. This formalism which extends both conventional automata and (max,+) linear representations covers a class of systems with synchronization phenomena and variable schedules. Performance evaluation is considered in the worst, mean, and optimal cases. A simple algebraic reduction is provided for the worst case. The last two cases are solved for the subclass of deterministic series (recognized by deterministic automata). Deterministic series frequently arise due to the finiteness properties of (max,+) linear projective semigroups. The mean performance is given by the Kolmogorov equation of a Markov chain. The optimal performance is given by a HamiltonJacobiBellman equation. KeywordsDiscrete Event Systems, (max,+) algebra, Automata, Rational Series, Performance Evaluation I. INTRODUCTION A UTOMATA with multiplicities [10] over the (max,+) or the dual (min,+) s...
Stationary Ergodic Jackson Networks: Results and CounterExamples
, 1996
"... This paper gives a survey of recent results on generalized Jackson networks, where classical exponential or i.i.d. assumptions on services and routings are replaced by stationary and ergodic assumptions. We first show that the most basic features of the network may exhibit unexpected behavior. Sever ..."
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Cited by 7 (1 self)
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This paper gives a survey of recent results on generalized Jackson networks, where classical exponential or i.i.d. assumptions on services and routings are replaced by stationary and ergodic assumptions. We first show that the most basic features of the network may exhibit unexpected behavior. Several probabilistic properties are then discussed, including a strong law of large numbers for the number of events in the stations, the existence, uniqueness and representation of stationary regimes for queue size and workload.
Specification, Simulation, and Verification of Timing Behavior
, 1993
"... Temporal behavior needs to be formally specified, validated, and verified, if systems that interface with the outside world are to be synthesized from highlevel specifications. Due to the high level of abstraction, the work presented in this thesis applies to systems that ultimately can be implem ..."
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Cited by 1 (0 self)
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Temporal behavior needs to be formally specified, validated, and verified, if systems that interface with the outside world are to be synthesized from highlevel specifications. Due to the high level of abstraction, the work presented in this thesis applies to systems that ultimately can be implemented using hardware, software, or a combination of both. In the area of specification, a generalization of the eventgraph specification paradigm is presented. The model supports the expression of complex functionalty using an operational semantics and cleanly integrates structure into the eventbased paradigm. Temporal relationships between systems events are specified using a denotational semantics that relies on both chronological and causal relationships to identify the discrete event occurrences bei...
and CounterExamples
, 1996
"... Jackson networks; stability; stationary regime; ergodic theory 1 INRIA SophiaAntipolis, France. 2 Novosibirsk State University, Russia. This paper gives a survey of recent results on generaIized Jackson networks, where classical exponential or i.i.d. assumptions on services and routings. are I&quo ..."
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Jackson networks; stability; stationary regime; ergodic theory 1 INRIA SophiaAntipolis, France. 2 Novosibirsk State University, Russia. This paper gives a survey of recent results on generaIized Jackson networks, where classical exponential or i.i.d. assumptions on services and routings. are I"~placed by stationary and. ergodic assumptIOns. We first show that the most basIc features of the network may exhibit unexpected behaviour. Several probabilistic properties are then discussed, including a strong law of large numbers for the number of events in the stations, the existence, uniqueness and representation of stationary regimes for queue size and workload.