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208
On Deterministic Traffic Regulation and Service Guarantees: A Systematic Approach by Filtering
 IEEE Transactions on Information Theory
, 1997
"... In this paper, we develop a filtering theory for deterministic traffic regulation and service guarantees under the (min; +)algebra. We show that traffic regulators that generate fupper constrained outputs can be implemented optimally by a linear time invariant filter with the impulse response f ..."
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Cited by 62 (4 self)
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In this paper, we develop a filtering theory for deterministic traffic regulation and service guarantees under the (min; +)algebra. We show that traffic regulators that generate fupper constrained outputs can be implemented optimally by a linear time invariant filter with the impulse response f under the (min; +)algebra, where f is the subadditive closure defined in the paper. Analogous to the classical filtering theory, there is an associate calculus, including feedback, concatenation, "filter bank summation" and performance bounds. The calculus is also applicable to the recently developed concept of service curves that can be used for deriving deterministic service guarantees. Our filtering approach not only yields easier proofs for more general results than those in the literature, but also allows us to design traffic regulators via systematic methods such as concatenation, filter bank summation, linear system realization, and FIRIIR realization. We illustrate the use of ...
Fault detection and diagnosis in distributed systems: an approach by partially stochastic Petri nets
 special issue on Hybrid Systems
, 1998
"... We address the problem of alarm correlation in large distributed systems. The key idea is to make use of the concurrence of events in order to separate and simplify the state estimation in a faulty network. Petri nets and their causality semantics are used to model concurrency. Special partially ..."
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Cited by 53 (10 self)
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We address the problem of alarm correlation in large distributed systems. The key idea is to make use of the concurrence of events in order to separate and simplify the state estimation in a faulty network. Petri nets and their causality semantics are used to model concurrency. Special partially stochastic Petri nets are developed, that establish some kind of equivalence between concurrence and independence. The diagnosis problem is defined as the computation of the most likely history of the net given a sequence of observed alarms. Solutions are provided in four contexts, with a gradual complexity on the structure of observations.
Theories and Models for Internet Quality of Service
, 2002
"... We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated serv ..."
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Cited by 49 (1 self)
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We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated services, and streaming media playback delays. We also present mechanisms and architecture for scalable support of guaranteed services in the Internet, based on the concept of a stateless core. Methods for scalable control operations are also briefly discussed. We then turn our attention to statistical performance guarantees, and describe several new probabilistic results that can be used for a statistical dimensioning of differentiated services. Lastly, we review recent proposals and results in supporting performance guarantees in a best effort context. These include models for elastic throughput guarantees based on TCP performance modeling, techniques for some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support.
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.
Application of Network Calculus to Guaranteed Service Networks
, 1998
"... We use recent network calculus results to study some properties of lossless multiplexing as it may be used in guaranteed service networks. We call network calculus a set of results that apply minplus algebra to packet networks. We provide a simple proof that shaping a traffic stream to conform to a ..."
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Cited by 37 (6 self)
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We use recent network calculus results to study some properties of lossless multiplexing as it may be used in guaranteed service networks. We call network calculus a set of results that apply minplus algebra to packet networks. We provide a simple proof that shaping a traffic stream to conform to a burstiness constraint preserves the original constraints satisfied by the traffic stream We show how all ratebased packet schedulers can be modeled with a simple rate latency service curve. Then we define a general form of deterministic effective bandwidth and equivalent capacity. We find that call acceptance regions based on deterministic criteria (loss or delay) are convex, in contrast to statistical cases where it is the complement of the region which is convex. We thus find that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to 0 may be strictly larger than the call acceptance region based on lossless mult...
Duality and separation theorems in idempotent semimodules
 Linear Algebra and its Applications 379 (2004), 395–422. Also arXiv:math.FA/0212294
"... Abstract. We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to sep ..."
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Cited by 35 (19 self)
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Abstract. We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert’s projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and halfspaces over the maxplus semiring. 1.
A programming model for timesynchronized distributed realtime systems
 In 13th IEEE Real Time and Embedded Technology and Applications Symposium, 2007. RTAS ’07
, 2007
"... Discreteevent (DE) models are formal system specifications that have analyzable deterministic behaviors. Using a global, consistent notion of time, DE components communicate via timestamped events. DE models have primarily been used in performance modeling and simulation, where time stamps are a m ..."
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Cited by 35 (24 self)
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Discreteevent (DE) models are formal system specifications that have analyzable deterministic behaviors. Using a global, consistent notion of time, DE components communicate via timestamped events. DE models have primarily been used in performance modeling and simulation, where time stamps are a modeling property bearing no relationship to real time during execution of the model. In this paper, we extend DE models with the capability of relating certain events to physical time. We propose a programming model, called PTIDES (Programming Temporally Integrated Distributed Embedded Systems), which has DE semantics, but with carefully chosen relations between model time and real time. Key to making this model effective is to ensure that constraints that guarantee determinacy in the semantics are preserved at runtime. To accomplish this, we give a distributed execution strategy that obeys DE semantics without the penalty of totally ordered executions based on time stamps. Our technique relies on having a distributed common notion of time, known to some precision. Based on causality analysis of DE models, we define relevant dependency and relevant orders to enable outoforder execution without compromising determinism and without requiring backtracking. 1
Phased Logic: Supporting the Synchronous Design Paradigm with DelayInsensitive Circuitry
, 1996
"... Phased logic is proposed as a solution to the increasing problem of timing complexity in digital design. It is a delayinsensitive design methodology that seeks to restore the separation between logical and physical design by eliminating the need to distribute lowskew clock signals and carefully ..."
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Cited by 34 (0 self)
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Phased logic is proposed as a solution to the increasing problem of timing complexity in digital design. It is a delayinsensitive design methodology that seeks to restore the separation between logical and physical design by eliminating the need to distribute lowskew clock signals and carefully balance propagation delays. However, unlike other methodologies that avoid clocks, phased logic supports the cyclic, deterministic behavior of the synchronous design paradigm. This permits the designer to rely chiefly on current experience and CAD tools to create phased logic systems. Marked graph theory is used as a framework for governing the interaction of phased logic gates that operate directly on LevelEncoded twophase DualRail (LEDR) signals. A synthesis algorithm is developed for converting clocked systems to phased logic systems and is applied to benchmark examples. Performance results indicate that phased logic tends to be tolerant of logic delay imbalances and has predictable...
Densities of Idempotent Measures and Large Deviations
 AMS, AND INRIA REPORT N
, 1995
"... Considering measure theory in which the semifield of positive real numbers is replaced by an idempotent semiring leads to the notion of idempotent measure introduced by Maslov. Then, idempotent measures or integrals with density correspond to supremums of functions for the partial order relation i ..."
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Cited by 33 (11 self)
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Considering measure theory in which the semifield of positive real numbers is replaced by an idempotent semiring leads to the notion of idempotent measure introduced by Maslov. Then, idempotent measures or integrals with density correspond to supremums of functions for the partial order relation induced by the idempotent structure. In this paper, we give conditions under which an idempotent measure has a density and show by many examples that they are often satisfied. These conditions depend on the lattice structure of the semiring and on the Boolean algebra in which the measure is defined. As an application, we obtain a necessary and sufficient condition for a family of probabilities to satisfy the large deviation principle as defined by Varadhan.