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308
A Calculus for Endtoend Statistical Service Guarantees
, 2001
"... The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. A drawback of the deterministic network calculus is that it only provides worstcase bounds. Here we present a network cal ..."
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Cited by 43 (8 self)
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The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. A drawback of the deterministic network calculus is that it only provides worstcase bounds. Here we present a network calculus for statistical service guarantees, which can exploit the statistical multiplexing gain of sources. We introduce the notion of an effective service curve as a probabilistic bound on the service received by an individual flw, and construct an effective service curve for a network where capacities are provisioned exclusively to aggregates of flows. Numerical examples demonstrate that the calculus is able to extract a significant amount of multiplexing gain in networks with a large number of flows.
Shrinking timed automata
 In FSTTCS’11, LIPIcs 13, p. 375–386. LeibnizZentrum für Informatik
, 2011
"... We define and study a new approach to the implementability of timed automata, where the semantics is perturbed by imprecisions and finite frequency of the hardware. In order to circumvent these effects, we introduce parametric shrinking of clock constraints, which corresponds to tightening these. We ..."
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Cited by 41 (12 self)
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We define and study a new approach to the implementability of timed automata, where the semantics is perturbed by imprecisions and finite frequency of the hardware. In order to circumvent these effects, we introduce parametric shrinking of clock constraints, which corresponds to tightening these. We propose symbolic procedures to decide the existence of (and then compute) parameters under which the shrunk version of a given timed automaton is nonblocking and can timeabstract simulate the exact semantics. We then define an implementation semantics for timed automata with a digital clock and positive reaction times, and show that for shrinkable timed automata, nonblockingness and timeabstract simulation are preserved in implementation.
Phased logic: Supporting the synchronous design paradigm with delayinsensitive circuitry
 IEEE Transactions on Computers
, 1996
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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 36 (10 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.
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.
Modeling and Validating Distributed Embedded RealTime Control Systems
, 2008
"... The development of complex embedded control systems can be improved significantly by applying formal techniques from control engineering and software engineering. It is shown how these approaches can be combined to improve the design and analysis of hightech systems, both in theory and practice. Th ..."
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Cited by 34 (14 self)
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The development of complex embedded control systems can be improved significantly by applying formal techniques from control engineering and software engineering. It is shown how these approaches can be combined to improve the design and analysis of hightech systems, both in theory and practice. The semantics of the integration of two established rigorous techniques has been defined formally in this work. The strength of this integrated semantics is demonstrated by means of a significant industrial case study: the embedded control of a printer paper path, whereby the full development lifecycle from model to realization is covered. The resulting modeldriven design approach fits the current engineering practice in industry and is both flexible and effective.
A minplus calculus for endtoend statistical service guarantees
 IEEE TRANSACTION ON INFORMATION THEORY
, 2006
"... The network calculus offers an elegant framework for determining worstcase bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic b ..."
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Cited by 33 (8 self)
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The network calculus offers an elegant framework for determining worstcase bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic bound on the service received by an individual flow or an aggregate of flows. The problem of concatenating pernode statistical service curves to form an endtoend (network) statistical service curve is explored. Two solution approaches are presented that can each yield statistical network service curves. The first approach requires the availability of time scale bounds at which arrivals and departures at each node are correlated. The second approach considers a service curve that describes service over time intervals. Although the latter description of service is less general, it is argued that many practically relevant service curves may be compliant to this description.
Performance Bounds in FeedForward Networks under Blind Multiplexing
, 2006
"... Bounding performance characteristics in communication networks is an important and interesting issue. In this study we assume uncertainty about the way different flows in a network are multiplexed, we even drop the common FIFO assumption. Under socalled blind multiplexing we derive new bounds for t ..."
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Cited by 27 (17 self)
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Bounding performance characteristics in communication networks is an important and interesting issue. In this study we assume uncertainty about the way different flows in a network are multiplexed, we even drop the common FIFO assumption. Under socalled blind multiplexing we derive new bounds for the tractable, yet nontrivial case of feedforward networks. This is accomplished for pragmatic, but general traffic and server models using network calculus. In particular, we derive an endtoend service curve for a flow of interest under blind multiplexing, establishing what we call the pay multiplexing only once principle. We specify the algorithms necessary to apply this result in a network of blind multiplexing nodes. Since these algorithms may have prohibitive computational costs, we present strategies to reduce the computational effort in a controlled manner such that the quality of the bounds is affected as little as possible. Finally we present some numerical results from a network calculus tool we developed and compare our bounds against the best known bounds for networks of blind multiplexing nodes.
Delay Bounds under Arbitrary Multiplexing
, 2007
"... Network calculus has proven as a valuable and versatile methodology for worstcase analysis of communication networks. One issue in which it is still lacking is the treatment of aggregate multiplexing, in particular if the FIFO property cannot be assumed when flows are merged. In this report, we add ..."
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Cited by 26 (8 self)
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Network calculus has proven as a valuable and versatile methodology for worstcase analysis of communication networks. One issue in which it is still lacking is the treatment of aggregate multiplexing, in particular if the FIFO property cannot be assumed when flows are merged. In this report, we address the problem of bounding the delay of individual traffic flows in feedforward networks under arbitrary multiplexing. Somewhat surprisingly, we find that direct application of network calculus results in loose bounds even in seemingly simple scenarios. The reasons for this failure of network calculus are discussed in detail and a method to arrive at tight delay bounds for arbitrary (aggregate) multiplexing is presented. This method is based on the solution of an optimization problem. For the special case of sinktree networks this optimization problem is solved explicitly, thus arriving at a closedform expression for the delay bound. Numerical experiments illustrate that in sinktree networks the improvement over bounds based on direct application of network calculus can be considerable.