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208
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 33 (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.
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 32 (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.
The Maslov Dequantization, Idempotent and Tropical Mathematics: a Very Brief Introduction
, 2005
"... ..."
An endtoend probabilistic network calculus with moment generating functions
 in Proc. IEEE 14th International Workshop on Quality of Servic (IWQoS
"... Abstract — Network calculus is a minplus system theory for performance evaluation of queuing networks. Its elegance stems from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worstcase assumptions of network calculus to develop a probabi ..."
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Cited by 28 (2 self)
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Abstract — Network calculus is a minplus system theory for performance evaluation of queuing networks. Its elegance stems from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worstcase assumptions of network calculus to develop a probabilistic equivalent that benefits from statistical multiplexing. Significant achievements have been made, owing for example to the theory of effective bandwidths, however, the outstanding scalability set up by concatenation of deterministic servers has not been shown. This paper establishes a concise, probabilistic network calculus with moment generating functions. The presented work features closedform, endtoend, probabilistic performance bounds that achieve the objective of scaling linearly in the number of servers in series. The consistent application of moment generating functions put forth in this paper utilizes independence beyond the scope of current statistical multiplexing of flows. A relevant additional gain is demonstrated for tandem servers with independent crosstraffic. I.
Random matrices, noncolliding processes and queues
 TO APPEAR IN SÉMINAIRE DE PROBABILITÉS XXXVI
, 2002
"... This is survey of some recent results connecting random matrices, noncolliding processes and queues. ..."
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Cited by 21 (2 self)
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This is survey of some recent results connecting random matrices, noncolliding processes and queues.
Analysis of stochastic service guarantees in communication networks: A server model
 In Proc. of the International Workshop on Quality of Service (IWQoS 2005
, 2005
"... Abstract. The arrival curve has been used as a powerful concept for deterministic service guarantee analysis in communication networks. Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly impo ..."
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Cited by 20 (8 self)
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Abstract. The arrival curve has been used as a powerful concept for deterministic service guarantee analysis in communication networks. Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly important and has attracted a lot of research attention in recent years. For this, several probabilistic versions of the arrival curve have been proposed in the literature. They extend the concept of arrival curve to the stochastic case based on its traffic amount property. In this paper, we explore another property, called the virtual backlog property, of an arrival curve. Based on the virtual backlog property, we introduce the concept of virtualbacklogcentric (v.b.c) stochastic arrival curve to facilitate the analysis of stochastic service guarantees. We prove that a v.b.c stochastic arrival curve has a similar duality as a (deterministic) arrival curve. With the concept of v.b.c stochastic arrival curve, we derive results for stochastic service guarantee analysis of systems with the timevarying setting. In addition, we prove that many wellknown types of traffic can be readily represented using v.b.c stochastic arrival curves.
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 20 (6 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.
A spectral theorem for convex monotone homogeneous maps
 In Proceedings of the Satellite Workshop on MaxPlus Algebras, IFAC SSSC’01
, 2001
"... Abstract. We consider convex maps f: R n → R n that are monotone (i.e., that preserve the product ordering of R n), and nonexpansive for the supnorm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the addition of constants). We show that the fixed point ..."
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Cited by 19 (9 self)
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Abstract. We consider convex maps f: R n → R n that are monotone (i.e., that preserve the product ordering of R n), and nonexpansive for the supnorm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the addition of constants). We show that the fixed point set of f, when it is nonempty, is isomorphic to a convex infsubsemilattice of R n, whose dimension is at most equal to the number of strongly connected components of a critical graph defined from the tangent affine maps of f. This yields in particular an uniqueness result for the bias vector of ergodic control problems. This generalizes results obtained previously by Lanery, Romanovsky, and Schweitzer and Federgruen, for ergodic control problems with finite state and action spaces, which correspond to the special case of piecewise affine maps f. We also show that the length of periodic orbits of f is bounded by the cyclicity of its critical graph, which implies that the possible orbit lengths of f are exactly the orders of elements of the symmetric group
Bounding Average Time Separations of Events in Stochastic Marked Graphs
 In Proc. International Symposium on Advanced Research in Asynchronous Circuits and Systems
, 1999
"... Stochastic timed marked graphs are graphical models of concurrent systems such as asynchronous circuits, embedded systems, queuing networks, manufacturing systems, and many automatic control systems. Unlike earlier works in which delays must be fixed or exponential, we allow the models to include ar ..."
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Cited by 19 (6 self)
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Stochastic timed marked graphs are graphical models of concurrent systems such as asynchronous circuits, embedded systems, queuing networks, manufacturing systems, and many automatic control systems. Unlike earlier works in which delays must be fixed or exponential, we allow the models to include arbitrary delay distributions as long as they have finite means. For such models, one important problem is to determine the average Time Separations of Events (TSE's). For example, an efficient means of finding TSE's in such models of asynchronous circuits facilitates both performance analysis as well as performancedriven synthesis. Towards this end, we present a novel technique to obtain upper and lower bounds on the average TSE for arbitrary pairs of system events. The bounds are formulated using a finite segment of the infinite unfolding of the marked graph and can be efficiently evaluated either using statistical sampling or, in some special cases, analytical methods. The resulting bounds...