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Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 250 (10 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
On the Performance of Synchronized Programs in Distributed Networks with Random Processing Times and Transmission Delays
, 1994
"... A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was stu ..."
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Cited by 15 (2 self)
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A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was studied in [ER1] and [ER2] under the assumption that message transmission delays and processing times are constant. In this paper we study the behavior of the simple synchronizer when processing times and transmission delays are random. Our main performance measure is the rate of a network, i.e., the average number of computational steps executed by a processor in the network, per unit time. We analyze the effect of the topology and the probability distributions of the random variables on the behavior of the network. For random variables with exponential distribution we provide tight (i.e. attainable) bounds and study the effect of a bottleneck processor on the rate. Keywords: Distributed Netwo...
On the Burnside problem for Semigroups of Matrices in the (max,+) Algebra
, 1996
"... We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max,+)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max,+)linear projective maps with rational entries. An application to the estimation of the Lyapuno ..."
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Cited by 11 (2 self)
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We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max,+)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max,+)linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed. 1. Introduction The "(max,+)algebra" is a traditional name for the semiring (R[f\Gamma1g; max; +), denoted Rmax in the sequel. This is a particular example of idempotent semiring (that is a semiring whose additive law satisfies a \Phi a = a), also known as dioid [17, 18, 2]. This algebraic structure has been popularized by its applications to Graph Theory and Operations Research [17, 8]. Linear operators in this algebra are central in HamiltonJacobi theory and in the study of exponential asymptotics [33]. The study of automata and semigroups of matrices over the analogous "tropical" semiring (N [ f+1g;min;+) has been ...
Queueingtheoretic solution methods for models of parallel and distributed systems
 Performance Evaluation of Parallel and Distributed Systems Solution Methods. CWI Tract 105 & 106
, 1994
"... This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solutio ..."
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Cited by 4 (3 self)
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This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solution methodology.
On Semigroups of Matrices in the (max,+) Algebra
, 1994
"... We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max; +)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max; +)linear projective maps with rational entries. An application to the estimation of the Lyap ..."
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Cited by 2 (1 self)
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We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max; +)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max; +)linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed.
BOUNDS ON MEAN CYCLE TIME IN ACYCLIC FORKJOIN QUEUEING NETWORKS
"... Mean cycle time Simple lower and upper bounds on mean cycle time in stochastic acyclic forkjoin networks are derived using the (max, +)algebra approach. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples a ..."
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Cited by 1 (1 self)
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Mean cycle time Simple lower and upper bounds on mean cycle time in stochastic acyclic forkjoin networks are derived using the (max, +)algebra approach. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented. 1