Results 1  10
of
10
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 ..."
Abstract

Cited by 369 (11 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
(Show Context)
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�1g; max; +)), and also for semigroups of (max,+)linear projective maps with rational entries. An application to the estimation of the Lyapunov expo ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
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�1g; 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.
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 ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
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
Using Stochastic Recursive Equations as a Tool for Modeling and Performance Evaluation of Parallel Processing Systems
"... This report presents the approach of stochastic recursive equations (SRE) for the modeling and performance analysis of parallel systems. The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recur ..."
Abstract
 Add to MetaCart
(Show Context)
This report presents the approach of stochastic recursive equations (SRE) for the modeling and performance analysis of parallel systems. The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recursive equations. Secondly, we give an assesment on the capability of the SRE approach. 1 Introduction In this report, we present modeling and performance analysis of several parallel processing systems using the approach based on stochastic recursive equations (SRE). The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recursive equations. Secondly, we give an assesment on the capability of the SRE approach. The use of such equations for performance analysis of parallel systems appeared first in [7, 8, 9]. In this paper, we extend the class of equations studied there to cope with the syst...
Duality and Equivalencies in Closed Tandem Queueing Networks
, 1993
"... Duality and Equivalencies in Closed Tandem Queueing Networks Equivalence relations between closed tandem queueing networks are established. Four types of models are under consideration: singleserver infinitecapacity buffer queues, infiniteserver queues with resequencing, singleserver unitcapaci ..."
Abstract
 Add to MetaCart
(Show Context)
Duality and Equivalencies in Closed Tandem Queueing Networks Equivalence relations between closed tandem queueing networks are established. Four types of models are under consideration: singleserver infinitecapacity buffer queues, infiniteserver queues with resequencing, singleserver unitcapacity buffer queues with blocking before service, and singleserver unitcapacity buffer queues with blocking after service. Using a customer/server duality we show that in a network consisting of singleserver infinitecapacitybuffer queues, customerdependent service times and serverdependent service times yield equivalent performance characteristics. We further show that for closed tandem queueing networks, a system consisting of singleserver infinitecapacitybuffer queues (resp. infiniteserver queues with resequencing) and a system consisting of singleserverunitcapacitybuffer queues with blocking before service (resp. blocking after service) have equivalent performance behaviors. As applications of these equivalence properties, we obtain new results on the analysis of symmetric closed tandem networks, where all