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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 279 (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 use of Kronecker operators for the solution of generalized stochastic Petri nets
, 1996
"... We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of markingdependent behavior for the transitions and the presence of immediate synchronizations. ..."
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Cited by 50 (13 self)
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We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of markingdependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulsebased reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the statespace explosion. In the conclusion, we point out ideas to parallelize our approach.
On Retiming of Multirate DSP Algorithms
 In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing
, 1996
"... In the paper retiming of DSP algorithms exhibiting multirate behavior is treated. Using the nonordinary marked graph model and the reachability theory, we provide a new condition for valid retiming of multirate graphs. We show that for a graph with n nodes the reachability condition can be split in ..."
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Cited by 14 (3 self)
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In the paper retiming of DSP algorithms exhibiting multirate behavior is treated. Using the nonordinary marked graph model and the reachability theory, we provide a new condition for valid retiming of multirate graphs. We show that for a graph with n nodes the reachability condition can be split into the reachability condition for the topologically equivalent unitrate graph (all rates set to one), and (n 2 \Gamma n)=2 ratedependent conditions. Using this property a class of equivalent graphs of reduced complexity is introduced which are equivalent in terms of retiming. Additionally, the circuitbased necessary condition for valid retiming of multirate graphs is extended for the sufficient part. 1. INTRODUCTION Retiming was introduced as a technique to optimize hardware circuits by redistributing registers without affecting functionality [1]. Retiming is also useful for DSP software design. It changes precedence constraints among instructions or tasks, and can improve singlepro...
Tight Polynomial Bounds for SteadyState Performance of Marked Graphs
, 1989
"... The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Marked Graphs is studied. In particular, Linear Programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., reachable) bounds for the t ..."
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Cited by 14 (11 self)
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The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Marked Graphs is studied. In particular, Linear Programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., reachable) bounds for the throughput of transitions for live and bounded Marked Graphs with time associated with transitions. These bounds depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed. 1 Introduction One of the main problems in the actual use of timed and stochastic Petri net models for the performance evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. Exact performance results are usually obtained from the numerical solu...
Topologybased optimization of maximal sustainable throughput in a latencyinsensitive system
, 2007
"... We consider the problem of optimizing the performance of a latencyinsensitive system (LIS) where the addition of backpressure has caused throughput degradation. Previous works have addressed the problem of LIS performance in different ways. In particular, the insertion of relay stations and the siz ..."
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Cited by 8 (5 self)
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We consider the problem of optimizing the performance of a latencyinsensitive system (LIS) where the addition of backpressure has caused throughput degradation. Previous works have addressed the problem of LIS performance in different ways. In particular, the insertion of relay stations and the sizing of the input queues in the shells are the two main optimization techniques that have been proposed. We provide a unifying framework for this problem by outlining which approaches work for different system topologies, and highlighting counterexamples where some solutions do not work. We also observe that in the most difficult class of topologies, instances with the greatest throughput degradation are typically very amenable to simplifications. The contributions of this paper include a characterization of topologies that maintain optimal throughput with fixedsize queues and a heuristic for sizing queues that produces solutions close to optimal in a fraction of the time.
Properties and SteadyState Performance Bounds for Petri Nets with Unique Repetitive Firing Count Vector
, 1989
"... The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Petri nets is studied. In particular, Linear Programming problems defined on the incidence matrix of underlying Petri net are used to compute bounds for the throughput of transitions for liv ..."
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Cited by 6 (6 self)
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The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Petri nets is studied. In particular, Linear Programming problems defined on the incidence matrix of underlying Petri net are used to compute bounds for the throughput of transitions for live and bounded nets with a unique possibility of steadystate behaviour. These classes of nets are defined and their characteristics are studied. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases); moreover they can be computed also for nonergodic models. Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed. 1 Introduction In this paper, which is a continuation of the companion paper [CCCS89], we study the possibility of obtaining (upper and lower) bounds on the steadystate perform...
Genetic Regulatory Mechanisms by means of Extended Interactive Petri Nets
, 1997
"... In our work we have chosen to integrate formalism for knowledge representation with formalism for process representation as a way to specify and regulate the overall activity of a multicellular agent. The result of this approach is XP i N , another formalism, wherein a distributed system can be mod ..."
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Cited by 2 (2 self)
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In our work we have chosen to integrate formalism for knowledge representation with formalism for process representation as a way to specify and regulate the overall activity of a multicellular agent. The result of this approach is XP i N , another formalism, wherein a distributed system can be modeled as a collection of interrelated subnets sharing a common explicit control structure. Each subnet represents a system of asynchronous concurrent threads modeled by a set of transitions. XP i N combines local state and control with interaction and hierarchy to achieve a highlevel abstraction and to model the complex relationships between all the components of a distributed system. Viewed as a tool XP i N provides a carefully devised conflict resolution strategy that intentionally mimics the genetic regulatory mechanism used in an organic cell to select the next genes to process.
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"... A general model for performance optimization of sequential systems ..."
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1TopologyBased Performance Analysis and Optimization of LatencyInsensitive Systems
"... Latencyinsensitive protocols allow systemonchip engineers to decouple the design of the computing cores from the design of the intercore communication channels while following the synchronous design paradigm. In a latencyinsensitive system (LIS) each core is encapsulated within a shell, a synth ..."
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Latencyinsensitive protocols allow systemonchip engineers to decouple the design of the computing cores from the design of the intercore communication channels while following the synchronous design paradigm. In a latencyinsensitive system (LIS) each core is encapsulated within a shell, a synthesized interface module that dynamically controls its operation. At each clock period, if new data has not arrived on an input channel or a stalling request has arrived on an output channel, the shell stalls the core and buffers other incoming valid data for future processing. The combination of finite buffers and backpressure from stalling can cause throughput degradation. Previous works addressed this problem by increasing buffer space to reduce the backpressure requests or inserting extra buffering to balance the channel latency around a LIS. We explore the theoretical complexity of these approaches and propose a heuristic algorithm for efficient queue sizing. We also practically characterize several LIS topologies and how the topology of a LIS can impact not only how much throughput degradation will occur, but also the difficulty of finding optimal queue sizing solutions.