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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 363 (11 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
Probabilistic Verification of Discrete Event Systems using Acceptance Sampling
 In Proc. 14th International Conference on Computer Aided Verification, volume 2404 of LNCS
, 2002
"... We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in ..."
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Cited by 120 (9 self)
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We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in two senses. First, the properties, expressed as CSL formulas, can be probabilistic. Second, the result of the verification is probabilistic, and the probability of error is bounded by two parameters passed to the verification procedure. The verification of properties can be carried out in an anytime manner by starting off with loose error bounds, and gradually tightening these bounds.
Likelihood Ratio Gradient Estimation For Stochastic Recursions
 Communications of the ACM
, 1995
"... . In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to certain types of perturbations in the underlying transition structure. Our main result provides conditions under which the stationary probability measure of an ..."
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Cited by 72 (7 self)
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. In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to certain types of perturbations in the underlying transition structure. Our main result provides conditions under which the stationary probability measure of an ergodic Harris recurrent Markov chain is differentiable in a certain strong sense. The approach is based on likelihood ratio "changeofmeasure" arguments, and leads directly to a "likelihood ratio gradient estimator" that can be computed numerically. Keywords: Harris recurrent Markov chain, likelihood ratio, gradient estimation, regeneration. 1 The research of this author was supported by the U. S. Army Research Office under Contract No. DAAL0391G 0101 and by the National Science Foundation under Contract No. DDM9101580. 2 This author's research was supported by NSERCCanada grant No. OGP0110050 and FCARQu'ebec grant No. 93ER1654. 1. Introduction In this paper, we will study the cl...
Solving Generalized SemiMarkov Decision Processes using Continuous Phasetype Distributions
 Proceedings of the Nineteenth National Conference of Artificial Intelligence, AAAI
"... We introduce the generalized semiMarkov decision process (GSMDP) as an extension of continuoustime MDPs and semiMarkov decision processes (SMDPs) for modeling stochastic decision processes with asynchronous events and actions. Using phasetype distributions and uniformization, we show how an arbi ..."
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Cited by 32 (4 self)
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We introduce the generalized semiMarkov decision process (GSMDP) as an extension of continuoustime MDPs and semiMarkov decision processes (SMDPs) for modeling stochastic decision processes with asynchronous events and actions. Using phasetype distributions and uniformization, we show how an arbitrary GSMDP can be approximated by a discretetime MDP, which can then be solved using existing MDP techniques. The techniques we present can also be seen as an alternative approach for solving SMDPs, and we demonstrate that the introduction of phases allows us to generate higher quality policies than those obtained by standard SMDP solution techniques.
BudgetDependent Convergence Rate Of Stochastic Approximation
 SIAM Journal on Optimization
, 1997
"... . Convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter `. Assuming that a gradient estimator is available and that both the bias and the variance of the estimator are (known) functions of the budget dev ..."
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Cited by 28 (11 self)
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. Convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter `. Assuming that a gradient estimator is available and that both the bias and the variance of the estimator are (known) functions of the budget devoted to its computation, the gradient estimator is employed in conjunction with a stochastic approximation (SA) algorithm. Our interest is to figure out how to allocate the total available computational budget to the successive SA iterations. The effort is devoted to solving the asymptotic version of this problem by finding the convergence rate of SA towards the optimizer, first as a function of the number of iterations, and then as a function of the total computational effort. As a result the optimal rate of increase of the computational budget per iteration can be found. Explicit expressions for the case where the computational budget devoted to an iteration is a polynomial in the iteratio...
An Overview of Derivative Estimation
, 1991
"... We explain the main techniques for estimating derivatives by simulation and survey the most recent developments in that area. In particular, we discuss perturbation analysis (PA), likelihood ratios (LR), weak derivatives (WD), finite differences (FD), and many of their variants. We also mention some ..."
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Cited by 28 (2 self)
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We explain the main techniques for estimating derivatives by simulation and survey the most recent developments in that area. In particular, we discuss perturbation analysis (PA), likelihood ratios (LR), weak derivatives (WD), finite differences (FD), and many of their variants. We also mention some other approaches. Our discussion emphasizes the relationships between the methods. For that purpose, all of them are presented in the same framework, which is based on L'Ecuyer (1990). 1. INTRODUCTION Simulation is a popular tool for estimating the expected (average) performance measure of a complex stochastic system. Various statistical techniques have been develop ed in that context. Estimating the derivative or sensitivity of such an expectation certainly looks more difficult, but is nevertheless important for many practical applications. For example, let ` be a realvalued (continuous) parameter and suppose that the performance measure of interest depends on ` either directly, or indi...
Stochastic Simulation of Event Structures
, 1996
"... Currently the semantics of stochastic process algebras are defined using (an extension) of labelled transition systems. This usually results in a semantics based on the interleaving of causally independent actions. The advantage is that the structure of transition systems closely resembles that of M ..."
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Cited by 14 (10 self)
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Currently the semantics of stochastic process algebras are defined using (an extension) of labelled transition systems. This usually results in a semantics based on the interleaving of causally independent actions. The advantage is that the structure of transition systems closely resembles that of Markov chains, enabling the use of standard solution techniques for analytical and numerical performance assessment of formal specifications. The main drawback is that distributions are restricted to be exponential. In [2] we proposed to use a partialorder semantics for stochastic process algebras. This allows the support of nonexponential distributions in the process algebra in a perspicuous way, but the direct resemblance with Markov chains is lost. This paper proposes to exploit discreteevent simulation techniques for analyzing our partialorder model, called stochastic event structures. The key idea is to obtain from event structures socalled (timehomogeneous) generalized semiMarkov ...
Computing Approximating Automata for a Class of Linear Hybrid Systems
 In Hybrid Systems V, Lecture Notes in Computer Science
, 1998
"... Approximating automata are finitestate representations of the sequential inputoutput behaviors of hybrid systems characterized by threshold events that trigger discrete changes in the continuous dynamic equations. Procedures proposed for constructing approximating automata require forward and backw ..."
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Cited by 13 (4 self)
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Approximating automata are finitestate representations of the sequential inputoutput behaviors of hybrid systems characterized by threshold events that trigger discrete changes in the continuous dynamic equations. Procedures proposed for constructing approximating automata require forward and backward mappings of sets of continuous state trajectories  mappings which are not available for arbitrary continuous dynamics. This paper develops the foundations for constructing approximating automata automatically for hybrid systems in which the continuous dynamics are defined by convex polytopes in the vector space of the derivatives of the continuous state trajectories. The computations are illustrated for a simple example which also demonstrates the use of approximating automata to solve verification problems that may be intractable using fixedpoint computations for linear hybrid automata. 1 Introduction This paper concerns the generation of purely discrete models (finite automata) for...
Bounded Model Checking for GSMP Models of Stochastic Realtime Systems
 In Proc. of HSCC’06, LNCS 3927
, 2006
"... Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GS ..."
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Cited by 13 (1 self)
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Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMP).
Fast simulation of steadystate availability in nonmarkovian highly dependable systems
 In Proceedings of the 23rd International Symposium on FaultTolerant Computing, 3847. IEEE Computer
, 1993
"... Thi s paper considers e f i c i en t simulation techniques f o r estimating steadystate quantities in models of highly dependable computing systems with general component failure and repair t ime distributions. Earlier approaches in this application setting fo r steadystate estimation rely o n th ..."
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Cited by 12 (3 self)
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Thi s paper considers e f i c i en t simulation techniques f o r estimating steadystate quantities in models of highly dependable computing systems with general component failure and repair t ime distributions. Earlier approaches in this application setting fo r steadystate estimation rely o n the regenerative method of simulation, which can be used when the failure t ime distributions are exponentially distributed. However, when the failure t imes are generally distributed the regenerative structure is lost and a new approach mus t be taken. The approach we take is to exploit a ratio representation f o r steadystate quantities in terms of cycles tha t are no longer independent and identically drstributed. A “splitting ” technique i s used in which importance sampling is used to speed u p the simulation of rare sys tem failure events during a cycle, and standard simulation is used to estzmate the expected cycle length. Experimental results show that the method is effective in practice. 1