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Xi-ren Cao - One of the best experts on this subject based on the ideXlab platform.
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Finite Perturbation Analysis
Perturbation Analysis of Discrete Event Dynamic Systems, 1991Co-Authors: Xi-ren CaoAbstract:One can view the basic goal of PA for DEDS as the reconstruction of an arbitrarily perturbed sample path from a nominal path. Under deterministic similarity, the simple infinitesimal Perturbation Analysis (IPA) rules described in Chapters 3 and 4 and extended in Chapter 5 compute a perturbed path infinitesimally different from the nominal for the purpose of gradient calculation. The computation of the Perturbation propagations can be efficiently done since the “critical timing path” or the “future event schedule” between the nominal and perturbed paths remains the same. However, as pointed out before in the limit of a path of a very long duration or an experiment with very large ensembles of runs, deterministic similarity will always be violated1. In such cases, the IPA rules which ignore the order changes of events have been proved to give unbiased and consistent estimates for performance gradients of only certain classes of DEDS (see Chapters 4 and 5). Although the domain of application of IPA is constantly being expanded, it is nevertheless important to devise methodologies which can overcome the basic problem of “event sequence order change,” or “discontinuous performance measure.” In other words, the key question is “how can one reconstruct the perturbed path from the nominal path short of essentially running a separate new simulation I experiment?” In this and the next chapter we address this question directly and suggest an alternative which we believe is more efficient than brute force reconstruction. To initiate the discussion, let us first dispel the seemingly intuitive notion that one cannot generate a sample path x(t;θ+Δθ,ξ) from an x(t;θ,ξ) when Δθ≠0. A simple view of this general problem of Perturbation Analysis of DEDS and the efficient construction of multiple sample paths of a DEDS under different values of a can be obtained by appealing to some fundamental procedures in discrete event simulation.
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Perturbation Analysis of closed queueing networks with general service time distributions
IEEE Transactions on Automatic Control, 1991Co-Authors: Xi-ren CaoAbstract:Perturbation Analysis of closed queuing networks with nonexponential service time distributions is studied. Perturbation Analysis formulas using realization probabilities are extended to these networks. A Perturbation generation function, which generalizes the Perturbation generation rule, is defined. equations for realization probability and formulas for sensitivity of the system throughput with respect to service time distribution parameters are presented. The formulas provide an analytical method of calculating throughput sensitivity and an explanation of the application of Perturbation Analysis algorithms for networks with general service time distributions. The author focuses on the extension of concepts and intuitive explanations of the formulas rather than on mathematical derivations. >
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Introduction to Perturbation Analysis
Perturbation Analysis of Discrete Event Dynamic Systems, 1991Co-Authors: Xi-ren CaoAbstract:To facilitate the discussion of Perturbation Analysis (PA), let us introduce some notations for DEDS. Let θ = system parameter(s) x(t) = a time history of the evolution of the DEDS, i.e., the (state, holding time) sequence as illustrated in Fig.1.1 In more physical terms, this may consist of the content of all the queues as a function of time, durations of all service intervals, etc. Since DEDS are often stochastic, x(t) will in general be dependent on the actual realized values of various random variables in the system. ξ= a vector of random variables, defined on the underlying probability space, that represents all the random phenomena of the DEDS or a particular realization of all the random variables in the system.
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Realization factors and Perturbation Analysis of open queueing networks
Proceedings of the 28th IEEE Conference on Decision and Control, 1Co-Authors: Xi-ren CaoAbstract:The Perturbation Analysis of open queuing networks is discussed. The concept of realization probability is extended to realization factors for open networks. A set of linear equations is derived for realization factors. It is shown that the Perturbation Analysis estimate of the sensitivity of a performance measure with respect to a mean service rate (or a mean interarrival rate) converges with probability one to the sensitivity of the steady-state performance measure, which simply equals the expected value of the realization factor. The results provide an analytical method of calculating performance sensitivity and form a theoretical foundation for Perturbation Analysis of open networks. >
Christos G. Cassandras - One of the best experts on this subject based on the ideXlab platform.
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Perturbation Analysis and optimization of stochastic hybrid systems
European Journal of Control, 2010Co-Authors: Christos G. Cassandras, Yorai Wardi, Christos G. Panayiotou, Chen YaoAbstract:We present a general framework for carrying out Perturbation Analysis in Stochastic Hybrid Systems (SHS) of arbitrary structure. In particular, Infinitesimal Perturbation Analysis (IPA) is used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters. These can be combined with standard gradient-based algorithms for optimization purposes and implemented on line with little or no distributional information regarding the stochastic processes involved. We generalize an earlier concept of “induced events” for this framework to include system features such as delays in control signals or modeling multiple user classes sharing a resource. We apply this generalized IPA to two SHS with different characteristics. First, we develop a gradient estimator for the performance of a linear switched system with control signal delays and a safety constraint and show that it is independent of the random delay's distributional characteristics. Second, we derive closed-form unbiased IPA estimators for a Stochastic Flow Model (SFM) of systems executing tasks subject to either hard or soft real-time constraints. These estimators are incorporated in a gradient-based algorithm to optimize performance by controlling a task admission threshold parameter. Simulation results are included to illustrate this optimization approach.
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Perturbation Analysis and optimization of stochastic flow networks
IEEE Transactions on Automatic Control, 2004Co-Authors: Gang Sun, Christos G. Cassandras, Yorai Wardi, Christos G. Panayiotou, G.f. RileyAbstract:We consider a stochastic fluid model of a network consisting of several single-class nodes in tandem and perform Perturbation Analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal Perturbation Analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in online environments and easily implementable for network management and optimization. This is illustrated by combining the IPA estimators with standard gradient based stochastic optimization methods and providing simulation examples.
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Perturbation Analysis of stochastic flow networks
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 1Co-Authors: Gang Sun, Christos G. Cassandras, Yorai Wardi, Christos G. PanayiotouAbstract:We consider a stochastic flow model (SFM) consisting of several single-class nodes in tandem and perform Perturbation Analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal Perturbation Analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in on-line environments and easily implementable for network management and control.
Christos G. Panayiotou - One of the best experts on this subject based on the ideXlab platform.
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Perturbation Analysis and optimization of stochastic hybrid systems
European Journal of Control, 2010Co-Authors: Christos G. Cassandras, Yorai Wardi, Christos G. Panayiotou, Chen YaoAbstract:We present a general framework for carrying out Perturbation Analysis in Stochastic Hybrid Systems (SHS) of arbitrary structure. In particular, Infinitesimal Perturbation Analysis (IPA) is used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters. These can be combined with standard gradient-based algorithms for optimization purposes and implemented on line with little or no distributional information regarding the stochastic processes involved. We generalize an earlier concept of “induced events” for this framework to include system features such as delays in control signals or modeling multiple user classes sharing a resource. We apply this generalized IPA to two SHS with different characteristics. First, we develop a gradient estimator for the performance of a linear switched system with control signal delays and a safety constraint and show that it is independent of the random delay's distributional characteristics. Second, we derive closed-form unbiased IPA estimators for a Stochastic Flow Model (SFM) of systems executing tasks subject to either hard or soft real-time constraints. These estimators are incorporated in a gradient-based algorithm to optimize performance by controlling a task admission threshold parameter. Simulation results are included to illustrate this optimization approach.
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Perturbation Analysis and optimization of stochastic flow networks
IEEE Transactions on Automatic Control, 2004Co-Authors: Gang Sun, Christos G. Cassandras, Yorai Wardi, Christos G. Panayiotou, G.f. RileyAbstract:We consider a stochastic fluid model of a network consisting of several single-class nodes in tandem and perform Perturbation Analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal Perturbation Analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in online environments and easily implementable for network management and optimization. This is illustrated by combining the IPA estimators with standard gradient based stochastic optimization methods and providing simulation examples.
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Perturbation Analysis of stochastic flow networks
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 1Co-Authors: Gang Sun, Christos G. Cassandras, Yorai Wardi, Christos G. PanayiotouAbstract:We consider a stochastic flow model (SFM) consisting of several single-class nodes in tandem and perform Perturbation Analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal Perturbation Analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in on-line environments and easily implementable for network management and control.
Bernd Heidergott - One of the best experts on this subject based on the ideXlab platform.
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A Smoothed Perturbation Analysis of Parisian Options
IEEE Transactions on Automatic Control, 2015Co-Authors: Bernd Heidergott, Haralambie Leahu, Warren Volk-makarewiczAbstract:In this technical note we provide a smoothed Perturbation Analysis (SPA) estimator of the sensitivity of a discrete time Parisian option with respect to the barrier level. The Analysis put forward is of interest in a broader context than that of exotic options as we provide an SPA Analysis for a problem where the critical event for the SPA estimator is based on an entire sample path, which is a novelty in the literature. Numerical examples illustrate the performance of the estimator.
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Perturbation Analysis of Markov chains
2008 9th International Workshop on Discrete Event Systems, 2008Co-Authors: Bernd HeidergottAbstract:We present a new approach to Perturbation Analysis of Markov chains. Our Analysis is based on bounding the distance of stationary distributions in a suitable functional space.
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Max-Plus Linear Stochastic Systems and Perturbation Analysis - Max-plus linear stochastic systems and Perturbation Analysis
The International Series on Discrete Event Dynamic Systems, 2006Co-Authors: Bernd HeidergottAbstract:Max-Plus Algebra.- Max-Plus Linear Stochastic Systems.- Ergodic Theory.- Perturbation Analysis.- A Max-Plus Differential Calculus.- Higher-Order D-Derivatives.- Taylor Series Expansions.
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max plus linear stochastic systems and Perturbation Analysis
The International Series on Discrete Event Dynamic Systems, 2006Co-Authors: Bernd HeidergottAbstract:Max-Plus Algebra.- Max-Plus Linear Stochastic Systems.- Ergodic Theory.- Perturbation Analysis.- A Max-Plus Differential Calculus.- Higher-Order D-Derivatives.- Taylor Series Expansions.
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Customer-Oriented Finite Perturbation Analysis for QueueingNetworks
Discrete Event Dynamic Systems, 2000Co-Authors: Bernd HeidergottAbstract:We consider queueing networks for which the performance measure J ( \theta ) depends on a parameter \theta, which can be a service time parameter or a buffer size, and we are interested in sensitivity Analysis of J ( \theta ) with respect to \theta . We introduce a new method, called customer-oriented finite Perturbation Analysis (CFPA), which predicts J ( \theta + \Delta ) for an arbitrary, finite Perturbation \Delta from a simulation experiment at \theta . CFPA can estimate the entire performance function (by using a finite number of chosen points and fitting a least-squares approximating polynomial to the observation) within one simulation experiment. We obtain CFPA by reformulating finite Perturbation Analysis (FPA) for customers. The main difference between FPA and CFPA is that the former calculates the sensitivities of timing epochs of events, such as external arrivals or service time completions, while the latter yields sensitivities of departure epochs of customers. We give sufficient conditions for unbiasedness of CFPA. Numerical examples show the efficiency of the method. In particular, we address sensitivity Analysis with respect to buffer sizes and thereby give a solution to the problem for which Perturbation Analysis was originally built.
Naoto Miyoshi - One of the best experts on this subject based on the ideXlab platform.
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Smoothed Perturbation Analysis for Stationary Single-Server Queues with Multiple Customer Classes
Discrete Event Dynamic Systems, 1997Co-Authors: Naoto MiyoshiAbstract:Recently, Konstantopoulos and Zazanis (1992, 1994) and Brémaud and Lasgouttes (1993) derive the infinitesimal Perturbation Analysis (IPA) estimators for the stationary and ergodic G/G/1/∞ queue using Palm calculus, where neither regenerative structure nor convex property are required and the strong consistency is ensured by ergodic theorem. This work has been motivated by them and derives the smoothed Perturbation Analysis (SPA) estimator on the stationary and ergodic framework. The problem here is how to treat the ‘catastrophic jumps’ on the sample path of the steady state and this is solved cleverly by using the Palm calculus. We deal with multi-class queues in this paper but our key formula is expected to be useful to any systems to which the SPA is applicable.
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Smoothed Perturbation Analysis for Stationary Single-ServerQueues with Multiple Customer Classes
Discrete Event Dynamic Systems, 1997Co-Authors: Naoto MiyoshiAbstract:Recently, Konstantopoulos and Zazanis (1992, 1994) and Bremaud and Lasgouttes (1993) derive the infinitesimal Perturbation Analysis (IPA) estimators for the stationary and ergodic G/G/1/∞ queue using Palm calculus, where neither regenerative structure nor convex property are required and the strong consistency is ensured by ergodic theorem. This work has been motivated by them and derives the smoothed Perturbation Analysis (SPA) estimator on the stationary and ergodic framework. The problem here is how to treat the ’catastrophic jumps‘ on the sample path of the steady state and this is solved cleverly by using the Palm calculus. We deal with multi-class queues in this paper but our key formula is expected to be useful to any systems to which the SPA is applicable.
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Smoothed Perturbation Analysis estimates for stationary multi-class queues
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1Co-Authors: Naoto MiyoshiAbstract:Recently, Konstantopoulos and Zazanis and Bremaud and Lasgouttes derive the infinitesimal Perturbation Analysis estimator for the stationary and ergodic G/G/1 queue using Palm calculus, where neither regenerative structure nor convex property are required and the strong consistency is ensured by ergodic theorem. This work has been motivated by them and derives the smoothed Perturbation Analysis (SPA) estimator on the stationary and ergodic framework. We deal with multi-class queues in this paper but our key formula is expected to be useful to the systems to which the SPA is applicable.