Convergence of perturbation analysis estimates for discontinuous sample functions: a general approach

1988 ◽  
Vol 20 (1) ◽  
pp. 59-78 ◽  
Author(s):  
Reuven Y. Rubinstein ◽  
Ferenc Szidarovszky
Keyword(s):  
Monte Carlo ◽  
Rate Of Convergence ◽  
Performance Measures ◽  
Dynamic Systems ◽  
Perturbation Analysis ◽  
Sample Path ◽  
Single Sample ◽  
Parameter Vector ◽  
Discrete Events ◽  
Convergence Conditions

Generalized perturbation analysis (PA) estimates to study sensitivity of performance measures of discrete events dynamic systems for discontinuous sample functions are introduced. Their convergence conditions and rate of convergence are given. It is shown that the PA estimates based on a single sample path always converge faster to the unknown sensitivity parameter (vector of parameters) than their counterpart—crude Monte Carlo ones.

Convergence of perturbation analysis estimates for discontinuous sample functions: a general approach

1988 ◽  
Vol 20 (01) ◽  
pp. 59-78
Author(s):  
Reuven Y. Rubinstein ◽  
Ferenc Szidarovszky
Keyword(s):  
Monte Carlo ◽  
Rate Of Convergence ◽  
Performance Measures ◽  
Dynamic Systems ◽  
Perturbation Analysis ◽  
Sample Path ◽  
Single Sample ◽  
Parameter Vector ◽  
Discrete Events ◽  
Convergence Conditions

Generalized perturbation analysis (PA) estimates to study sensitivity of performance measures of discrete events dynamic systems for discontinuous sample functions are introduced. Their convergence conditions and rate of convergence are given. It is shown that the PA estimates based on a single sample path always converge faster to the unknown sensitivity parameter (vector of parameters) than their counterpart—crude Monte Carlo ones.

The Maclaurin series for performance functions of Markov chains

1998 ◽  
Vol 30 (3) ◽  
pp. 676-692 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Markov Chains ◽  
Performance Measures ◽  
Sample Path ◽  
Single Sample ◽  
Maclaurin Series ◽  
Transition Matrices ◽  
Engineering Problems ◽  
Realization Factors ◽  
Derivatives Of ◽  
Steady State Performance

We derive formulas for the first- and higher-order derivatives of the steady state performance measures for changes in transition matrices of irreducible and aperiodic Markov chains. Using these formulas, we obtain a Maclaurin series for the performance measures of such Markov chains. The convergence range of the Maclaurin series can be determined. We show that the derivatives and the coefficients of the Maclaurin series can be easily estimated by analysing a single sample path of the Markov chain. Algorithms for estimating these quantities are provided. Markov chains consisting of transient states and multiple chains are also studied. The results can be easily extended to Markov processes. The derivation of the results is closely related to some fundamental concepts, such as group inverse, potentials, and realization factors in perturbation analysis. Simulation results are provided to illustrate the accuracy of the single sample path based estimation. Possible applications to engineering problems are discussed.

The Maclaurin series for performance functions of Markov chains

1998 ◽  
Vol 30 (03) ◽  
pp. 676-692 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Markov Chains ◽  
Performance Measures ◽  
Sample Path ◽  
Single Sample ◽  
Maclaurin Series ◽  
Transition Matrices ◽  
Engineering Problems ◽  
Realization Factors ◽  
Derivatives Of ◽  
Steady State Performance

We derive formulas for the first- and higher-order derivatives of the steady state performance measures for changes in transition matrices of irreducible and aperiodic Markov chains. Using these formulas, we obtain a Maclaurin series for the performance measures of such Markov chains. The convergence range of the Maclaurin series can be determined. We show that the derivatives and the coefficients of the Maclaurin series can be easily estimated by analysing a single sample path of the Markov chain. Algorithms for estimating these quantities are provided. Markov chains consisting of transient states and multiple chains are also studied. The results can be easily extended to Markov processes. The derivation of the results is closely related to some fundamental concepts, such as group inverse, potentials, and realization factors in perturbation analysis. Simulation results are provided to illustrate the accuracy of the single sample path based estimation. Possible applications to engineering problems are discussed.

A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Convergence Conditions ◽  
Principal Angles ◽  
Factorization Formula ◽  
Ill Posed

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

Constructing Attractors via the Improved Eugenics Genetic Algorithm

2014 ◽  
Vol 989-994 ◽  
pp. 1786-1789
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Zi Yang Han
Keyword(s):  
Genetic Algorithm ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Genetic Drift ◽  
Chaotic Attractors ◽  
Parameter Vector ◽  
Distance Limit

The paper introduces Monte Carlo method and Eugenics genetic algorithm, which be used to generate a great diversity of chaotic attractors firstly. By an analysis of their algorithms, a improved eugenics genetic algorithm is presented to avoid the "genetic drift" phenomenon in attractor graphics. A parameter vector distance limit is adopted to solve the problem and lots of experiments applying equivalent mappings of frieze group are finished to validate effectiveness for algorithm.

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (03) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

Sign in / Sign up

Export Citation Format

Share Document