SPLITTING TECHNIQUES in VS .NET

Creation QR Code in VS .NET SPLITTING TECHNIQUES
SPLITTING TECHNIQUES
Printing QR Code JIS X 0510 In .NET Framework
Using Barcode creation for .NET Control to generate, create QR image in VS .NET applications.
level provides an unbiased estimate of the theoretical entrance distribution of the chain at that level (the distribution of the state when it hits that level for the rst time) under the original probabilities With splitting implementations where chains may have different weights, and with IS, this is true only for the weighted (and rescaled) empirical distributions, where each observation keeps its weight when we de ne the distribution There are also situations where it is simpler and easier to construct a good importance function for splitting than for IS, because IS can be more sensitive to the behavior of the importance function near the boundaries of the state space, as explained in [9, 12] (see also Section 323) One limitation of splitting with respect to IS is the requirement to decompose the state space into subsets (or layers) determined by the levels of some importance function, such that the probability of reaching the next level starting from the current one is not so small When such a decomposition can be found, splitting can be ef ciently applied However, there are situations where the most probable paths that lead to the rare event have very few steps (or transitions), and where rarity comes from the fact that each of these steps has a very low probability For example, in a reliability setting, suppose that the rare event is a system failure and that the most likely way that this failure occurs is by a failure of two components of the same type, which happens from two transitions of the Markov chain, where each transition has a very small probability In such a situation, splitting cannot be effectively applied, at least not directly It would require a trick to separate the rare transitions into several phases IS, on the other hand, can handle this easily by increasing the probability of occurrence of these rare transitions It is also important to recognize that in the case of large models (such as a large queuing system with many state variables), the state-cloning operations can easily induce a signi cant overhead in CPU time This chapter is organized as follows Section 32 describes the general principles of splitting techniques and the main versions (or implementations) found in the literature Section 33 provides an asymptotic analysis of the method in a simpli ed setting that involves assuming that reaching the next level from the current one can be modeled by a Bernoulli random variable independent of the current state (given that we have just reached the current level) This is equivalent to assuming that there is a single entrance state at each level We then discuss how much we should split and how many levels we should de ne to minimize the variance, or its work-normalized version (the variance multiplied by the expected computing time), in an asymptotic setting In Section 34 we provide an analysis based on interacting particle systems, following the general framework of [10] This permits us to obtain a central limit theorem in a general setting, in an asymptotic regime where the number of initial trajectories (or particles) increases to in nity While previous results focused on a speci c case of splitting where the number of trajectories at each level is xed, we additionally provide versions of the central limit theorem for other splitting implementations Section 35 applies different versions of the splitting technique to a simple example of a tandem queue, used earlier by several authors It illustrates the effectiveness of the
Recognizing QR-Code In .NET Framework
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications.
SPLITTING TECHNIQUES
Encode Bar Code In .NET Framework
Using Barcode drawer for Visual Studio .NET Control to generate, create barcode image in Visual Studio .NET applications.
method, and also the dif culties and the critical issue of nding an appropriate importance function Note that both IS and splitting techniques were introduced and investigated with the Monte Carlo method as early as in the mid 1940s in Los Alamos [21, 22, 29] The main relevant issues, such as an analysis of the optimal splitting strategies and the de nition of the importance function, were already identi ed at that time
Recognize Barcode In VS .NET
Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET framework applications.
Quick Response Code Creator In C#
Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in VS .NET applications.
Generating QR Code JIS X 0510 In VB.NET
Using Barcode generation for .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications.
Generate Bar Code In .NET
Using Barcode generator for .NET Control to generate, create barcode image in VS .NET applications.
Creating EAN128 In .NET Framework
Using Barcode drawer for .NET Control to generate, create UCC-128 image in Visual Studio .NET applications.
ECC200 Maker In Java
Using Barcode encoder for Java Control to generate, create Data Matrix ECC200 image in Java applications.
Read Barcode In .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
Printing Code-128 In Visual Basic .NET
Using Barcode creator for Visual Studio .NET Control to generate, create Code 128B image in VS .NET applications.
Code-39 Printer In Java
Using Barcode creation for Java Control to generate, create Code 39 Extended image in Java applications.