Importance Sampling Simulation Research Articles

Importance sampling simulation of concatenated block codes

An importance sampling (IS) simulation of block codes is considered, based on the serial or parallel concatenation of simple codes. At very low bit error rates, traditional Monte Carlo simulations cannot be performed due to the very long simulation time that would be required. IS techniques can be very helpful in these cases. It is shown how IS can be applied to evaluate the performance of optimal MAP bit-per-bit decoders, and of non-optimal (turbo-like) iterative decoders.

Efficient estimation of overflow probabilities in queues with breakdowns

Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.

A new adaptive importance sampling scheme for reliability calculations

An adaptive importance sampling methodology is proposed to compute the multidimensional integrals encountered in reliability analysis. It is based on a Markov simulation algorithm due to Metropolis et al. (Metropolis, Rosenbluth, Rosenbluth and Teller, Equations of state calculatons by fast computing machines. Journal of Chemical Physics, 1953;21(6): 1087-1092). In the proposed methodology, samples are simulated as the states of a Markov chain and are distributed asymptotically according to the optimal importance sampling density. A kernel sampling density is then constructed from these samples which is used as the sampling density in an importance sampling simulation. The Markov chain samples populate the region of higher probability density in the failure region and so the kernel sampling density approximates the optimal importance sampling density for a large variety of shapes of the failure region. This adaptive feature is insensitive to the probability level to be estimated. A variety of numerical examples demonstrates the accuracy, efficiency and robustness of the methodology.

Multiparametric importance sampling for simulation of radar systems

The performances of the importance sampling (IS) techniques are improved by using multiparametric distortions of the input random processes. The analysis of different constant false-alarm rate (CFAR) algorithms confirms the usefulness of this method. The potential of this new approach is fully exploited if optimization techniques are used to obtain the optimum distortions and to avoid bias in the estimates.

Fast simulation of networks of queues with effective and decoupling bandwidths

A significant difficulty when using Monte Carlo simulation for the performance analysis of communication networks is the long runtime required to obtain accurate statistical estimates. Under the proper conditions, importance sampling (IS) is a technique that can speed up simulations involving rare events in network (queuing) systems. Large speed-up factors in simulation runtime can be obtained with IS if the modification or bias of the underlying probability measures of certain random processes is carefully chosen. Fast simulation methods based on large deviation theory (LTD) have been successfully applied in many cases. In this paper, we set up an IS-based simulation of various elementary network topologies. These configurations are frequenly encountered in broadband ATM-based network components such as switches and multiplexers. Our objective in this study is to obtain the optimal or near-optimal biasing parameter values of the arrival processes for the importance sampling simulation. For this purpose we appropriately apply a technique presented by Chang et al. for certain portions of the networks (intree) while we develop a new algorithm, inspired by the work of De Veciana et al. on decoupling bandwidths, for the non-intree portion of the network.

A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques

A class of Monte Carlo algorithms for probability propagation in belief networks is given. The simulation is based on a two steps procedure. The first one is a node deletion technique to calculate the ‘a posteriori’ distribution on a variable, with the particularity that when exact computations are too costly, they are carried out in an approximate way. In the second step, the computations done in the first one are used to obtain random configurations for the variables of interest. These configurations are weighted following importance sampling methodology. Different particular algorithms are obtained depending on the approximation procedure used in the first step and the way of obtaining the random configurations. In this last case, a stratified sampling technique is used, which has been adapted for application to very large networks without round-off error problems.

Cycle-slip analysis of the Mth-power NDA feedforward carrier synchronizer for MPSK

We analyze the cycle-slipping behavior of the Mth-power nondecision-aided (NDA) feedforward carrier synchronizer for M-ary phase-shift keying (MPSK). The averaging filter is a block window accumulator, and postprocessing is used to eliminate equivocation. An asymptotic (high E/sub s//N/sub o/) expression for the cycle-slip probability is derived and verified by computer simulation. A hybrid approach, combining analytical results with importance sampling simulation techniques, allows for the fast and accurate determination of the cycle-slip probability for all E/sub s//N/sub o/ values of practical interest.

The optimal IS simulation distribution of MMPP/D/1 queuing

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

The optimal IS simulation distribution of MMPP/D/1 queuing

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

方向重点サンプリング・シミュレーション法に基づく構造システムの信頼性評価法の研究

This paper provides an improved directional simulation method to estimate the structural failure probability. A method is proposed to construct a directional importance sampling density, which generates more samples of direction vectors in the direction where the limit state surfaces are closer to the origin. The proposed method is composed of two-stage procedures. In the first stage, a preliminary simulation is executed to search the distances from the origin to the limit state surfaces in the directions normal to finite element meshes allocated on the unit sphere. A directional importance sampling density is constructed so as to be proportional to the upper probability of chi-square distribution corresponding to each distance. In the second stage, a directional importance sampling simulation is executed to estimate the structural failure probability.All samples are effectively generated to estimate the structural failure probability and the proposed method is effective for the reliability assessment of the structural systems. Numerical examples are provided to show the validity of the proposed method.

Reliability analysis of structural components under fatigue environment including random overloads

A method is proposed for estimating the hazard rate and reliability function of structural components under the fatigue environment including random overloads. The fatigue crack propagation process is stochastically analyzed by the use of a Markov approximation method in consideration of the retardation effect due to the overloads. The retardation effect is expressed by the probability distribution of the total delay time for the crack propagation process. Firstly, the theoretical approach on the random crack growth is applied under the condition of random occurrence of overloads. The hazard rate of structural components with respect to the ductile failure as well as the fatigue failure is secondly investigated with the aid of the numerical calculation known as the importance sampling simulation. The reliability function for the failure of structural component is shown as the result of the hazard rate. One of the interesting results is that the possibility of failure by overloads is more dominant than the retardation effect of crack growth due to overloads in the high reliability range.

A randomized bias technique for the importance sampling simulation of Bayesian equalizers

An importance sampling (IS) simulation technique is presented for Bayesian equalizers, based on the large deviations theory approach developed by Sadowsky and Bucklew (see ibid., vol.36, no.5, p.579, 1990). The resulting simulation density consists of a sum of exponentially twisted distributions. For the additive Gaussian channel, this simulation density is equivalent to the conventional (mean-shift) noise biasing IS method, but with the bias vector chosen from a fixed set in a random manner. In order to properly select the bias vectors, the asymptotic decision boundary of the Bayesian equalizer is first determined. It is shown that the boundary is formed by multiple hyperplanes, and that the appropriate bias vectors are orthogonal to the hyperplanes. The simulation technique is then extended to the recursive symbol-by-symbol detector of Abend and Fritchman (A-F algorithm) proposed in 1970, and simulation results are presented for both recursive and non-recursive equalizers. >

Importance sampling for analysis of direct detection optical communication systems

Analytical solutions of the performance of optical communication systems are difficult to obtain and often, Monte Carlo simulations are used to achieve realistic estimates of the performance of such systems. However, for high performance systems, this technique requires a large number of simulation trials for the estimates to be in a reasonable interval of confidence, with the number of trials increasing linearly with the performance of the system. We apply an importance sampling technique to estimate the performance of direct detection optical systems, where the gain of importance sampling over Monte Carlo simulations is shown to increase linearly with the system performance. Further, we use this technique to study the performance of optical communication systems employing avalanche photodetectors as well as fibre-optic code division multiple access systems (FO-CDMA). We also show that the quick simulation technique developed can be used for a wide variety of coding schemes, and for the first time, we present a comparative analysis of the performance of FO-CDMA systems employing optical orthogonal codes and prime sequences. In all cases, it is shown that importance sampling simulations require less than 50-100 trials for estimating error probabilities of 10/sup -10/ and below. >

破損領域重点サンプリング・シミュレーションに基づく構造システムの信頼性解析

This paper is concerned with a reliability assessment of structural systems based on an improved importance sampling simulation, in which the importance sampling density is determined within the limit of the failure region. Basic random variables are assumed to be stochastically independent normal variates and the minimum reliability index β of the system to be known beforehand. The first step of the proposed method is to execute simulations, refered to the preliminary simulations, to get a rough estimate of the failure probability and data about the sample distribution. These data are utilized to determine the importance sampling density as a frequency distribution with respect to radius in polar coordinates. In the second step, the structural failure probabilities are estimated through the importance sampling simulations, samples of which are generated from the estimator of the importance sampling density determined in the first step.The proposed method is compared in a numerical example with the Monte Carlo simulation combined with partition of the region technique and ISPUD for multi mode failure etc. It can be said that the proposed method is effective for the estimation of structural failure probabilities.

Importance Sampling Simulation in UltraSAN

Traditional simulation techniques perform poorly when estimating performance measures based on rare events. One solution to this problem is the use of importance sampling. However, two problems that have limited the use of importance sampling are the lack of a formal framework for specifying importance sampling strategies, and the fact that in most cases the simulations must be hand-coded — a very time-consuming process. This paper presents a software tool that facilitates experimentation with importance sampling by addressing these two problems. First, the tool is based on a flexible framework for specifying importance sampling simulations in terms of stochastic activity networks. Second, once specified, the importance sampling simulation program is automatically generated by the tool, freeing the researcher to focus on the modeling problem. The effectiveness of the software is demonstrated through the solution of a machine-repairman model with Weibull distributed failure times and a delayed group repair policy. Orders of magnitude reduction in the CPU time required to obtain a specified relative accuracy were achieved.

Probability methods for the fracture of composite materials

The reliability calculation for a composite material may be performed using a variety of approximation methods. These methods are broadly divided into fast probability integration (FPI) methods of either first or second order, and the Monte Carlo-based simulation methods. Using the Tsai-Hill and Tsai-Wu failure criteria as examples, these methods are described and illustrated. The methods are compared for accuracy, difficulty of implementation, and sensitivity to uncertainty in the parameters of the strength (or stress) distributions. The two methods of choice for speed, accuracy and innate conservatism are: importance sampling simulation, and the FPI rotational parabaloid. Under most conditions, the results of a linear approximation are also acceptable.

Soft decision decoding of Reed-Solomon codes using trellis methods

Soft decision decoding of Reed-Solomon codes has been implemented by using trellis decoding methods. Trellis decoding schemes make it possible to incorporate both hard and soft decision methods easily. To establish maximum likelihood performance, the Viterbi decoding algorithm has been used. To reduce the decoder complexity caused by full search Viterbi decoding, reduced search methods have been tried, and a computationally efficient reduced search algorithm is suggested. Importance sampling simulation techniques have been used to reduce simulation time. The simulation results for the (15, 13) and the (15, 11) Reed-Solomon code showed that soft decision trellis decoding could give 2 dB and 2.5 dB coding gains relative to hard decision, respectively, and that the performance of reduced search decoding could approximate that of the Viterbi method with reductions in computation of one to two orders of magnitude.

An importance sampling analysis of a noninterleaved Viterbi decoder in an RFI environment

This paper presents an importance sampling simulation model which analyzes a communications system consisting of a noisy channel, a transmitter/receiver, and a convolutional encoder/Viterbi decoder. The model determines the amount of signal degradation caused by any noise environment that can be modeled as a Markov chain. The specific example of a Radio Frequency Interference (RFI) noise environment is discussed in detail. The model uses importance sampling to determine low bit error rates (BERs) for a wide range of noise environments. It is faster than a conventional simulation because the required run time is independent of the BER. It is more flexible than existing analytic models, as these make major assumptions, such as that symbol errors are independent (interleaving), or that all bursts have infinite power. The model increases the simulation efficiency by biasing the channel statistics so that more codeword errors occur and adjusts for this by using a weighting function whose value is calculated through the use of a Markov chain. The results show that using interleaving results in a significant performance improvement when the lengths of the interfering bursts are long relative to the data symbol length.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new importance sampling technique for the evaluation of performance in digital communication systems

Importance sampling simulation is an efficient tool for the evaluation of the probability of rare events and performs well while estimating low probability errors in digital communication systems. After a brief description of principalis techniques, we present a new technique which uses probability density functions of the « generalized Rayleigh tail » category. The good performance of this technique is demonstrated by computing the associated estimation variance and asymptotic confidence interval. Analytical and simulation results show that the proposed technique is robust with respect to parameter variations. The optimal parameters are also obtained for the minimised estimation variance. Finally, we present a random variable generation method adapted to our technique.

Rare events in series of queues

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.