29,423 research outputs found
Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks
In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies
Efficient rare-event simulation for the maximum of heavy-tailed random walks
Let be a sequence of i.i.d. r.v.'s with negative mean. Set
and define . We propose an importance sampling
algorithm to estimate the tail of that is strongly
efficient for both light and heavy-tailed increment distributions. Moreover, in
the case of heavy-tailed increments and under additional technical assumptions,
our estimator can be shown to have asymptotically vanishing relative variance
in the sense that its coefficient of variation vanishes as the tail parameter
increases. A key feature of our algorithm is that it is state-dependent. In the
presence of light tails, our procedure leads to Siegmund's (1979) algorithm.
The rigorous analysis of efficiency requires new Lyapunov-type inequalities
that can be useful in the study of more general importance sampling algorithms.Comment: Published in at http://dx.doi.org/10.1214/07-AAP485 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Semiparametric Cross Entropy for rare-event simulation
The Cross Entropy method is a well-known adaptive importance sampling method
for rare-event probability estimation, which requires estimating an optimal
importance sampling density within a parametric class. In this article we
estimate an optimal importance sampling density within a wider semiparametric
class of distributions. We show that this semiparametric version of the Cross
Entropy method frequently yields efficient estimators. We illustrate the
excellent practical performance of the method with numerical experiments and
show that for the problems we consider it typically outperforms alternative
schemes by orders of magnitude
Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes
We propose a class of strongly efficient rare event simulation estimators for
random walks and compound Poisson processes with a regularly varying
increment/jump-size distribution in a general large deviations regime. Our
estimator is based on an importance sampling strategy that hinges on the
heavy-tailed sample path large deviations result recently established in Rhee,
Blanchet, and Zwart (2016). The new estimators are straightforward to implement
and can be used to systematically evaluate the probability of a wide range of
rare events with bounded relative error. They are "universal" in the sense that
a single importance sampling scheme applies to a very general class of rare
events that arise in heavy-tailed systems. In particular, our estimators can
deal with rare events that are caused by multiple big jumps (therefore, beyond
the usual principle of a single big jump) as well as multidimensional processes
such as the buffer content process of a queueing network. We illustrate the
versatility of our approach with several applications that arise in the context
of mathematical finance, actuarial science, and queueing theory
Analysis of State-Independent Importance-Sampling Measures for the Two-Node Tandem Queue
We investigate the simulation of overflow of the total population of a Markovian two-node tandem queue model during a busy cycle, using importance sampling with a state-independent change of measure. We show that the only such change of measure that may possibly result in asymptotically efficient simulation for large overflow levels is exchanging the arrival rate with the smallest service rate. For this change of measure, we classify the model's parameter space into regions of asymptotic efficiency, exponential growth of the relative error, and infinite variance, using both analytical and numerical techniques
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
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