Rare Event Simulation using Monte Carlo Methods (original) (raw)

The Rare Event Simulation Method RESTART: Efficiency Analysis and Guidelines for Its Application

Lecture Notes in Computer Science, 2011

This paper is a tutorial on RESTART, a widely applicable accelerated simulation technique for estimating rare event probabilities. The method is based on performing a number of simulation retrials when the process enters regions of the state space where the chance of occurrence of the rare event is higher. The paper analyzes its efficiency, showing formulas for the variance of the estimator and for the gain obtained with respect to crude simulation, as well as for the parameter values that maximize this gain. It also provides guidelines for achieving a high efficiency when it is applied. Emphasis is placed on the choice of the importance function, i.e., the function of the system state used for determining when retrials are made. Several examples on queuing networks and ultra reliable systems are exposed to illustrate the application of the guidelines and the efficiency achieved.

Rare event provoking simulation techniques

1995

Importance sampling is the rare event provoking technique that is most frequently used for speed-up simulation of dependability and traffic models. Due to its sensitivity to the parameter settings, it is not yet ready for practical use. There exists a number of approaches for finding optimal, or at least good, parameters. The applicability of these and necessary extensions are discussed with reference to the typical characteristics of state models used for simulation.

The Study of Rare Event Systems' Behavior Using Simulation

Simulation is a useful tool in the design process when building a large-scale system. It helps to analyze several design factors like feasibility, cost, impact, outcome and risk in advance. Simulation is resource intensive when systems become large and complex. Especially, when we try to simulate a special type of systems called " rare event systems " , the determination of the probability of such rare events with reasonable confidence interval can be a challenge in terms of computational resource, time, and budget. In this type of systems, the chance of the interested event's occurrence is slim. But the consequence of that is severe. Examples of this type of systems include: space exploration endeavors, air traffic control systems, nuclear reactors control systems, etc. Any rare accidental events in such systems could mean a missed opportunity to find a life in space, the loss of human lives, or the demise of entire life in the planet. The challenge of simulating this type of systems stems from the fact that we dare not miss important cases (have to cover those rare but important possibilities even though some of these are very low, thus a lot of computing time). In this paper, we will present a general-purpose rare event simulation framework package called " SPLITSIM " that is developed and promoted (distributed as open-source software) by us to address rare event simulation challenges; we will give descriptions about the architecture of our software design and give comments on essential parts of our implementation source code; we will also show features and advantages of our open-source package.

Rare event simulation for a slotted time M/G/s model

Queueing Systems, 2009

This paper develops a rare-event simulation algorithm for a discrete time version of the M=G=s loss system and a related Markov modulated variant of the same loss model. The algorithm is shown to be e¢ cient in the many server asymptotic regime in which the number of servers and the arrival rate increase to in…nity in …xed proportion. A key idea is to study the system as a measure-valued Markov chain and to steer the system to the rare event through a randomization of the time horizon over which the rare event is induced.

New measures of robustness in rare event simulation

2005

Rare event simulation requires acceleration techniques in order to i) observe the rare event and ii) obtain a valid and small confidence interval for the expected value. A "good" estimator has to be robust when rarity increases. This paper aims at studying robustness measures, the standard ones in the literature being Bounded Relative Error and Bounded Normal Approximation. By considering the problem of estimating the reliability of a static model for which simulation time per run is the critical issue, we show that actually those measures do not validate the satisfying behavior of some techniques. We thus define Bounded Relative Efficiency and generalized bounded normal approximation properties of the two previous measures in order to encompass the simulation time. We also illustrate how a user can have a look at the coverage of the resulting confidence interval by using the so-called coverage function.

Rare-event simulation for infinite server queues

Winter Simulation Conference, 2002

We discuss rare-event simulation methodology for computing tail probabilities for infinite-server queues. Our theoretical discussion also offers some new simulation insights into the change-of-measure associated with the Gartner-Ellis theorem of large deviations.

Rare event simulation techniques: An introduction and recent advances

Simulation, 2006

SG Henderson and BL Nelson (Eds.), Handbook in OR & MS, Vol. 13 Copyright© 2006 Elsevier BV All rights reserved DOI: 10.1016/S0927-0507 (06) 13011-X Chapter 11 Rare-Event Simulation Techniques: An Introduction and Recent Advances S. Juneja School of Technology and ...

Difficult queuing simulation problems: rare-event simulation for infinite server queues

Proceedings of the 34th Conference on Winter Simulation Exploring New Frontiers, 2002

We discuss rare-event simulation methodology for computing tail probabilities for infinite-server queues. Our theoretical discussion also offers some new simulation insights into the change-of-measure associated with the Gärtner-Ellis theorem of large deviations.