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Shortle J.F.,4400 University Dr | Shortle J.F.,George Mason University | Chen C.-H.,4400 University Dr | Crain B.,4400 University Dr | And 2 more authors.
IIE Transactions (Institute of Industrial Engineers) | Year: 2012

Simulation is a popular tool for analyzing large, complex, stochastic engineering systems. When estimating rare-event probabilities, efficiency is a big concern, since a huge number of simulation replications may be needed in order to obtain a reasonable estimate of the rare-event probability. The idea of splitting has emerged as a promising variance reduction technique. The basic idea is to create separate copies (splits) of the simulation whenever it gets close to the rare event. Some splitting methods use an equal number of splits at all levels. This can compromise the efficiency and can even increase the estimation variance. This article formulates the problem of determining the number of splits as an optimization problem that minimizes the variance of an estimator subject to a constraint on the total computing budget. An optimal solution for a certain class of problems is derived that is then extended to the problem of choosing the better of two designs, where each design is evaluated via rare-event simulation. Theoretical results for the improvements that are achievable using the methods are provided. Numerical experiments indicate that the proposed approaches are efficient and robust. © 2012 "IIE".


Meyers T.,DecisionTek LLC | Stambouli A.,DecisionTek LLC | McClure K.,Federal Railroad Administration | Brod D.,DecisionTek LLC
Transportation Research Record | Year: 2012

The risk assessment of positive train control (PTC) presents a number of challenges that can be addressed through simulation, a common tool for analyzing large, complex stochastic systems. The combined analysis of a simulated rail system with safety models that track the propagation of human errors and equipment failures toward hazards and accidents (or their eventual safe resolution) enables the prediction of accidents and their probability of occurrence for a base case without PTC and an alternate case with PTC. Accidents are rare events, and when probabilities of rare events are estimated, efficiency is a major concern because the computer resources required for statistically reliable estimates are usually overwhelming. The problem of efficiency can be addressed through multilevel splitting, or staged simulation. The basic idea of splitting is to create separate copies of the simulation whenever it approaches the rare event. The FRA generalized train movement simulator (GTMS) integrates a rail system simulator with safety models and staged simulation to arrive at metrics of safety and risk that meet federal regulatory requirements. The simulation techniques used and a description of their implementation in the GTMS are presented. The paper concludes with a case study risk assessment that uses the GTMS of a nonvital overlay PTC system for a Class I railroad.

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