Rare events are events that are expected to occur infrequently or, more technically, those that have low probabilities (say, order of 10 3 or less) of occurring according to a probability model. In the context of uncertainty quantification, the rare events often correspond to failure of systems designed for high reliability, meaning that the system performance fails to meet some design or opera...

for n large. The approximation (1.1) asserts that the “easy problem instances” arise when α is either close to 0 or 1, and that the “hardest problem instances” arise when α ≈ 1/2. This (perhaps surprising) conclusion arises because (1.1) is describing the absolute error associated with the computation. But in rare-event simulation, we are concerned with relative error, not absolute error (i.e. ...

This class presents recent advances in the theory for control, verification, and simulation of hybrid dynamical systems, and shows the application of the theory to the design of the control architecture for complex, large scale systems. Hybrid dynamical systems are continuous time, continuous variable systems with a phased operation. The phases of operation capture the system’s discrete event o...

The acceptance of the right project which leads to the realization of the set objectives is one of the most important issues in project-oriented companies. Therefore, corporate managers prefer to work on those projects which ensures the achievement of goals such as increasing financial profits or being the top brands in their rivals market. The present  research aimed at introducing  a systemat...

Discrete event simulation as a method for performance evaluation has become an indispensable tool in many fields, e.g., teletraffic engineering. New communication networks and services pose extreme requirements regarding the quality of service, e.g., cell loss probabilities in ATM1 networks in the order of 10 . Straightforward simulation for this type of rare event leads to simulation run times...

In simulating applications for execution on specific computing systems, the simulation performance figures must be known in a short period of time. One basic approach to the problem of reducing the required simulation time is the exploitation of parallelism. However, in parallelizing the simulation new problems arise. Due to the distributed generation of events causality errors can occur, as a ...

Discrete-event simulation represents modeling, simulating, and analyzing systems utilizing the computational and mathematical techniques, while creating a model construct of a conceptual framework that describes a system. The system is father simulates by performing experiment(s) using computer implementation of the model and analyzed to draw conclusions from output that assist in decision maki...

This paper deals with estimations of probabilities of rare events using fast simulation based on the splitting method. In this technique, the sample paths are split into multiple copies at various stages in the simulation. Our aim is to optimize the algorithm and to obtain a precise confidence interval of the estimator using branching processes. The numerical results presented suggest that the ...