There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state dependent importance sampling method which partitions the state space and applies the...

We develop a methodology for studying ''large deviations type'' questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are...

We develop a methodology for studying "large deviations type" questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are...

We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture technique, and show by experiments the superiority of...

A sequence of real numbers (<I>x_n</I>) is Benford if the significands, i.e. the fraction

A version of the classical secretary problem is studied, in which one is interested in selecting one of the <I>b</I> best out of a group of <I>n</I> differently ranked persons who are presented one by one in a random order. It is assumed that <I>b</I> is bigger than or equal to 1 is a preassigned number. It is...</i></i></i>

This paper applies importance sampling simulation for estimating rare event probabilities of the first passage time in the infinite server queue with renewal arrivals and general service time distributions. We consider importance sampling algorithms which are based on large deviations results of...

We develop a methodology for studying ''large deviations type'' questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are...

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...

In this paper we describe a Sequential Importance Sampling (SIS) procedure for counting the number of vertex covers in general graphs. The performance of SIS depends heavily on how close the SIS proposal distribution is to a uniform one over a suitably restricted set. The proposed algorithm...