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We analyse the deviant behavior of a queue fed by a large number of traac streams. In particular, we explicitly give the most likely trajectory (oròptimal path') to buuer overrow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov uid sources and periodic sources. Apart from a number of ramiications of(More)
We address the issue of call acceptance and routing in ATM networks. Our goal is to design an algorithm that guarantees bounds on the fraction of cells lost by a call. The method we propose for call acceptance and routing does not require models describing the trafflc. Each switch estimates the additional fraction of cells that would be lost if new calls(More)
This paper reports simulation experiments, applying the cross entropy method such as the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failure biasing schemes that have been proved to give estimators with bounded relative errors. The results from the(More)
In this paper we consider the Newsvendor Problem. Intuition may lead to the hypothesis that in this stochastic inventory problem a higher demand variability results in larger variances and in higher costs. In a recent paper, Song (1994a) has proved that the intuition is correct for many demand distributions that are commonly used in practice, such as for(More)
This paper deals with the transient behavior of the Erlang loss model. After scaling both arrival rate and number of trunks, an asymptotic analysis of the blocking probability is given. Apart from that, the most likely path to blocking is given. Compared to Shwartz and Weiss [14], more explicit results are obtained by using probabilistic arguments. The(More)
This article analyzes the transient buffer content distribution of a queue fed by a large number of Markov fluid sources. We characterize the probability of overflow at time <i>t</i>, given the current buffer level and the number of sources in the on-state. After scaling buffer and bandwidth resources by the number of sources <i>n</i>, we can apply large(More)
Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the introduction of computers. This increased computer power has(More)
In this paper we apply the minimum cross-entropy method (MinxEnt) for estimating rare-event probabilities for the sum of i.i.d. random variables. MinxEnt is an analogy of the Maximum Entropy Principle in the sense that the objective is to minimize a relative (or cross) entropy of a target density h from an unknown density f under suitable constraints. The(More)
  • Ad Ridder
  • European Journal of Operational Research
  • 2009
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 the infinite server queue, and we consider an algorithm based(More)