Affiliation:
1. CWI, Amsterdam, NETHERLANDS
2. University of Amsterdam, The Netherlands
3. CWI, Amsterdam and Eindhoven University of Technology, NETHERLANDS
Abstract
This article focuses on evaluating the probability that both components of a two-dimensional stochastic process will ever, but not necessarily at the same time, exceed some large level
u
. An important application is in determining the probability of large delays occurring in two correlated queues. Since exact analysis of this probability seems prohibitive, we focus on deriving asymptotics and on developing efficient simulations techniques. Large deviations theory is used to characterise logarithmic asymptotics. The second part of this article focuses on efficient simulation techniques. Using “nearest-neighbour random walk” as an example, we first show that a “naive” implementation of importance sampling, based on the decay rate, is not asymptotically efficient. A different approach, which we call
partitioned
importance sampling, is developed and shown to be asymptotically efficient. The results are illustrated through various simulation experiments.
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Science Applications,Modelling and Simulation
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