A goal of modern broadband networks is their ability to provide stringent QoS guarantees to different classes of users. This feature is often related to events with a small probability of occurring, but with severe consequences when they occur. In this paper we focus on the overflow probability estimation and analyze the performance of Bridge Monte-Carlo (BMC), an alternative to Importance Sampling (IS), for the Monte-Carlo estimation of rare events with Gaussian processes. After a short description of BMC estimator, we prove that the proposed approach has clear advantages over the widespread single-twist IS in terms of variance reduction. Finally, to better highlight the theoretical results, we present some simulation outcomes for a single server queue fed by fraction Brownian motion, the canonical model in the framework of long range dependent traffic.
Rare events of Gaussian processes: a performance comparison between Bridge Monte-Carlo and Importance Sampling
GIORDANO, STEFANO;GUBINELLI, MASSIMILIANO;PAGANO, MICHELE
2007-01-01
Abstract
A goal of modern broadband networks is their ability to provide stringent QoS guarantees to different classes of users. This feature is often related to events with a small probability of occurring, but with severe consequences when they occur. In this paper we focus on the overflow probability estimation and analyze the performance of Bridge Monte-Carlo (BMC), an alternative to Importance Sampling (IS), for the Monte-Carlo estimation of rare events with Gaussian processes. After a short description of BMC estimator, we prove that the proposed approach has clear advantages over the widespread single-twist IS in terms of variance reduction. Finally, to better highlight the theoretical results, we present some simulation outcomes for a single server queue fed by fraction Brownian motion, the canonical model in the framework of long range dependent traffic.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
