Rate-tilting for fast simulation of level/phase processes
type: Item
instance of: scholarly article
title: Rate-tilting for fast simulation of level/phase processes
zbMATH Open document ID: 1050.65008
author: Jingxiang Luo
author: Winfried K. Grassmann
published in: Linear Algebra and its Applications
publication date: 2004-08-04T00:00:00Z
review text: Efficient simulation methods for stochastic processes involving rarely occurring events is in the center of this work. The process considered is the so-called level/phase process, a Markov process in which the ``level'' and the ``phase'' are two state variables. Changes of ``level'' and ``phase'' are induced by events, which have rates that are independent of the level except at a ``boundary''. If a system typically stays at lower levels, then reaching a high level \(n\) is a rare event, thus direct simulation is very inefficient. The authors suggest to change the events rates in a level/phase process to accelerate simulation, and find the so-called hitting probability entering a rare event by simulation. This method is called ``rate-tilting''. A proper construction of ``rate-tilting'' relates to a generalized eigenvalue problem involving the infinitesimal generator matrix \(Q\) of the process being considered. It is shown that the relative estimation error of the hitting probability resulting from the proposed simulation remains bounded as the level increases, provided that the boundary set of the state space satisfies certain conditions. They provide criteria when ``rate-tilting'' is advantageous. However, it may be noted that ``rate-tilting'' is not always increasing the efficiency of simulations.
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 65C40
zbMATH DE Number: 2081266
zbMATH Keywords: simulation
zbMATH Keywords: rare events
zbMATH Keywords: level/phase process
zbMATH Keywords: rate-tilting
zbMATH Keywords: importance sampling
zbMATH Keywords: efficiency
zbMATH Keywords: QBD process
zbMATH Keywords: relative estimation error
zbMATH Keywords: Markov process
zbMATH Keywords: generalized eigenvalue problem
MaRDI profile type: Publication
full work available at URL: j.laa.2004.02.001
OpenAlex ID: W1972805479
cites work: Q4878849
cites work: Q3938929
cites work: Q5687229
cites work: Non-Skip-Free M/G/1 and G/M/1 Type Markov Chains
cites work: Multilevel splitting for estimating rare event probabilities
cites work: Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
cites work: An analytical solution for a tandem queue with blocking
cites work: A Tandem Queuewith a Movable Server: An Eigenvalue Approach
cites work: Fast simulation of rare events in queueing and reliability models
cites work: Large deviations of uniformly recurrent Markov additive processes
cites work: Markov chain models - rarity and exponentiality
cites work: Efficient simulation of a tandem Jackson network
cites work: Introduction to Matrix Analytic Methods in Stochastic Modeling
cites work: Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method
cites work: Q3923308
cites work: Q4733209
cites work: Markov additive processes. I: Eigenvalue properties and limit theorems
cites work: A quick simulation method for excessive backlogs in networks of queues
cites work: Q4405301
cites work: Q4324960
cites work: Queueing Analysis of a Jockeying Model
DOI: 10.1016/J.LAA.2004.02.001
description: scientific article; zbMATH DE number 2081266