Large deviations and fast simulation in the presence of boundaries
(2002) In Stochastic Processes and their Applications 102(1). p.1-23- Abstract
- Let c(x) = inf {t > 0: Q(t) greater than or equal to x} be the time of first overflow of a queueing process 1001 over level x (the buffer size) and Z = P(T(X) less than or equal to T). Assuming that {Q(t)) is the reflected version of a Levy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {tau(X) less than or equal to T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a... (More)
- Let c(x) = inf {t > 0: Q(t) greater than or equal to x} be the time of first overflow of a queueing process 1001 over level x (the buffer size) and Z = P(T(X) less than or equal to T). Assuming that {Q(t)) is the reflected version of a Levy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {tau(X) less than or equal to T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a way out of counterexamples in the literature on the scope of the large deviations approach to rare events simulation. We also add a counterexample of this type and give various theoretical results on asymptotic properties of Z=P(tau(x) less than or equal to T), both in the reflected Levy process setting and more generally for regenerative processes in a regime where T is so small that the exponential approximation for T(x) is not a priori valid. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/325126
- author
- Asmussen, Sören LU ; Fuckerieder, P ; Jobmann, M and Schwefel, HP
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- rare, queueing theory, local time, Levy process, importance sampling, filtered Monte Carlo, buffer overflow, exponential change of measure, event, reflection, regenerative process, saddlepoint
- in
- Stochastic Processes and their Applications
- volume
- 102
- issue
- 1
- pages
- 1 - 23
- publisher
- Elsevier
- external identifiers
-
- wos:000178575400001
- scopus:0036829392
- ISSN
- 1879-209X
- DOI
- 10.1016/S0304-4149(02)00152-7
- language
- English
- LU publication?
- yes
- id
- b3de0098-715a-4c70-880d-a76dada27a47 (old id 325126)
- date added to LUP
- 2016-04-01 16:03:13
- date last changed
- 2022-04-22 19:15:34
@article{b3de0098-715a-4c70-880d-a76dada27a47,
abstract = {{Let c(x) = inf {t > 0: Q(t) greater than or equal to x} be the time of first overflow of a queueing process 1001 over level x (the buffer size) and Z = P(T(X) less than or equal to T). Assuming that {Q(t)) is the reflected version of a Levy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {tau(X) less than or equal to T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a way out of counterexamples in the literature on the scope of the large deviations approach to rare events simulation. We also add a counterexample of this type and give various theoretical results on asymptotic properties of Z=P(tau(x) less than or equal to T), both in the reflected Levy process setting and more generally for regenerative processes in a regime where T is so small that the exponential approximation for T(x) is not a priori valid.}},
author = {{Asmussen, Sören and Fuckerieder, P and Jobmann, M and Schwefel, HP}},
issn = {{1879-209X}},
keywords = {{rare; queueing theory; local time; Levy process; importance sampling; filtered Monte Carlo; buffer overflow; exponential change of measure; event; reflection; regenerative process; saddlepoint}},
language = {{eng}},
number = {{1}},
pages = {{1--23}},
publisher = {{Elsevier}},
series = {{Stochastic Processes and their Applications}},
title = {{Large deviations and fast simulation in the presence of boundaries}},
url = {{http://dx.doi.org/10.1016/S0304-4149(02)00152-7}},
doi = {{10.1016/S0304-4149(02)00152-7}},
volume = {{102}},
year = {{2002}},
}