Large deviations and fast simulation in the presence of boundaries
(2002) In Stochastic Processes and their Applications 102(1). p.123 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:
http://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
 1879209X
 DOI
 10.1016/S03044149(02)001527
 language
 English
 LU publication?
 yes
 id
 b3de0098715a4c70880da76dada27a47 (old id 325126)
 date added to LUP
 20070807 16:12:29
 date last changed
 20180107 08:59:23
@article{b3de0098715a4c70880da76dada27a47, 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 = {1879209X}, keyword = {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 = {123}, 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/S03044149(02)001527}, volume = {102}, year = {2002}, }