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Passage time distributions in large Markov chains

2002
*
Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02
*

Setting s = 0 yields moments while the full

doi:10.1145/511334.511345
dblp:conf/sigmetrics/HarrisonK02
fatcat:3gpydizwszap7cuqulvnva64yu
*passage**time**distribution*is obtained using a novel*distributed*Laplace transform inverter based on the Laguerre method. ... Probability*distributions*of response*times*are important*in*the design and analysis of transaction processing systems and computercommunication systems. ... ACKNOWLEDGEMENTS The authors would like to thank their M.Sc. student Teresa Au-Young for bringing the Laguerre method to their attention*in*her M.Sc. thesis "Numerical Techniques for Laplace Transform ...##
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Passage time distributions in large Markov chains

2002
*
Performance Evaluation Review
*

Setting s = 0 yields moments while the full

doi:10.1145/511399.511345
fatcat:vo2cgdcbubaizctv7xbggtdgxq
*passage**time**distribution*is obtained using a novel*distributed*Laplace transform inverter based on the Laguerre method. ... Probability*distributions*of response*times*are important*in*the design and analysis of transaction processing systems and computercommunication systems. ... ACKNOWLEDGEMENTS The authors would like to thank their M.Sc. student Teresa Au-Young for bringing the Laguerre method to their attention*in*her M.Sc. thesis "Numerical Techniques for Laplace Transform ...##
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Passage time distributions in large Markov chains

2002
*
Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02
*

Setting s = 0 yields moments while the full

doi:10.1145/511344.511345
fatcat:hzhmq2t6k5abxbd6xavp4a5sau
*passage**time**distribution*is obtained using a novel*distributed*Laplace transform inverter based on the Laguerre method. ... Probability*distributions*of response*times*are important*in*the design and analysis of transaction processing systems and computercommunication systems. ... ACKNOWLEDGEMENTS The authors would like to thank their M.Sc. student Teresa Au-Young for bringing the Laguerre method to their attention*in*her M.Sc. thesis "Numerical Techniques for Laplace Transform ...##
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Distribution of First Passage Times for Lumped States in Markov Chains

2015
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Journal of Mathematics and System Science
*

First

doi:10.17265/2159-5291/2015.08.002
fatcat:buvdd6zjnzfnvivubgw5mozqta
*passage**time**in**Markov**chains*is defined as the first*time*that a*chain*passes a specified state or lumped states. ...*In*this study, obtaining*distribution*of the first*passage**time*relating to lumped states which are constructed by gathering the states through lumping method for a irreducible*Markov**chain*whose state ...*Distribution*of First*Passage**Times*for Lumped States*in**Markov**Chains*321*Distribution*of First*Passage**Times*for Lumped States*in**Markov**Chains*322*Distribution*of First*Passage**Times*for Lumped ...##
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THE DISTRIBUTION OF MIXING TIMES IN MARKOV CHAINS

2013
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Asia-Pacific Journal of Operational Research
*

Some new results for the

doi:10.1142/s0217595912500455
fatcat:6u2t2u4gxvc3lnvcn5qkvcz5sm
*distribution*of recurrence and first*passage**times**in*three-state*Markov**chain*are also presented. ... Hunter, Variances of first*passage**times**in*a*Markov**chain*with applications to mixing*times*, Linear Algebra Appl. 429 (2008) 1135-1162]. ... Thus these expectations depends on the stationary*distribution*of the*Markov**chain*and the mean first*passage**times*from state i to the other states*in*the state space. ...##
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When Translocation Dynamics Becomes Anomalous

2003
*
Biophysical Journal
*

Recent single molecule experiments probing the

doi:10.1016/s0006-3495(03)74699-2
pmid:14507739
pmcid:PMC1303500
fatcat:o536nl7dvfasbops4z7abttsgy
*passage*process of a short single-stranded DNA (ssDNA) through a membrane channel (translocation) allow to measure the*passage**time**distribution*. ... J. 77, 1824 (1999)), which has been demonstrated to be valid for*chains*of up to ≃ 300 nucleotides and therefore well applies to the system we have*in*mind, we discuss the consequences if the associated ...*In*a recent experiment (Bates et al., 2003) , it was noted that the first*passage**time**distribution*contains nonnegligible contributions over a*large**time*range even*in*the presence of a low driving voltage ...##
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Page 4489 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
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Mathematical Reviews
*

Kindermann (Brookings, SD)
92h:60106 60310 Latouche, Guy (B-VUB) First

*passage**times**in*nearly decomposable*Markov**chains*. Numerical solution of*Markov**chains*, 401-411, Probab. ... Here N(u) = min{n;S, > u} denotes the first-*passage**time*for a random walk of the form S, = S77_, Ux(&-1,¢%), where 0,1, --: is a finite*Markov**chain*and where {U;,(i, j)}? ...##
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Transient calculations on process algebra derived Markov chains

2009
*
IET Software
*

the cumulative

doi:10.1049/iet-sen.2009.0002
fatcat:bws7nvdqq5dgfh4yxuwk26wljy
*distribution*and probability density functions of the*passage**in*question. ... The process of obtaining transient measures from a*Markov**chain*as implemented*in*the software, ipclib is described. The software accepts models written*in*PEPA, Bio-PEPA or as a Petri net. ... The ipc/Hydra tool*chain*has been developed*in*co-operation with Jeremy Bradley, Will Knottenbelt and Nick Dingle of Imperial College, London. ...##
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Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

2017
*
Journal of Energy in Southern Africa
*

This paper presents a

doi:10.17159/2413-3051/2017/v28i4a2329
fatcat:q6duztc4svdwhdjk7ystx5h7fy
*Markov**chain*analysis to determine stationary*distributions*(steady state probabilities) of*large*daily changes*in*peak electricity demand. ... The analysis used on South African daily peak electricity demand data from 2000 to 2011 and on a simple two-state discrete-*time**Markov**chain*modelling framework was adopted to estimate steady-state probabilities ... This is consistent with the*Markov**chain*analysis discussed*in*Section 3. Extreme*large*increases*in*inter-day changes*in*peak electricity demand are likely to occur*in*May, as shown*in*Figure 7 . ...##
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Past states of continuous-time Markov models for ecological communities

2008
*
Mathematical Biosciences
*

We show how to obtain the

doi:10.1016/j.mbs.2007.08.006
pmid:17931668
fatcat:qxnrglygzbfhrg6nrjww4a5zge
*distribution*of*time*since the last occurrence of a state of interest for a continuous-*time*homogeneous*Markov**chain*. ... A recent study showed how the*time*-reversal of such a*Markov**chain*can be used to estimate the*distribution*of*time*since the last occurrence of some state of interest (such as empty space) at a point, ... first*passage**times*to state j*in*the*time*-reversed*chain*. ...##
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Using the First Passage Times in Markov Chain Model to Support Financial Decisions on the Stock Exchange

2016
*
Dynamic Econometric Models
*

*In*this context, there is a possibility of determining easily the value at risk with the accepted probability. K e y w o r d s:

*Markov*

*Chain*, First

*passage*

*times*, Normal white noise, VaR. ... The purpose of this article is to present the possibilities of using such a tool as

*Markov*

*Chain*to analyse the dynamics of returns observed at the Warsaw Stock Exchange. ... were as follows: the First

*Passage*

*Times*

*in*

*Markov*

*Chain*Model... ...

##
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Page 384 of Geographical Analysis Vol. 6, Issue 4
[page]

1974
*
Geographical Analysis
*

*In*the

*Markov*-

*chain*approach, which utilizes the mean first

*passage*

*time*property, linkages with a

*large*number of indirect flows are penalized. ... A

*large*number of indirect flows between state A and state B, for example, would be reflected

*in*a relatively

*large*mean first

*passage*

*time*value for the A-B dyad; and,

*in*terms of the

*Markov*

*chain*mean ...

##
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Page 958 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

A new analytical approach

*in*prov- ing the strong law of*large*numbers for*Markov**chains*is presented, the crucial part of which is to construct the*Markov**chain*with the given initial*distribution*and ... Moreover, a canonical representation formula for the generating function of a*passage**time**distribution*is presented.” ...##
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Phase-type distributions and the structure of finite Markov chains

1993
*
Journal of Computational and Applied Mathematics
*

We show that all discrete phase-type

doi:10.1016/0377-0427(93)90040-i
fatcat:oap2kiqvkfdndhux663moqgo6q
*distributions*arise as first*passage**times*(i.e., absorption*times*)*in*finite-state*Markov**chains*with a certain recursive internal structure. ... absorption*time**distribution*. ... Introduction The*distribution*of any first*passage**time**in*a finite-state*Markov**chain*is said to be of phase-type [5] . ...##
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Mixing times with applications to perturbed Markov chains

2006
*
Linear Algebra and its Applications
*

A measure of the "mixing

doi:10.1016/j.laa.2006.02.008
fatcat:s2tgcafr6ncbpmkrt3dllr4o3a
*time*" or "*time*to stationarity"*in*a finite irreducible discrete*time**Markov**chain*is considered. ... When η is*large*the stationary*distribution*of the*Markov**chain*is very sensitive to perturbations of the transition probabilities. ... If -1< d < 1, the*Markov**chain*is regular and this stationary*distribution*is*in*fact the limiting*distribution*. ...
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