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Passage time distributions in large Markov chains

Peter G. Harrison, William J. Knottenbelt
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 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  ... 
doi:10.1145/511334.511345 dblp:conf/sigmetrics/HarrisonK02 fatcat:3gpydizwszap7cuqulvnva64yu

Passage time distributions in large Markov chains

Peter G. Harrison, William J. Knottenbelt
2002 Performance Evaluation Review  
Setting s = 0 yields moments while the full 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  ... 
doi:10.1145/511399.511345 fatcat:vo2cgdcbubaizctv7xbggtdgxq

Passage time distributions in large Markov chains

Peter G. Harrison, William J. Knottenbelt
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 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  ... 
doi:10.1145/511344.511345 fatcat:hzhmq2t6k5abxbd6xavp4a5sau

Distribution of First Passage Times for Lumped States in Markov Chains

Murat Gül, Salih Çelebioğlu
2015 Journal of Mathematics and System Science  
First 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  ... 
doi:10.17265/2159-5291/2015.08.002 fatcat:buvdd6zjnzfnvivubgw5mozqta

THE DISTRIBUTION OF MIXING TIMES IN MARKOV CHAINS

JEFFREY J. HUNTER
2013 Asia-Pacific Journal of Operational Research  
Some new results for the 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.  ... 
doi:10.1142/s0217595912500455 fatcat:6u2t2u4gxvc3lnvcn5qkvcz5sm

When Translocation Dynamics Becomes Anomalous

Ralf Metzler, Joseph Klafter
2003 Biophysical Journal  
Recent single molecule experiments probing the 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  ... 
doi:10.1016/s0006-3495(03)74699-2 pmid:14507739 pmcid:PMC1303500 fatcat:o536nl7dvfasbops4z7abttsgy

Page 4489 of Mathematical Reviews Vol. , Issue 92h [page]

1992 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)}?  ... 

Transient calculations on process algebra derived Markov chains

A. Clark, S. Gilmore
2009 IET Software  
the cumulative 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.  ... 
doi:10.1049/iet-sen.2009.0002 fatcat:bws7nvdqq5dgfh4yxuwk26wljy

Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

Caston Sigauke, Delson Chikobvu
2017 Journal of Energy in Southern Africa  
This paper presents a 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 .  ... 
doi:10.17159/2413-3051/2017/v28i4a2329 fatcat:q6duztc4svdwhdjk7ystx5h7fy

Past states of continuous-time Markov models for ecological communities

Matthew Spencer
2008 Mathematical Biosciences  
We show how to obtain the 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.  ... 
doi:10.1016/j.mbs.2007.08.006 pmid:17931668 fatcat:qxnrglygzbfhrg6nrjww4a5zge

Using the First Passage Times in Markov Chain Model to Support Financial Decisions on the Stock Exchange

Józef Stawicki
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...  ... 
doi:10.12775/dem.2016.003 fatcat:dk7otnuy6ndyzgw6ydvdg27eau

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  ... 

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.”  ... 

Phase-type distributions and the structure of finite Markov chains

Robert S. Maier
1993 Journal of Computational and Applied Mathematics  
We show that all discrete phase-type 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] .  ... 
doi:10.1016/0377-0427(93)90040-i fatcat:oap2kiqvkfdndhux663moqgo6q

Mixing times with applications to perturbed Markov chains

Jeffrey J. Hunter
2006 Linear Algebra and its Applications  
A measure of the "mixing 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.  ... 
doi:10.1016/j.laa.2006.02.008 fatcat:s2tgcafr6ncbpmkrt3dllr4o3a
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