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A measure of the " mixing time " or " time to stationarity " in a finite irreducible discrete time Markov chain is considered. The statistic η π i i j j m j m = = ∑ 1 , where {π j } is the stationary distribution and m ij is the mean first passage time from state i to state j of the Markov chain, is shown to be independent of the state i that the chain… (More)

Stationary distributions of perturbed finite irreducible discrete time Markov chains are intimately connected with the behaviour of associated mean first passage times. This interconnection is explored through the use of generalized matrix inverses. Some interesting qualitative results regarding the nature of the relative and absolute changes to the… (More)

- J. J. HUNTER
- 2006

In an earlier paper the author introduced the statistic η π i i jj j m m = = ∑ 1 as a measure of the " mixing time " or " time to stationarity " in a finite irreducible discrete time Markov chain with stationary distribution {p j } and m ij as the mean first passage time from state i to state j of the Markov chain. This was shown to be independent of the… (More)

- Jeffrey J. Hunter
- APJOR
- 2007

In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential inter-arrivals to the queueing system, are considered. Two of these models… (More)

In an earlier paper (Hunter, 2002) it was shown that mean first passage times play an important role in determining bounds on the relative and absolute differences between the stationary probabilities in perturbed finite irreducible discrete time Markov chains. Further when two perturbations of the transition probabilities in a single row are carried out… (More)

- Jeffrey J. Hunter
- APJOR
- 2007

The derivation of mean first passage times in Markov chains involves the solution of a family of linear equations. By exploring the solution of a related set of equations, using suitable generalized inverses of the Markovian kernel I – P, where P is the transition matrix of a finite irreducible Markov chain, we are able to derive elegant new results for… (More)

Progress in the eld of Computer Vision/Image Understanding has long been hampered by the lack of standard software environments for research and application development. The Image Understanding Environment (IUE) is being implemented to provide a freely distributed standard software environment appropriate for a wide range of research and development… (More)

- Jeffrey J. Hunter
- APJOR
- 2013

The distribution of the " mixing time " or the " time to stationarity " in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the… (More)

- Misha E. Kilmer, Dianne O’Leary, Steve Kirkland, Nicholas J. Higham, Dario A. Bini, Yuji Nakatsukasa +18 others
- 2002

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