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  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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The Computation of the Mean First Passage Times for Markov Chains

Hunter, J
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Commissioned Report (3.601Mb)
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http://hdl.handle.net/10292/12124
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Abstract
A survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented. The author recently developed a new accurate computational technique, an Extended GTH Procedure, Hunter (Special Matrices, 2016) similar to that developed by Kohlas (Zeit. fur Oper. Res., 1986). In addition, the author recently developed a variety of new perturbation techniques for finding key properties of Markov chains including finding the mean first passage times, Hunter (Linear Algebra and its Applications, 2016). These recently developed procedures are compared with other procedures including the standard matrix inversion technique using the fundamental matrix (Kemeny and Snell, 1960), some simple generalized matrix inverse techniques developed by Hunter (Asia Pacific J. Oper. Res., 2007), and some modifications to the FUND technique of Heyman (SIAM J Matrix Anal. and Appl., 1995). MATLAB is used to compute errors and estimate computation times when the techniques are used on some test problems that have been used in the literature together with some large sparse state-space cases. For accuracy a preference for the procedure of the author is exhibited for the test problems. However it appears that the procedure, as presented, requires longer computational times.
Date
January 15, 2017
Source
arXiv:1701.07781 [math.NA]
Item Type
Commissioned Report
Publisher
Cornell University Library
Publisher's Version
https://arxiv.org/abs/1701.07781
Rights Statement
Authors retain the right to place his/her publication version of the work on a personal website or institutional repository for non commercial purposes. The definitive version was published in (see Citation). The original publication is available at (see Publisher’s Version).

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