Waiting time problems for patterns in a sequence of multi-state trials

Bara Kim; Jeongsim Kim; Jerim Kim

doi:10.3390/math8111893

Waiting time problems for patterns in a sequence of multi-state trials

Bara Kim, Jeongsim Kim, Jerim Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

Original language	English
Article number	1893
Pages (from-to)	1-16
Number of pages	16
Journal	Mathematics
Volume	8
Issue number	11
DOIs	https://doi.org/10.3390/math8111893
Publication status	Published - 2020 Nov

Keywords

Matrix analytic method
Pattern
Sooner waiting time
Stopping probability

ASJC Scopus subject areas

Mathematics(all)

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10.3390/math8111893

Cite this

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title = "Waiting time problems for patterns in a sequence of multi-state trials",

abstract = "In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.",

keywords = "Matrix analytic method, Pattern, Sooner waiting time, Stopping probability",

author = "Bara Kim and Jeongsim Kim and Jerim Kim",

note = "Funding Information: Funding: The first author{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). The second author{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568). Publisher Copyright: {\textcopyright} 2020 by the authors. Licensee MDPI, Basel, Switzerland.",

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N1 - Funding Information: Funding: The first author’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). The second author’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568). Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2020/11

Y1 - 2020/11

N2 - In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

AB - In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

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KW - Sooner waiting time

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Waiting time problems for patterns in a sequence of multi-state trials

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Keywords

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