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Waiting Time Problems for Patterns in a Sequence of Multi-State Trials
- Authors
- Kim, Bara; Kim, Jeongsim; Kim, Jerim
- Issue Date
- Nov-2020
- Publisher
- MDPI
- Keywords
- pattern; sooner waiting time; stopping probability; matrix analytic method
- Citation
- MATHEMATICS, v.8, no.11
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICS
- Volume
- 8
- Number
- 11
- ISSN
- 2227-7390
- 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.
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Related Researcher
- Kim, Ba ra
- College of Science (Department of Mathematics)