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.
Bibliographical noteFunding 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).
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.
- Matrix analytic method
- Sooner waiting time
- Stopping probability
ASJC Scopus subject areas