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

Bara Kim, Jeongsim Kim, Jerim Kim

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish
Article number1893
Pages (from-to)1-16
Number of pages16
Issue number11
StatePublished - Nov 2020


  • Matrix analytic method
  • Pattern
  • Sooner waiting time
  • Stopping probability


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