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.

No abstract

No abstract

No abstract

We develop a stochastic model of contagion with two individual types by extending an archetypal SIS CTMC model. Our results include the analyses of the contagion duration and the number of individual afflictions. Numerical applications with the minority and majority types are provided to consider various contagions.