出版社：Japan Science and Technology Information Aggregator, Electronic
摘要：We consider a bivariate Markov process {( U ( t ), S ( t )); t ≥ 0 }, where U ( t ) ( t ≥ 0) takes values in [0, ∞) and S ( t ) ( t ≥ 0) takes values in a finite set. We assume that U ( t ) ( t ≥ 0) is skip-free to the left, and therefore we call it the M/G/1-type Markov process. The M/G/1-type Markov process was first introduced as a generalization of the workload process in the MAP/G/1 queue and its stationary distribution was analyzed under a strong assumption that the conditional infinitesimal generator of the underlying Markov chain S ( t ) given U ( t ) > 0 is irreducible. In this paper, we extend known results for the stationary distribution to the case that the conditional infinitesimal generator of the underlying Markov chain given U ( t ) > 0 is reducible. With this extension, those results become applicable to the analysis of a certain class of queueing models.
