Asymptotic analysis of nonhomogeneous hierarchical Markov processes and applications in models of the consolidation of queueing systems. (English. Ukrainian original) Zbl 0923.60028

Anisimov, V. V.

Theory Probab. Math. Stat. 56, 49-60 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 48-60 (1997).

Limit theorems for inhomogeneous in time hierarchical Markov processes, which admit asymptotical merging of states, are investigated. The theorem on asymptotic merging in the class of processes, which are switched, is used for the proof. As applications, asymptotical properties of some models of inhomogeneous in time queueing systems with local characteristics dependent on current state and random Markov media are studied.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60F05	Central limit and other weak theorems
60F17	Functional limit theorems; invariance principles
60K99	Special processes
60J25	Continuous-time Markov processes on general state spaces
60G99	Stochastic processes

Keywords:

inhomogeneous Markov chains; asymptotic merging of states; switching processes; queueing systems