Diffusion approximation of systems with repeated calls. (Russian) Zbl 0764.60038

Anisimov, V. V.; Atadzhanov, Kh. L.

Teor. Veroyatn. Mat. Stat., Kiev 44, 3-8 (1991).

The authors investigate an embedded Markov chain for an \(M/G/1\) type retrial queue. It is proved that under low rate of retrials the scaled process converges to a solution of an ordinary differential equation and the centered and normalized process converges to a solution of a stochastic differential equation. The analysis is based on a general theory for recursive stochastic sequences which was developed before by the authors.

Reviewer: G.Falin (Moskva)

MSC:

60F17	Functional limit theorems; invariance principles
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60J60	Diffusion processes
60K25	Queueing theory (aspects of probability theory)
90B22	Queues and service in operations research

Keywords:

diffusion approximation; unreliable server; embedded Markov chain; retrial queue; low rate of retrials; stochastic differential equation