Calculation of the exponential ergodicity exponent for birth-death processes. (English. Ukrainian original) Zbl 0948.60079

Kartashov, M. V.

Theory Probab. Math. Stat. 57, 53-60 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 51-59 (1997).

A new formula for the approximation of the exponential ergodicity index for birth-and-death processes with continuous time is proposed. The approach is based on the solution of some optimization problem. Examples of some Markov queueing systems are considered. These examples prove that the found values are exact ones.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60K25	Queueing theory (aspects of probability theory)
60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)

Keywords:

birth-and-death process; exponential ergodicity index; queueing theory