On one discrete queueing model. (English. Ukrainian original) Zbl 0861.60050

Velikoivanenko, O. I.; Shvets, Je. M.

Theory Probab. Math. Stat. 50, 55-60 (1995); translation from Teor. Jmovirn. Mat. Stat. 50, 55-60 (1994).

Summary: A discrete queueing model that describes the functioning of a computing system consisting of input and service processors and a memory shared by both processors is described. The Markov property and ergodicity of the model are proved, the transition probabilities and the stationary probabilities of sojourn in states of the system are found. The asymptotic probability of loss of a unit and the mean time of sojourn of a unit in the system in the stationary regime are computed. The asymptotic distribution of queue length is found.

MSC:

60G25	Prediction theory (aspects of stochastic processes)
60K25	Queueing theory (aspects of probability theory)
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)

Keywords:

queueing model; Markov property; ergodicity; asymptotic distribution of queue length