Equivalent definitions of the probabilistic characteristics of models with repeated calls and their application.

*(English. Russian original)*Zbl 0692.90053
Probl. Inf. Transm. 25, No. 2, 145-153 (1989); translation from Probl. Peredachi Inf. 25, No. 2, 79-90 (1989).

The authors considers a multichannel retrial queue in steady state. The mean number of retrials per one primary call which is one of the most important characteristics of the system can be introduced in three ways. The main result states that all these definitions are equivalent. The method of solving the problem is based on stochastic monotonicity and comparability of some Markov chains. As applications of the main result, the asymptotic behaviour of the mean number of retrials under light traffic and the accuracy of a numerical method of calculating characteristics of systems with repeated calls are studied.

Reviewer: G.Falin

##### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |