Queueing system with control by admission of retrial requests depending on the number of busy servers and state of the underlying process of Markov arrival process of primary requests

A multi-server retrial queuing model is under study. Arrivals occur according to the Markov arrival process (MAP). Aiming to increase the probability of immediate access of arriving requests to service, control by the admission of retrying requests, which did not succeed to start service immediately after arrival, is supposed. A control strategy is determined by the set of the integer thresholds defined for each value of the underlying Markov chain of the MAP. Any retrying request is accepted for service if the number of busy servers is less than the threshold corresponding to the current state of the underlying Markov chain. Retrying requests are impatient and can depart from the system without receiving service. Dynamics of the system is described by the three-dimensional Markov chain. Its generator is obtained, steady-state probabilities are computed and formulas for computation of certain performance measures are given. Numerical examples are presented including illustration of a possibility to use the obtained results for managerial goals.