MMN-3347

# RQwDFB: analysis of retrial queues with delayed feedback

• Agassi Melikov, Institute of Control Systems, National Academy of Science, Baku AZ1141, Azerbaijan, agassi.melikov@gmail.com
• Sevinj Aliyeva, Information Technology and Programming, Applied Mathematics and Cybernetics, Baku State University, Baku AZ1141, Azerbaijan, s@aliyeva.info
• János Sztrik, Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, Debrecen 4032, Hungary, sztrik.janos@inf.unideb.hu

## Abstract

The models of retrial queues M/M/K/K with delayed feedback are considered. If upon arrival of primary call (\textit{p}-call) there are free channels then it occupies one of them for a some exponentially distributed time; otherwise, it in accordance to Bernoulli scheme either leaves the system forever or go to orbit for retrial calls (\textit{r}-calls). After the customer is served completely, it will decide based on Bernoulli scheme either to join the orbit for re-service after some delay (delayed feedback) or to leave the system forever. If upon arrival \textit{r}-call there is a free server, then the arriving call begins to be served immediately; otherwise, it in accordance to Bernoulli scheme either leaves the orbit or return to orbit. An approximate method to calculation of the steady-state probabilities of the appropriate two-dimensional Markov chain as well as performance measures of the system is developed. Results of numerical experiments are demonstrated.

Vol. 22 (2021), No. 2, pp. 769-782
DOI: 10.18514/MMN.2021.3347