Efficiency of retrial queueing system under N threshold during vacation

In the present study, a queueing system with a single server, N-threshold in the vacation state and k-multiple working breakdown and repair conditions are considered. The server operates at a different speed during breakdown. The server enters setup state to begin service after the state of repair. Customers have to wait in retrial class before going to busy state at the time of retry and will get the service when the system is ready. A matrix-analytical method is used to achieve the static queue length distribution. The lengths of the anticipated busy periods, working breakdown periods, mean waiting times, and average delays are all calculated. To validate the analytical portion of the paper, numerical findings are computed. Sensitivity analysis has been performed to examine the effect of individual parameters. A comparative study is also accomplished to determine the minimum cost, using a genetic algorithm (GA).