Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

Abstract

We consider a single server Markovian queueing system with Bernoulli feedback, balking, server's states-dependent reneging, and retention of reneged customers under variant of multiple vacation policy. We obtain the steady-state solution of the considered queueing system based on the use of probability generating functions (PGFs). Then, the closed-form expressions of different system characteristics are derived.
Finally, we present some numerical results in order to show the impact of the parameters of impatience timer rates on performance measures of the system.