Effect of impatient patrons in queueing system with differentiated vacations

This study examines a Markovian queueing system with a single server and an infinite capacity which involves differentiated vacation with balking. In the first model, a M/M/1 queue, balking occurs in every state, but in the second model, balking only happens during vacations. Using the PGF method, the system’s steady state probabilities can be obtained. Different performance metrics are analyzed. Numerous real-world systems, including computer networks, call centers, and manufacturing systems, have applications for the proposed queueing paradigm. Finally, a number of numerical examples are given to illustrate the behavior of the different model parameters.