Cost Optimization of Queueing System with Working Vacation, Setup, Feedback, Reneging, and Retention of Reneged Customers

In this manuscript, Markovian queueing system with working vacation, Bernoulli schedule interruption, setup time under feedback, reneging of impatient customers, and retention of reneged customers are analyzed. The unsatisfied customers on service completion may either leave the system with probabilities  or may rejoin the queue with complementary probabilities during working vacations and regular service, respectively. The waiting customers in the queue may lose patience due to vacations and decide to leave without getting the service with probability q. They may be retained in the system via some convincing mechanisms with probability (1-q). The mean system length, probability of server in various states, mean sojourn time are obtained using the probability generating function method. The MATLAB software is used for representing the observed behavior graphically.