M/M/c/N queuing systems with encouraged arrivals, reneging, retention and feedback customers

Customers often get attracted by lucrative deals and discounts offered by firms. These attracted customers are termed as encouraged arrivals. Four multi-server Markovian queuing models with encouraged arrivals are developed in this paper. Model-1 deals with multi-server finite capacity queuing system with encouraged arrivals. Model-2 is an extension of model-1 with reneging. Model-2 is then extended with feedback in Model-3. Model-4 is a further extension of Model-3 with retention of reneged customers. The stationary system size probabilities are obtained recursively for each model and various underlying special cases are discussed.