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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.

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