An M/M/c/N queuing system with reneging and retention of reneged customers

The customer impatience due to reneging results into loss of potential customers. But, if we have certain mechanism to retain such impatient customers, a significant amount of revenue can be increased. In this paper, we have developed a Markovian, finite capacity, multi-server queuing system which deals with retention of reneged customers. Accordingly, a reneged customer can be made (convinced) to stay in the queuing system for his further service with some probability, say q and he may abandon the queue without receiving the service with probability p (= 1 − q). The steady-state solution of the model has been derived. The different measures of effectiveness of the queuing model have been obtained. The effect of probability of customer retention on the expected system size has been studied. A comparative analysis of some queuing models has been carried out to see the impact of customer retention on the expected system size. Some queuing models have been derived as particular cases of this model.

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