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A Markovian feedback queue with retention of reneged customers and balking. (English) Zbl 1332.90080
Summary: We consider a single server, finite capacity Markovian feedback queue with reneging, balking and retention of reneged customers in which the inter-arrival and service times follow exponential distribution. The reneging times are assumed to be exponentially distributed. Feedback in queueing literature represents customer dissatisfaction because of inappropriate quality of service. In case of feedback, after getting partial or incomplete service, customer retries for service. After the completion of service,each customer may rejoin the system as a feedback customer for receiving another regular service with probability \(p_1\) or he can leave the system with probability \(q_1\) where \(p_1 + q_1 = 1\). A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Thus, a reneged customer can be retained in the queuing system with some probability \(q_2\) or he may leave the queue without receiving service with probability \(p_2\) (\(=1- q_2\)). Balking refers to reluctance of a customer to join a queue. In this paper, we extend the work of S. K. Sharma and R. Kumar [“A Markovian feedback queue with retention of reneged customers”, Adv. Model.Optim. 14, No. 3, 673-679 (2012)] by including balking to take into consideration the broader perspective of customer impatience. The steady-state solution of the model is obtained iteratively. Some performance measures are also derived. Finally, some important queuing models are derived as special cases of this model.

90B22 Queues and service in operations research
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