A Markovian Feedback Queue with Retention of Reneged Customers and Balking

Abstract

We consider a single server, nite 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 p1 or he can leave the system with probability q1 where p1 + q1 = 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 q2 or he may leave the queue without receiving service with probability p2(= 1 q2).Balking refers to reluctance of a customer to join a queue.