Customer Impatience and Feedback Mechanism in MX/G/1 Retrial Queue with, Unreliable Server, Bernoulli Vacation and Customer Search Strategies

This article examines a complex retrial queueing system characterized by unreliable batch arrival, three phases of service, customer impatience, feedback mechanism, Bernoulli vacation policy and customer search behaviors. In this system, customer arrivals follow a Poisson process. When the server is idle, one customer from the batch receives service while the others enter a retrial group. The server offers essential service to all the incoming customers. If the server is busy upon arrival, customers may choose to leave (balk) or wait in the retrial group for the server to become available. Customers who retry either rejoin the service if the server is free or abandon the system if their retrial attempts fail (renege). The server may randomly breakdown during any phases of service and the repair starts immediately. After completion of repair, the server continues to serve the interrupted customer in the system. After completing each phase of service, the customer may either opt for optional service, or join the retrial group as a feedback customer, or leave the system. Upon completion of the first essential phase or second optional phase, if the server is idle, it searches for customers if available in the retrial group with a certain probability. After completing the third optional phase, the server goes on a Bernoulli vacation with certain probability. The retrial, service, repair and vacation times are arbitrarily distributed. By using the supplementary variable technique, various system state measures and reliability measures are derived. The effects of various parameters on these system measures are analyzed through numerical examples.