A group arrival retrial G - queue with multi optional stages of service, orbital search and server breakdown

Abstract

A group arrival feedback retrial queue with k optional stages of service and orbital search policy is studied. Any arriving group of customer finds the server free, one from the group enters into the first stage of service and the rest of the group join into the orbit. After completion of the ith stage of service, the customer under service may have the option to choose (i+1)th stage of service with θi probability, with pI probability may join into orbit as feedback customer or may leave the system with probability. Busy server may get to breakdown due to the arrival of negative customers and the service channel will fail for a short interval of time. At the completion of service or repair, the server searches for the customer in the orbit (if any) with probability α or remains idle with probability 1-α. By using the supplementary variable method, steady state probability generating function for system size, some system performance measures are discussed.