On a Queue with Postponed Work Under N-Policy

Abstract

Models with postponement are an alternative to finite capacity queues in which overflow jobs are irrevocably lost. If the buffer is empty, an arriving customer enters in to it and his service starts immediately. In case the buffer is non-empty, but not full, with some probability depending on the number of works in the buffer direct entry to buffer is permitted. When a customer is rejected from the buffer, he is offered a pool of postponed work of infinite capacity. In this case the customer chooses to enter the pool with certain probability. On the contrary, if the buffer is full at a customer arrival epoch, the customer decides to join the orbit with certain probability; however the system may reject him with some probability. At a service completion epoch, if the number of customers in the buffer is less than a pre-assigned quantity, head of the pooled customers will be transferred to the buffer with a specified probability. In the N-policy introduced in this paper, the number of continuously served customers, taken from the buffer, is counted at each service completion epoch. When it reaches a pre-assigned number N, then the one ahead of all waiting in the pool gets transferred to the buffer for immediate service. We study its long run behaviour. Several system performance measures, and a few numerical illustrations are provided. A game theoretical approach to the queue is also introduced.