Abstract
A non-preemptive M/GI/1 queue with several job classes is considered. At the completion of the service time the multiple feedback occurs. The objective is to maximize the expected discounted reward with the infinite horizon. Using the Harrison's method, the model is formulated as a bandit problem and its optimal policy is characterized by the index rule. Next it is considered that the service time is decomposed into quantum of the unit span. This model is a queueing system of a single feedback, Using the index rule, three type of optimal job schedulings are discussed.
