M/G/1 Queue with Processor Sharing and Its Relation to a Feedback Queue

摘要

The central model studied is an M/M/1 queue with a general probabilistic feedbackmechanism. When a customer completes his i-th service, he departs from the system with probability 1-p(i) and he cycles back with probability p(i). The mean service time of each customer is the same for each cycle. The joint distribution of successive sojourn times of a tagged customer at his loops through the system is determined. The mean service time at each loop is allowed to shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant. The behavior of the feedback queue then approaches that of an M/G/1 processor sharing queue, different choices of the feedback probabilities leading to different service time distribution in the M/G/1 queue with processor sharing. Some variants are considered an M/M/1 feedback queue with additional customers who are always present, and an M/G/1 processor sharing queue with feedback.