Sojurn Times in Feedback and Processor Sharing Queues

摘要

The paper considers an M/M/1 queue with a general probabilistic feedback mechanism. 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 the customer is the same for each cycle. If this mean service time shrinks to zero, while the feedback probabilities approach one in such a way that the mean total required service time remains a positive constant, then the behavior of the feedback queue approaches that of an M/G/1 processor sharing queue. Different choices of the feedback probabilities lead to different service time distributions in the processor sharing model. In a recent paper the authors derived the joint distribution of the successive sojourn times of a customer in the feedback queue. They now exploit those results to analyze sojourn times in the M/G/1 queue with processor sharing. In particular, new results will be presented for the sojourn time variance of a customer with given total service request.