Response time distributions for a multi-class queue with feedback

A single server queue with feedback and multiple customer classes is analyzed. Arrival processes are independent Poisson processes. Each round of service is exponentially distributed. After receiving a round of service, a customer may depart or rejoin the end of the queue for more service. The number of rounds of service required by a customer is a random variable with a general distribution. Our main contribution is characterization of response time distributions for the customer classes. Our results generalize in some respects previous analyses of processor-sharing models. They also represent initial efforts to understand response time behavior along paths with loops in local balanced queueing networks.