We consider an M/G/1 queue with feedback, in which customers, after receiving service, either return to the tail of the queue or depart the system, according to some feedback policy. We derive simple expressions for the expected response time for feedback policies that include Bernoulli feedback and feeding back a fixed number of times. Our results reveal some interesting and nonintuitive properties of the behavior of such feedback policies when the coefficient of variation of service time is varied. One result shows that for the Bernoulli feedback and fixed feedback policies with an equal mean number of visits to the queue, the expected response time for the Bernoulli policy is smaller than for the fixed policy if the coefficient of variation of service time is greater than 1. The relationship reverses if the coefficient of variation is less than 1.
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research