Sojourn times in the M/G/1 FB queue with light-tailed service times

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the Foreground-Background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimises the decay rate in the class of work-conserving disciplines.