  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.
