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

ABSTRACT
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 lighttailed 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.
2000 Mathematics Subject Classification: Primary 60K25, Secondary 68M20; 90B22
Keywords and Phrases: decay rate, sojourn time, Foreground-Background (FB), LAST, service discipline, light tails, busy period