Sojourn time tails in the single server queue with heavy-tailed service times

Abstract

We consider the GI/GI/1 queue with regularly varying service requirement distribution of index ??. It is well known that, in the M/G/1 FCFS queue, the sojourn time distribution is also regularly varying, of index 1??, whereas in the case of LCFS or Processor Sharing, the sojourn time distribution is regularly varying of index ??. That raises the question whether there exist service disciplines that give rise to a regularly varying sojourn time distribution with any index ???[??,1??]. In this paper that question is answered affirmatively.