Extreme values of queue lengths in M/G/1 and GI/M/1 systems
Mathematics of Operations Research
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
The Foreground-Background queue: A survey
Performance Evaluation
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This paper treats the maximum queue length M, in terms of the number of customers present, in a busy cycle in the M/G/1 queue. The distribution of M depends both on the service time distribution and on the service discipline. Assume that the service times have a logconvex density and the discipline is Foreground Background (FB). The FB service discipline gives service to the customer(s) that have received the least amount of service so far. It is shown that under these assumptions the tail of M is bounded by an exponential tail. This bound is used to calculate the time to overflow of a buffer, both in stable and unstable queues.