Mathematics – Probability
Scientific paper
2003-08-05
Mathematics
Probability
12 pages
Scientific paper
In this paper we study the maximum queue length $M$ (in terms of the number of customers present) in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy-tailed) service-time distributions the Foreground Background service discipline is optimal. This discipline gives service to the customer(s) that have received the least amount of service so far. It is shown that under this discipline $M$ has an exponentially decreasing tail. From the behaviour of $M$ we obtain asymptotics of the maximum queue length $M(t)$ over the interval $(0,t)$ for $t\to\infty$. These are applied to calculate the time to overflow of a buffer, both in stable and unstable queues.
No associations
LandOfFree
The maximum queue length for heavy tailed service times does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The maximum queue length for heavy tailed service times, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The maximum queue length for heavy tailed service times will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-571968