Fixed points for multi-class queues

Details Fixed points for multi-class queues Fixed points for multi-class queues

2010-03-15

arxiv.org/abs/1003.3024v1

Mathematics

Probability

25 pages

Scientific paper

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result to multi-type queues, in which different types of customer have different levels of priority. We work with a model of a queueing server which includes discrete-time and continuous-time M/M/1 queues as well as queues with exponential or geometric service batches occurring in discrete time or at points of a Poisson process. The fixed-point results are proved using interchangeability properties for queues in tandem, which have previously been established for one-type M/M/1 systems. Some of the fixed-point results have previously been derived as a consequence of the construction of stationary distributions for multi-type interacting particle systems, and we explain the links between the two frameworks. The fixed points have interesting "clustering" properties for lower-priority customers. An extreme case is an example of a Brownian queue, in which lower-priority work only occurs at a set of times of measure 0 (and corresponds to a local time process for the queue-length process of higher priority work).

Affiliated with

Also associated with

No associations

Rating

Fixed points for multi-class queues 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 Fixed points for multi-class queues, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fixed points for multi-class queues will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-244549