Critically loaded queueing models that are throughput suboptimal

Details Critically loaded queueing models that are throughput suboptimal Critically loaded queueing models that are throughput suboptimal

2009-06-12

arxiv.org/abs/0906.2305v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 521-555

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP551 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP551

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and heterogenous, exponential servers. Servers are dynamically chosen to serve customers, and buffers are available for customers waiting to be served. The arrival rates and the number of servers are scaled up in such a way that the processes representing the number of class-$i$ customers in the system, $i\in\mathcal{I}$, fluctuate about a static fluid model, that is assumed to be critically loaded in a standard sense. At the same time, the fluid model is assumed to be throughput suboptimal. Roughly, this means that the servers can be allocated so as to achieve a total processing rate that is greater than the total arrival rate. We show that there exists a dynamic control policy for the queueing model that is efficient in the following strong sense: Under this policy, for every finite $T$, the measure of the set of times prior to $T$, at which at least one customer is in the buffer, converges to zero in probability as the arrival rates and number of servers go to infinity. On the way to prove our main result, we provide a characterization of throughput suboptimality in terms of properties of the buffer-station graph.

Affiliated with

Also associated with

No associations

Rating

Critically loaded queueing models that are throughput suboptimal 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 Critically loaded queueing models that are throughput suboptimal, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critically loaded queueing models that are throughput suboptimal will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135196