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The Annals of Applied Probability 2009, Vol. 19, No. 2, 521555
 

Summary: The Annals of Applied Probability
2009, Vol. 19, No. 2, 521555
DOI: 10.1214/08-AAP551
Institute of Mathematical Statistics, 2009
CRITICALLY LOADED QUEUEING MODELS THAT ARE
THROUGHPUT SUBOPTIMAL1
BY RAMI ATAR AND GENNADY SHAIKHET
Technion--Israel Institute of Technology and Carnegie Mellon University
This paper introduces and analyzes the notion of throughput suboptimal-
ity for many-server queueing systems in heavy traffic. The queueing model
under consideration has multiple customer classes, indexed by a finite set 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 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 through-
put 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

  

Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology

 

Collections: Engineering