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The Annals of Applied Probability 2006, Vol. 16, No. 4, 17641804
 

Summary: The Annals of Applied Probability
2006, Vol. 16, No. 4, 17641804
DOI: 10.1214/105051606000000358
Institute of Mathematical Statistics, 2006
QUEUEING SYSTEMS WITH MANY SERVERS: NULL
CONTROLLABILITY IN HEAVY TRAFFIC1
BY RAMI ATAR, AVI MANDELBAUM AND GENNADY SHAIKHET
Technion--Israel Institute of Technology
A queueing model has J 2 heterogeneous service stations, each con-
sisting of many independent servers with identical capabilities. Customers of
I 2 classes can be served at these stations at different rates, that depend on
both the class and the station. A system administrator dynamically controls
scheduling and routing. We study this model in the central limit theorem (or
heavy traffic) regime proposed by Halfin and Whitt. We derive a diffusion
model on RI with a singular control term that describes the scaling limit of
the queueing model. The singular term may be used to constrain the diffusion
to lie in certain subsets of RI at all times t > 0. We say that the diffusion
is null-controllable if it can be constrained to X-, the minimal closed sub-
set of RI containing all states of the prelimit queueing model for which all
queues are empty. We give sufficient conditions for null controllability of the

  

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

 

Collections: Engineering