Summary: The Annals of Applied Probability
2005, Vol. 15, No. 1B, 820­852
DOI 10.1214/105051604000000963
© Institute of Mathematical Statistics, 2005
A DIFFUSION MODEL OF SCHEDULING CONTROL IN
QUEUEING SYSTEMS WITH MANY SERVERS1
BY RAMI ATAR
Technion--Israel Institute of Technology
This paper studies a diffusion model that arises as the limit of a queueing
system scheduling problem in the asymptotic heavy traffic regime of Halfin
and Whitt. The queueing system consists of several customer classes and
many servers working in parallel, grouped in several stations. Servers in
different stations offer service to customers of each class at possibly different
rates. The control corresponds to selecting what customer class each server
serves at each time. The diffusion control problem does not seem to have
explicit solutions and therefore a characterization of optimal solutions via
the Hamilton­Jacobi­Bellman equation is addressed. Our main result is the
existence and uniqueness of solutions of the equation. Since the model is
set on an unbounded domain and the cost per unit time is unbounded, the
analysis requires estimates on the state process that are subexponential in

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

Collections: Engineering