INDUSTRIAL ENGINEERING AND
OPERATIONS RESEARCH
PRESENTS
IEOR MONDAY SEMINAR
State Space Collapse in Many-Server Diffusion
Limits of Parallel Server Systems
Tolga Tezcan
Georgia Institute of Technology
Abstract
We consider a class of queueing systems that
consist of server pools in parallel and multiple customer classes. Customer
service times are assumed to be exponentially distributed. We study the
asymptotic behavior of these queueing systems in a heavy traffic regime that is
known as the
Halfin and Whitt many-server asymptotic regime
where the number of servers and arrival rates grow to infinity in a certain
manner. Specifically, we extend the state space collapse framework of Bramson
[1] to show that a class of state space collapse results in the Halfin and
Whitt many-server diffusion limits of a parallel server system hold if the
hydrodynamic limits of the same system satisfy certain conditions. We also show
that the hydrodynamic limits satisfy a set of deterministic equations known as
the hydrodynamic model equations that are related to but different from the
fluid model equations.
We illustrate the application of our results in an
inverted-V parallel server system that consists of multiple server pools and a
single customer class. We propose the load-balancing (LB) routing policy to
balance the utilizations of all the servers in the system with no unnecessary
idling. We show that this policy balances both the long-run and finite-time
average utilizations over all the server pools in the Halfin and Whitt regime.
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