  In this thesis, we propose and analyze a multi-server model that captures a
performance trade-off between centralized and distributed processing. In our
model, a fraction $p$ of an available resource is deployed in a centralized
manner (e.g., to serve a most-loaded station) while the remaining fraction
$1-p$ is allocated to local servers that can only serve requests addressed
specifically to their respective stations.
  Using a fluid model approach, we demonstrate a surprising phase transition in
the steady-state delay, as $p$ changes: in the limit of a large number of
stations, and when any amount of centralization is available ($p>0$), the
average queue length in steady state scales as $\log_{1/(1-p)} 1/(1-\lambda)$
when the traffic intensity $\lambda$ goes to 1. This is exponentially smaller
than the usual M/M/1-queue delay scaling of $1/(1-\lambda)$, obtained when all
resources are fully allocated to local stations ($p=0$). This indicates a
strong qualitative impact of even a small degree of centralization.
  We prove convergence to a fluid limit, and characterize both the transient
and steady-state behavior of the finite system, in the limit as the number of
stations $N$ goes to infinity. We show that the sequence of queue-length
processes converges to a unique fluid trajectory (over any finite time
interval, as $N$ approaches infinity, and that this fluid trajectory converges
to a unique invariant state $v^I$, for which a simple closed-form expression is
obtained. We also show that the steady-state distribution of the $N$-server
system concentrates on $v^I$ as $N$ goes to infinity.
