On the Power of Centralization in Distributed Processing

Abstract:

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 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 $\log_{\frac{1}{1-p}}{\frac{1}{1-\lambda}}$ when the traffic intensity $\lambda$ goes to 1. This is exponentially smaller than the normal $M/M/1$-queue delay scaling of $\frac{1}{1-\lambda}$, 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 queue-length process converges to a unique fluid trajectory (over any finite time interval as $N \rightarrow \infty$), and that this fluid trajectory converges to a unique invariant state $\mathbf{v}^I$, for which a simple closed-form expression is obtained. We also show that the steady-state distribution of the $N$-server system concentrates on $\mathbf{v}^I$ as $N$ goes to infinity.

Biography:

Kuang Xu is a second-year graduate student in LIDS, working under the supervision of Professor John N. Tsitsiklis. His current research interests are applied probability theory and their applications in resource allocation problems in networks. He graduated from the University of Illinois at Urbana-Champaign in 2009 with a Bachelor's degree in Electrical Engineering. Apart from research, Kuang works with the Graduate Student Council (GSC) at MIT, where he serves as co-chair of the MIT Graduate Student Orientation Committee.