On the power of centralization in distributed processing

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 --> [infinity]), and that this fluid trajectory converges to a unique invariant state vI, for which a simple closedform expression is obtained. We also show that the steady-state distribution of the N-server system concentrates on vI as N goes to infinity.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2011

Author dc:creator

• Xu, Kuang, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• John N. Tsitsiklis.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/66480

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/66480