On the Power of (even a little) Centralization in Distributed Processing
Author(s)Tsitsiklis, John N.; Xu, Kuang
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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 [subscript 1/1-p] 1/1-λ when the traffic intensity λ goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of 1/1-λ, 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 → ∞), and that this fluid trajectory converges to a unique invariant state v[superscript 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[superscript I] as N goes to infinity.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems (SIGMETRICS '11)
Association for Computing Machinery (ACM)
John N. Tsitsiklis and Kuang Xu. 2011. On the power of (even a little) centralization in distributed processing. In Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems (SIGMETRICS '11). ACM, New York, NY, USA, 161-172.
Author's final manuscript