State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
The power of two choices in randomized load balancing
The power of two choices in randomized load balancing
Randomized load balancing with general service time distributions
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
On the power of (even a little) centralization in distributed processing
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Markov chains with discontinuous drifts have differential inclusion limits
Performance Evaluation
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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 (p0), the average queue length in steady state scales as log 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 vI, for which a simple closed-form expression is obtained. We also show that the steady-state distribution of the N-server system concentrates on vI as N goes to infinity.