Fully decentralized emulation of best-effort and processor sharing queues

Control of large distributed cloud-based services is a challenging problem. The Distributed Rate Limiting (DRL) paradigm was recently proposed as a mechanism for tackling this problem. The heuristic nature of existing DRL solutions makes their behavior unpredictable and analytically untractable. In this paper we treat the DRL problem in a mathematical framework and propose two novel DRL algorithms that exhibit good and predictable performance. The first algorithm Cloud Control with Constant Probabilities (C3P) solves the DRL problem in best effort environments, emulating the behavior of a single best-effort queue in a fully distributed manner. The second problem we approach is the DRL in processor sharing environments. Our algorithm, Distributed Deficit Round Robin (D2R2), parameterized by parameter α, converges to a state that is, at most, O(1/α) away from the exact emulation of centralized processor sharing queue. The convergence and stability properties are fully analyzed for both C3P and D2R2. Analytical results are validated empirically through a number of representative packet level simulations. The closed-form nature of our results allows simple design rules which, together with extremely low communication overhead, makes the presented algorithms practical and easy to deploy.

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