Asynchronous Load Balancing and Auto-scaling: Mean-Field Limit and Optimal Design
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We introduce a Markovian framework for load balancing where classical algorithms such as Power-of-d are combined with asynchronous auto-scaling features. These allow the net service capacity to scale up or down in response to the current load within the same timescale of job dynamics. This is inspired by serverless frameworks such as Knative, used among others by Google Cloud Run, where servers are software functions that can be flexibly instantiated in milliseconds according to user-defined scaling rules. In this context, load balancing and auto-scaling are employed together to optimize both user-perceived delay performance and energy consumption. In the literature, these mechanisms are synchronous or rely on a central queue. The architectural novelty of our work is to consider an asynchronous and decentralized system, as in Knative, which takes scalability to the next level. Under a general assumption on the auto-scaling process, we prove a mean-field limit theorem that provides an accurate approximation for the system dynamics when the mean demand and nominal service capacity grow large in proportion. We characterize the fixed points of the mean-field limit model and provide a simple condition telling whether or not all the available servers need to be turned on to handle the incoming demand. Then, we investigate how to design optimal auto-scaling rules and find a general condition able to drive the mean-field dynamics to delay and relative energy optimality, a situation where the user-perceived delay and the relative energy wastage induced by idle servers vanish. The proposed optimality condition suggests to scale up capacity if and only if the mean demand exceeds the overall rate at which servers become idle and active. This yields the definition of tractable optimization frameworks to trade off between energy and performance, which we show as an application of our work.
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