Abstract
In this paper, we develop the optimal minimum-energy scheduler for the dynamic online joint allocation of the task sizes, computing rates, communication rates and communication powers in virtualized Networked Data Centers (NetDCs) that operates under hard per-job delay-constraints. The referred NetDC's infrastructure is composed by multiple frequency-scalable Virtual Machines (VMs), that are interconnected by a bandwidth and power-limited switched Local Area Network (LAN). Due to the nonlinear power-vs.-communication rate relationship, the resulting Computing-Communication Optimization Problem (CCOP) is inherently nonconvex. In order to analytically compute the exact solution of the CCOP, we develop a solving approach that relies on the following two main steps: (i) we prove that the CCOP retains a loosely coupled structure, that allows us to perform the loss-less decomposition of the CCOP into the cascade of two simpler sub-problems; and, (ii) we prove that the coupling between the aforementioned sub-problems is provided by a (scalar) constraint, that is linear in the offered workload. The resulting optimal scheduler is amenable of scalable and distributed online implementation and its analytical characterization is in closed-form. After numerically testing its actual performance under randomly time-varying synthetically generated and real-world measured workload traces, we compare the obtained performance with the corresponding ones of some state-of-the-art static and sequential schedulers. (C) 2013 Published by Elsevier B.V.