Optimal CPU Scheduling in Data Centers via a Finite-Time Distributed Quantized Coordination Mechanism

Abstract

We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation whereas the second one exhibits asynchronous operation. Both algorithms share salient features. Specifically, the algorithms operate exclusively with quantized values, which means that the information stored, processed and exchanged between neighboring nodes is subject to deterministic uniform quantization. The algorithms rely on event-driven updates in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage. Finally, once the algorithms converge, nodes distributively terminate their operation. We prove that our algorithms converge in a finite number of iterations to the exact optimal solution depending on the quantization level, and we present applications of our algorithms to (i) optimal task scheduling for data centers, and (ii) global model aggregation for distributed federated learning. We provide simulations of these applications to illustrate the operation, performance, and advantages of the proposed algorithms. Additionally, it is shown that our proposed algorithms compare favorably to algorithms in the current literature. Quantized communication and asynchronous updates increase the required time to completion, but finite-time operation is maintained.

Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics

“…Optimizing the workloads over network of CPUs (or computing servers) is considered as an example here. The local cost of each CPU is defined in quadratic form as [6]- [8],…”

“…For the simulation, we consider the sum of the workloads as K = 1000; max and min workloads at every computing server are 7 and 3 (the box constraints). The chosen numerical values are only for the sake of simulation and may not necessarily follow the specifications in [6]- [8]. As an academic example, a random dynamic network of n = 100 nodes switching between the 4 networks in Fig.…”

“…These techniques further found their way into vehicular technology, and intelligent transportation systems, e.g., Internet-of-Connected-Vehicles (IoCV) [3], [4] and platoons of autonomous cars [5]. The concepts of computing-workload management over a network of CPUs [6]- [8], optimal scheduling of reserving batteries [9], optimal electricity generation for greener smart grid [10]- [14], optimal scheduling of plug-in EV charging [15], and proportional task allocation [16]- [19] are relevant to this research area. Another example is to address the best performance of the power-constrained solutions for localized coverage and deployment control of mobile facilities This work is supported in part by the European Commission through the H2020 Project Finest Twins under Agreement 856602. and service-providing units [17].…”

“…Some existing models addressing specific nonlinearities are listed here. Quantized consensus [24] with applications to finite-time CPU scheduling [8] (based on the results of [6], [7]) is considered, where the cost function needs to be quadratic. Sign-based solutions [17], [25] are proposed to address saturation constraints and advance the linear models in coordination of intelligent mobile robots for optimal coverage control [26] and linear machine learning optimization methods [27].…”

Optimal Database Allocation in Finite Time with Efficient Communication and Transmission Stopping over Dynamic Networks

“…In practical applications of wireless computer networks, devices need to exchange information messages with finite length (i.e., quantized messages) which allows for a more efficient usage of the available network resources (e.g., energy, processing power, etc.). Also, they need to operate over networks which may be dynamic due to changes over the sensing radius of the various devices [3], [4]. Additionally, in order to preserve available energy resources, it is desirable for devices to converge in finite time and to stop transmitting once convergence has been achieved [2], [4].…”