## 2 Related Works
A multi objective problem was formulated to reduce energy consumption by forecasting CPU and memory utilization in the forthcoming slot based on the previous history [39]. The result outcomes were compared with a grey forecasting model. A constrained optimization problem was formulated with virtual machine (VM) and physical machine (PM) profiles. New heuristic information was embedded in an ant colony algorithm to achieve energy efficiency [40]. A mixed-integer non-linear programming model was proposed for systematical allocation of workloads, considering the electricity price diversity of geo-distributed data centers and DVFS of servers without violating QoS requirements [41; 42]. A tradeoff between energy consumption and cost was achieved by exploiting the electricity price, data center location, and energy source in the context of internet services sensitive to response time [43]. Reinforcement-learning-based resource management was optimized for information storage with QoS and power consumption as reward function [44]. The revenue from different tasks was considered as a QoS parameter and VM migration and network communication were considered for power consumption. Geo-distributed resource allocation was performed based on two heuristic force-directed load distribution (FDLD) methods, namely task-aware over provisioning and simple over provisioning with co-location interference, in order to estimate the co-location effects of different task execution rates [45]. Genetic-algorithm-based co-location-aware load distribution was also performed and compared with FDLD, with the result showing energy cost reductions with over provisioning elimination, making this an optimal choice. Regarding data center power efficiency measurement, PUE and carbon usage effectiveness metrics play vital roles. Most of the energy consumption in data centers is caused by the cooling load [46]. This work considers all three triangular dependent parameters, namely the power dissipation of the processor regarding the operating frequency, cooling device power consumption, and dynamic PUE. The carbon-aware power-efficient optimal frequency (C-PEF) and carbon conscious first-fit optimal frequency (C-FFF) algorithms proposed in this work distribute the load and maintain the lowest possible utilization level in all servers for the current workload. The placement algorithm considers the following factors:  
* Selection of data centers and clusters is performed based on the PUE and CO2 emission rate, aiming to reduce the overall carbon footprints of the data centers;
* Load balancing is done by identifying a feasible server with a minimal operating frequency for the current workload with the required quality of service, aiming to reduce hot spots in CPU heat dissipation, which have a direct impact on hardware lifetime and performance;
* The impacts of static and dynamic power usage effectiveness (PUE) on placement decisions are analyzed, along with cooling load power impacts. The rest of this paper is organized as follows. In Section 1, the general facts about power consumption in data centers are outlined. Section 2 surveys several closely associated research approaches related to this work. Sections 3 and 4 detail the system models and the research problem formulation. Subsequently, Section 5 elaborates on the algorithms proposed in this research work for solving the formulated stochastic problem. Then, the experimental set-up is presented in Section 6. Section 7 presents the simulation results and discussions about the significance of load balancing using the optimal frequency and the dynamic cooling load. Finally, Section 8 presents the findings of this research work.