## 2 Related Works  
Complications in workload allotment in servers with reduced power consumption mean that optimal power management is required, which is dependent on the arrival rate of the tasks and the processor's power-to-frequency relationship. Thus, it is vital to perform a quantitative analysis of the association between dynamic voltage frequency scaling (DVFS) and power consumption to optimize the use of servers [11]. The worst-fit decreasing (WFD) strategy has been proposed as a load balancing approach for task allocation and energy consumption reduction [12], where by DVFS-based fixed discrete CPU utilization levels were considered and 34% power reduction was achieved [13]. A polynomial complexity algorithm was presented, with the assumption that the energy consumption of servers with lower workloads is comparably less than higher workloads [14]. When optimizing power consumption, most of the research work has focused on optimizing the CPU and cooling devices, as they are the components that consume the most power. The CPU consumes 46% and the cooling device consumes 15% of the total power in a data center [15]. The DVFS-based approach can be used when there is a lower workload and no need to run the servers at their maximum performance level [16; 17; 18]. The job scheduling approach was used for workload management to achieve maximum utilization of servers with reduced energy consumption [19; 20; 21]. Many heuristic methods for VM placement have been used with constrained combinatorial optimization problems for different objectives, such as to identify energy-efficient hosts for VMs [22; 23; 24], to reduce the number of migrations [25], and to increase the number of idle hosts [26; 27]. In heterogeneous environments, heuristic techniques generally cannot guarantee optimal long-term solutions [28]. Reducing power consumption through the VM migration approach involves limiting the number of powered servers operating at highest utilization level.This approach is not energy free, rather it is dependent on VM size and bandwidth [29]. The energy requirement for the live migration of idle VMs is estimated using their proposed power model [30]. The consecutive sequential migration of several VMs also has an energy impact [31]. DVFS is mainly applied to non-critical workloads to improve energy-efficient scheduling of idle servers or light-loaded servers [32]. The genetic algorithm-based model was proposed for VM placement to minimize energy consumption [33]. A multiobjective model of the VM placement problem was proposed to maximize resource utilization and minimize energy consumption and network traffic, with VM placement formulated as a bin-packing problem and the network traffic reduction formulated as a quadratic assignment problem, with resources constraints [34]. An optimization model with multiobjective formulation was considered to maximize server utilization and minimize the number of active servers with memory and CPU resource constraints [35]. The algorithm was designed in order to form an optimal initial population and to reduce the search space, and was evaluated on a small-scale data center. The author of [36] disagreed with the work performed in [35], insisting on the need for an exhaustive approach in order to arrive at an optimal solution for difficult NPproblems. Approaches for bin-packing-based modified best fit decreasing (BFD) placement and dynamic placement of VMs were considered to reduce operation costs and environmental impacts [37]. In the modified BFD approach, the VMs with the best utilization were placed in the physical machine (PM) with the least energy consumption. A multi dimension space partition model was used to balance resource utilization and energy consumption. Energy efficient virtual machine placement algorithm with balanced resource utilization was proposed to reduce power consumption by reducing the number of PMs [38].