## 2 Related Work  
VM placement and VM migration are the backbone to the VM consolidation process [15]. VM placement involves deciding the PM to which a VM must be assigned and is similar to the multidimension bin packing problem (BPP), which concerns filling the maximum number of items into minimum number of bins. Here, the PM is considered as the bin, and the VM is considered as the item in VM placement. BPP can be a two-dimensional or three-dimensional problem, and the dimensions of the BPP comprise width, depth, and height. For VM placement, the number of dimensions increase according to the number of resources (CPU, memory, bandwidth, etc.). Specifically, VM placement is defined as a multidimensional vector packing problem with independence of each dimension, as shown in Figure 2. VM placement has the characteristic that a problem starts with a VM that is already assigned to the PM because the DC is operated throughout the year and differs from the BPP as it places the item in an empty bin [13; 16]. The VM consolidation framework uses a separate monitoring tool, as shown in Figure 3, where the PM is monitored to minimize the number of active PMs using the idle switch in the event of an overload or underload. VM placement is then implemented if certain conditions are met. The key element of VM consolidation is VM placement, which consists of the source PM selection to determine which PM is placed in the power-saving mode, VM selection to determine which VM to migrate from the source PM, and destination PM selection to determine which PM is assigned the selected VM. It detects PM overload or underload; the detected PM then selects the VM to migrate from the VMs assigned to the source PM, and VM placement is implemented to decide the PM to migrate to. Threshold-based algorithm (THR), which is the most basic methodology to detect PM overload, calculates the average CPU usage for a specific time period \(t\) and determines that the PM is overloaded if the defined threshold is exceeded. The THR is a simple method but difficult to apply to dynamic and unpredictable environments [17]. Therefore, to overcome the THR limitations, an adaptive utilization threshold-based algorithm is suggested to analyze the collected workloads of the virtual machines statically and adjust the thresholds automatically [8; 18]. The median absolute deviation (MAD) and interquartile range (IQR) are used as statistical measures. The MAD is a technique that uses the median instead of the average to find the absolute deviation, and IQR measures the overload using the quartile range. This is a general technique for measuring outliers, and the PM overload can also be interpreted in a manner similar to searching for outliers. The adaptive utilization threshold algorithm is more suited for dynamic environments than the static utilization threshold, but its overload forecast performance is poor. Local regression methods such as the median absolute deviation, and IQR are used as the median absolute deviation. The MAD is a technique that uses the median instead  
as local regression robust (LRR) are suggested for better performances than the static and adaptive thresholds. PM with overload detection is used to decide the VM to which migration must occur. The VM selection policies suggested are dynamic management algorithm (DMA) policy, which selects the VM with the lowest CPU utilization to minimize migration cost, minimum migration time (MMT) policy, which selects the VM with the lowest migration completion time, random selection (RS) policy, which selects a random VM [19], and maximum correlation (MC) policy, which selects the VM that has the highest CPU utilization correlation with the original VM [20]. Comparison of the results for each policy shows that the MMT has better results than RS and MC, suggesting that minimizing of VM migration time is an important objective. For DMA, MMT, and MC, the use of the fixed standard renders the policies unsuitable for dynamic environments.