# Energy-Aware Online Non-Clairvoyant Scheduling Using Speed Scaling with Arbitrary Power Function
## 2 Related Work  
In this section, review of some related work on the online non-clairvoyant job scheduling algorithms using the traditional power function is presented. [PERSON] et al. [27] proposed a concept of migration of jobs and gave an online non-clairvoyant algorithm Selfish Migrate (SelMig). SelMig is O(\(\alpha^{2}\))-competitive using traditional power function with an objective of minimizing the total weighted flow time plus energy on unrelated machines. [PERSON] et al. [11] presented an online non-clairvoyant uni-processor algorithm NC, wherein all jobs arrive with uniform density (i.e., \(weight/size=1\)). NC is \(\left(2+\frac{1}{\alpha-1}\right)\)-competitive using the traditional power function with an objective of minimizing the fractional flow time plus energy. NC uses unbounded speed model. Most of the studies using arbitrary power function have been conducted with clairvoyant settings. [PERSON] et al. [12] showed that an online clairvoyant algorithm ALG (Algorithm proposed by [PERSON] et al.) is \(\gamma\)-competitive with an objective of minimizing the fractional weighted/importance-based flow time plus energy. ALG uses Highest Density First (HDF) for job selection. The competitive ratio \(\gamma=\left(\frac{2(\alpha-1)}{\alpha-(\alpha-1)^{1-\frac{1}{(\alpha-1)}}} \right)\), more specifically \(\gamma=2\) for \(1<\alpha\leq 2\), \(\gamma=2(\alpha-1)\) for \(\alpha>2\), \(\gamma\leq\alpha-1\) for \(\alpha\geq 2+e\). For large \(\alpha\), the value of \(\gamma\approx\left(\frac{2\alpha}{\gamma n\alpha}\right)\). [PERSON] et al. [10] introduced the concept of arbitrary power function and proved that an online clairvoyant algorithm (OCA) is \((2+\epsilon)\)-competitive with an objective of minimizing the fractional weighted flow time plus energy. Authors presented [28] an expert and intelligent system that applies various energy policies to maximize the energy-efficiency of data-center resources. Authors claimed that around 20% of energy consumption can be saved in without exerting any noticeable impact on data-center performance. [PERSON] et al. [29] described a design, implementation, and evaluation of a green scheduling algorithm using a neural network predictor to predict future load demand based on historical demand for optimizing server power consumption in cloud computing. The algorithm turns off unused servers (and restarts them whenever required) to minimize the number of running servers; thus, minimizing the energy consumption. Authors defined [30] an architectural framework and principles for energy-efficient cloud computing. They presented an energy-aware resource provisioning heuristics that improves energy efficiency of the data center, while delivering the negotiated Quality of Service. [PERSON] et al. [31] introduced a Bayesian Belief Network. It learns over time that which of the overloaded virtual machines is best to be removed from a host. The probabilistic choice is made among virtual machines that are grouped by their degree of Central processingunit (CPU) usage. [PERSON] et al. [32] proposed a real-time dynamic scheduling system to execute efficiently task-based applications on distributed computing platforms in order to minimize the energy consumption. They presented a polynomial-time algorithm that combines a set of heuristic rules and a resource allocation technique in order to get good solutions on an affordable time scale. In OCA, the work and weights/importance are arbitrary. It uses HDF for job selection and the power consumed is calculated on the basis of speed of a processor, which is a function of fractional weights of all active jobs. [PERSON] et al. [26] showed that an online non-clairvoyant job scheduling algorithm named Weighted Latest Arrival Processor Sharing (WLAPS) is \(16\left(1+\frac{1}{\epsilon}\right)^{2}\)-competitive under the arbitrary power model with an objective of minimizing the weighted flow time plus energy, where \(\epsilon>1\). The value of \(\alpha\) is commonly believed to be 2 or 3 [26].