Fox et al proposed a

Fox et al. (2013) proposed a non-clairvoyant algorithm Weighted Latest Arrival Processor Sharing with Energy (WLAPS+E), which is (1+6τ)-speed (5/τ2)-competitive, where , for the objective of weighted flow time plus energy. WLAPS+E schedules late arriving jobs and a job can use number of machines proportioned by job weight. In WLAPS+E all processors are not taken in use, rather some processors remain inactive to save energy. Sun et al. (2014) studied non-clairvoyant scheduling algorithm Non-uniform Equi-partitioning (N-EQUI) for a set of parallel jobs in two circumstances: first, where all jobs are released at the same time; second, where jobs are coming over time, i.e. with arbitrary release time. Sun et al. (2014) proved that N-EQUI is O(ln1/αP)-competitive and O(lnP)-competitive for the objective of minimizing the total flow time plus buy guanidine hydrochloride in first and second circumstances, respectively, where P is the total number of processors. Bell and Wong (2014) proposed an 24(+2−1)-competitive deterministic online energy efficient deadline scheduling algorithm Dual-Classified Round Robin (DCRR) on multiprocessors, where P is the ratio of the maximum to the minimum job size. DCRR uses traditional power function and classify the jobs according to densities as well as sizes. Im et al. (2015) gave the first analysis of the instantaneously fair algorithm Round Robin (RR), which is 2k(1+10τ)-speed O(k/τ)-competitive for all and the -norms of flow time for temporal fairness in the multiple identical machines setting (general meaning of -norms of flow time considered is (∑(−))1/). At any time, if jobs are more than machines, allocate machines to jobs equally or process each job on a machine completely. Angelopoulos et al. (2015) proposed a framework to study online scheduling algorithms on a uniprocessor system. This framework is based on primal–dual and dual-fitting techniques for design and analysis of algorithms to solve generalized flow time problems (GFP). The proofs are independent of potential functions and based on intuitive geometric interpretations of the primal/dual objectives. In their primal–dual approach when a new job arrives, the dual variables for jobs can be updated without affecting the past portion of the schedule. Angelopoulos et al. (2015) proved that Highest Density First (HDF) is (1+τ)-speed (1+τ/τ)-competitive for GFP with concave functions; this reflects the improvement in analysis of WLAPS (Im et al., 2014b), which is (1+τ)-speed O(1+τ/τ2)-competitive.
We study online non-clairvoyant speed scaling algorithm against an offline adversary. The objective considered is to minimize weighted flow time plus energy consumption. In this paper, the analysis of online non-clairvoyant algorithm is presented using competitive analysis, i.e. the worst case comparison of an online algorithm and optimal offline algorithm. To minimize the cost function of weighted flow time plus energy, an online algorithm is c-competitive, if for any input the cost incurred is never more than c times the cost of optimal offline algorithm. The objective of minimizing weighted flow time plus energy consumption has a natural interpretation, as it can be measured in monetary terms (Chan et al., 2011a). The assumption perceives that the user is eager to pay a unit of energy to decrease certain units (say ρ units) of weighted flow time. Energy is of more concern if there is a large value of ρ and if ρ=0 then the problem is converted to the traditional weighted flow time scheduling. In this paper, an online non-clairvoyant scheduling algorithm Executed-time Round Robin (EtRR) is proposed, wherein the weights of jobs are not system generated, rather they are generated using the executed time of a job by the scheduler, i.e. current time minus release time of a job. The resource augmentation is used along with speed bounded model.
The rest of the paper is divided into the following sections: Section 2 describes notations used in our paper and definitions necessary for discussion. In Section 3, we have given some scheduling algorithms related to our work and their results. In Section 4, we present the online non-clairvoyant algorithm Executed-time Round Robin (EtRR) and compare EtRR against an optimal offline algorithm Opt using amortized analysis (potential function). Section 5 draws some concluding remarks and future scope of our study.