## 2 Related Work
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Meaning** \\ \hline \(E\) & Energy consumed by processors \\ \(G\) & Total IBr+E \\ \(c\) & Competitiveness \\ \(\mu\) & A constant (\(0<\mu<1\)), its value depends on the value of \(\Delta\) \\ \(G_{\mathrm{a}}(t)\) or \(G_{\mathrm{a}}\) and \(G_{\mathrm{c}}(t)\) or \(G_{\mathrm{c}}\) & IBr+E acquired still time if by the MBS and Opt, respectively \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) or \(\frac{\mathrm{ad}G_{\mathrm{c}}(t)}{\mathrm{a}t}\) and \(\frac{\mathrm{ad}G_{\mathrm{c}}(t)}{\mathrm{a}t}\) or \(\frac{\mathrm{ad}G_{\mathrm{c}}}{\mathrm{a}t}\) & Rate of change (RcC) of \(G_{\mathrm{a}}\) due to MBS and \(G_{\mathrm{c}}\) due to Opt at time \(t\), respectively \\ \(G_{\mathrm{a}}(t)\) or \(G_{\mathrm{a}}\) and \(G_{\mathrm{a}}(t)\) or \(G_{\mathrm{a}}(t)\) or \(G_{\mathrm{a}}(t)\) & IBr+E acquired on a processor \(u\) till time if by the MBS and Opt, respectively \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) or \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) and \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) or \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) & RoC of \(G_{\mathrm{a}}\) due to MBS and Opt at time \(t\) on a processor \(u\), respectively \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) or \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) & A constant (\(0\)) \\ \(\sigma_{i}\) & Coefficient of a job \(i\) at time \(t\) \\ \(\omega_{i}\) & Difference of pending work of a job \(j_{i}\) using MBS and Opt at time \(t\) \\ \(\delta\) & A constant depends on \(\alpha_{i}\), its value is \(\left(\frac{1}{\alpha_{i}}\right)\) \\ \(L\alpha_{i}\) & A set of tagging jobs using MBS on a processor \(u\) \\ \(LG\) & A set of all lagging jobs using MBS on all \(m\) processors \\ \(\vartheta(t)\) or \(\vartheta\) & Total potential value of all \(m\) processors at time \(t\) \\ \(\vartheta_{u}(t)\) or \(\vartheta_{u}\) & Potential value of a processor \(u\) at time \(t\) \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) and \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) & Rc of \(\vartheta\) due to Opt and MBS, respectively \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) & \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) & RoC of \(\vartheta\) due to Opt and MBS \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) and \(\frac{\mathrm{ad}G_{\mathrm{a}}(t)}{\mathrm{a}t}\) & RoC of \(\vartheta\) due to Opt and MBS on a processor \(u\), respectively \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) & \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) & RoC of \(\vartheta\) due to Opt and MBS on a processor \(u\) \\ \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) & \(\frac{\mathrm{ad}G_{\mathrm{a}}}{\mathrm{a}t}\) & RoC of \(\vartheta\) due to Opt and MBS on a processor \(u\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. residing at the tail of the queue (like Latest Arrival Processor Sharing (LAPS) and Weighted Latest Arrival Processor Sharing (WLAPS)). [PERSON] et al. (2019) proposed an online deterministic clairvoyant algorithm dual-classified round robin (DCRR) for the multiprocessor system using the traditional power function. The motive of \(\left(2^{4a}\left(log^{a}P+\alpha^{a}2^{a-1}\right)\right)\)-competitive DCRR is to schedule the jobs so that they can be completed within deadlines using minimum energy, i.e., the objective is to maximize the throughput and energy consumption. In DCRR, the sizes and the maximum densities (= size/(deadline - release time)) of jobs are known and the classification of jobs depends on the size and the maximum density both. The competitive ratio of DCRR is high, as it considers the jobs with deadlines and using a variation of round robin with the speed scaling. [PERSON] et al. (2019) gave an ON-C scheduling algorithm NC-PAR (Non-Clairvoyant for Parallel Machine) for the identical parallel machines, wherein the job migration is not permitted.