# Energy-Aware Online Non-Clairvoyant Scheduling Using Speed Scaling with Arbitrary Power Function
## 5 Illustrative Example
In the speed growth graph of processor using HSIF, more than six maxima and minima are available; it shows that the speed of a processor increases on arrival of a new job, i.e., increases on accumulation of scaled importance based flow time. It eliminates the possibility of starvation condition and improves the performance. It shows that HSIF is capable to adjust the speed for maintaining and improving the performance. Figure 2a shows that initially, at any time the total energy consumed by processor using HSIF is higher than NC, but at the later stage the total energy consumed by processor using NC increases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Job**} & \multicolumn{2}{c}{**Energy Consumed by**} & \multicolumn{2}{c}{**Importance Based Flow**} & \multicolumn{2}{c}{**Importance Based Flow**} \\  & \multicolumn{2}{c}{**Individual Job**} & \multicolumn{2}{c}{**Time of Individual Job**} & \multicolumn{2}{c}{**Time Plus Energy of**} \\  & **HSIF** & **NC** & **HSIF** & **NC** & **HSIF** & **NC** \\ \hline
**J1** & 59.77377 & 62.24247 & **253.36673** & 429.27161 & 313.1405 & 490.5141 \\
**J2** & 54.20484 & 107.6397 & **333.41095** & 1348.8623 & 387.6158 & 1456.502 \\
**J3** & 209.4849 & 20.23206 & **5397.3745** & 316.85458 & 5606.859 & 337.0866 \\
**J4** & 82.46035 & 218.886 & **584.23193** & 5219.856 & 666.6923 & 5438.742 \\
**J5** & 208.9329 & 388.0375 & 2226.1519 & **13632.101** & 2435.085 & 14020.14 \\
**J6** & 90.82497 & 44.05148 & **2118.0612** & 1816.3544 & 2208.886 & 1860.406 \\
**J7** & 82.03271 & 324.3166 & 906.74077 & **14714.469** & 988.7735 & 15038.79 \\ \hline
**Total** & 787.7144 & 1165.406 & **11819.338** & 37477.769 & 12607.05 & 38642.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Three objectives values for jobs using HSIF and NC. Figure 2: Energy Consumption of processes and jobs. The total flowtime of all active jobs when executed using NC is more than HSIF; consequently, the energy consumed by processor when using NC is more than HSIF. The energy consumed by most of the individual jobs when they are executed by HSIF is more than NC, as shown is Figure 2b. The importance based flow time and importance based flow time plus energy values of individual jobs are shown in the Figures 3 and 4 respectively. Most of the individual jobs are having the lesser values of importance based flow time and importance based flow time plus energy when they are executed by using HSIB than NC. HSIF and NC both are competing to reduce the value of the sum of importance based flow time and importance based flow time plus energy, as shown in Figures 3a and 4a, respectively. In the later stage the total values for HSIF is lesser than NC. The total value of importance based flow time and importance based flow time plus energy for a processor by using HSIF is lesser than NC. The value of objective considered is lesser at most of the time when using HSIF. From the above observation, it is concluded that the performance of the HSIF is better and consistent than the best known algorithm NC. To extend the analysis of the performance of HSIF, a second set of ten jobs and the traditional power model is considered. The jobs arrived along with their importance but the size of jobs was only known at their completion. This case is designed by assuming that the jobs arrive in the increasing order of size. The jobs are executed by using algorithms HSIF and NC (the best known to date [11]); their executions are simulated. The analysed data is mentioned in the Tables 5 and 6. In the Table 5 the  
Figure 4: Importance based flow time with energy of jobs. Figure 3: Importance based flow time of jobs. job's arrival time and importance are mentioned. The size is computed and observed at the completion of the jobs. On the basis of the arrival time, starting time of execution and computed completion time the metrics of quality are computed. In this analysis, the metrics of quality considered are turnaround time, response time, power consumed and important based flow time.