## 7 Experimental Results
### CPU Utilization Bound  
As discussed in previous sections, the utilization bound is very crucial in assessing the feasibility analysis of the system. For most of the algorithms, utilization bound value greater than one would \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Tasks** & **Period Range** & **Execution Time Range** & **Arrival Time Range** \\ \hline
10 & 1–10 & 1–15 & 1–15 \\
10 & 1–10 & 1–20 & 1–20 \\
10 & 1–10 & 1–25 & 1–25 \\
10 & 1–10 & 1–30 & 1–30 \\
10 & 1–10 & 1–35 & 1–35 \\
10 & 1–10 & 1–40 & 1–40 \\
10 & 1–10 & 1–45 & 1–45 \\
10 & 1–10 & 1–50 & 1–50 \\
10 & 1–10 & 1–60 & 1–60 \\
10 & 1–10 & 1–70 & 1–70 \\
10 & 1–10 & 1–80 & 1–80 \\
10 & 1–10 & 1–90 & 1–90 \\
10 & 1–10 & 1–100 & 1–100 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Scenario: Changing execution time and arrival time range. Figure 9: Scenario 3: The effect of varying Execution and Arrival Range, given No. of Tasks = 10, Period Range = 1–10. (**a**) execution time range; (**b**) arrival time range. imply that some tasks might not get CPU cycles and will be dropped eventually. The RM algorithm schedules tasks by assigning fixed priorities, and this has been done offline. The priority of a task relies upon its deadline. The shorter the deadline will be, the higher the priority of that task will be. On the other hand, the priority of the EDF is computed dynamically but also relied upon the deadline. The sooner the deadline of a task will be, the higher the priority will be. The utilization bound for RM is 0.69 (Equation (10)), but for EDF it should be less than 1 (Equation (9)). Ideally, 0.69 utilization means that 30% of the CPU is idle which indicates under-utilization. The harmonization approach increases the utilization near to 100% for RM algorithm, and this is one major motivation behind this approach. In this part of experiments, RM and EDF algorithms are applied to four approaches; no threshold, static threshold, harmonization and optimal threshold and the utilization bound is measured. Figure 10a shows the behaviour of RM for the four approaches. The plots show that the utilization bound for smaller task sets, i.e., less than 20, falls within 0.69. That being said, all the approaches meet the schedulability requirements of input tasks. In this case, the proposed algorithm is superior in a sense that the range of period choices is broader as compared to other approaches. When the number of tasks increases, the utilization bound is also increased. The main reason for this is that tasks may have a high execution time as compared to the period and thus contributes to more CPU utilization. The static threshold approach and no threshold give rise to utilization bound more than 0.69, and thus some tasks are likely to miss the deadline. The proposed approach is better regarding utilization bound as compared to harmonization, but the harmonization can schedule tasks even if utilization bound near to 1 at the cost of discrete period values. For the two remaining approaches, when the number of tasks increases more than 50, the utilization bound starts to rise more sharply, and, for 100 tasks, it is more than one, which would mean that some tasks will not be scheduled. When no threshold is applied, even for just over 20 tasks, the utilization bound gives higher values. Thus, it means that, even for a small set of tasks, some tasks will be missed. In Figure 10b, the effect of EDF using the same approaches is investigated. Since the utilization bound for EDF is more than the RM, for harmonization, the optimal threshold and static threshold approaches, the utilization bound is close to 1. When no threshold is applied, if the number of tasks increases beyond 15, the tasks will not be scheduled due to a higher utilization bound. The utilization bound for feasible schedulability in the case of EDF is higher than RM since the priorities are dynamically computed and are changed according to the execution of tasks. Nevertheless, the approach to find a utilization bound for EDF is the same as RM.