## 3 RT-IoT System Model
Combining Equations (1)-(3) gives rise to Equation (5):  
\[E=V_{cc}xIxN_{cc}xC_{p}, \tag{4}\]  
if the remaining parameters are kept constant, and then power and energy are directly proportional to the number of clock cycles:  
\[E\propto N_{cc}. \tag{5}\]  
Therefore, in this paper, we design a strategy to control the clock-cycles of scheduling algorithms based on the careful design of input tasks. The effectiveness of an algorithm contributes to how many clock cycles it consumes during its lifespan, and it is known as computational complexity. Many algorithms define static complexity, which can be determined a priori. In contrast, many algorithms' complexities are subjected to the input they take and vary according to the input provided. Figure 1: General System block representation of the proposed work. Scheduling algorithms like RM, DM and EDF compute the hyper-period of input tasks to know the number of times the CPU clock runs. Thus, the computational complexity becomes dependent on the input tasks' period. In this paper, we assume a multi-core platform comprised of \(c\) cores with the only constraint of \(c\geq 2\). The task set denoted by \(\Gamma=\{\tau_{1},\tau_{2},\tau_{3}\ldots\tau_{n}\}\). Every task instance has been characterized by three parameters: worst-case execution time of task \(\tau_{i}\) denoted by \(wect_{i}\), \(P_{i}\) is the inter-arrival time i.e., period of any two consecutive instances of task \(\tau_{i}\) and \(p_{i}\) is the priority of \(\tau_{i}\). Other crucial factors are worth considering regarding tasks that are CPU utilization, which is denoted by \(u_{i}\) and process utilization which is denoted by \(U\). These two factors find whether a given task set \(\Gamma\) is schedulable on a given CPU of \(c\) cores. The CPU utilization and process utilization can be found by Equations (6) and (7), respectively:  
\[u_{i}=wect_{i}/P_{i}, \tag{6}\]  
\[U=\sum_{i=1}^{n}u_{i}. \tag{7}\]  
Historically, many researchers have suggested various criteria for the schedulability test. For instance, in [43; 44], it has been pointed out that tasks will be schedulable for an RM algorithm on \(m\) processors if the utilization \(u_{i}\) of every individual task \(\tau_{i}\) does not exceed \(m/3m-2\) and the total utilization is at most \(m^{2}/3m-1\). It is discussed in [45] that [PERSON] and [PERSON] (1973) proposed the conditions of basic schedulability for RM and EDF to be a function of CPU Utilization bound, which is found in Equation (7). A set of \(n\) periodic tasks is schedulable by the RM algorithm if  
\[\sum_{i=1}^{n}U_{i}\leq n(2^{1/n}-1). \tag{8}\]  
For EDF, under the same assumption, the same set of \(n\) periodic tasks is schedulable if  
\[\sum_{i=1}^{n}U_{i}\leq 1. \tag{9}\]  
The utilization bound of RM is dependent on the number of tasks, and, for an infinite number of tasks, the utilization bound can be found by Equation (10). \[E=PxT, \tag{2}\]0  
This schedulability test is of paramount importance given the critical nature of hard real-time systems. The fact is that, in hard real-time systems, there is no luxury of even a mundane chance of failure out of the entire span of execution time. The problem arises when the algorithm passes the schedulability test, but the embedded IoT objects do not have sufficient resources to execute tasks due to the requirement of higher clock cycles than devices can support. It is pointed out that the primary wellspring of the issue is the high value of hyper-period. The computational complexity is the function of hyper-period and is computed in Equation (11):  
\[E=PxT, \tag{2}\]1  
where \(n\) is the number of input tasks, \(k\) is the task instance to be run in each period and \(H\) is the hyper-period. Each algorithm forms task instances according to their implementation so \(k\) could be changed from one algorithm to another. Moreover, the hyper-period \(H\) of set of \(n\) tasks \(\Gamma\) can be found by Equation (12):  
\[E=PxT, \tag{2}\]2  
where LCM is the least common multiple of tasks' period and \(\tau_{i}\) is an individual task.