@@ -67,7 +67,7 @@ A set of tasks is \textcolor{red}{schedulable} if there exists an algorithm that

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\ownsubsection{Earliest Deadline Due (Jackson's Rule) (6-18)}

\textbf{Algorithm: }Task with earliest deadline is processed first. (Arrival times are equal for all tasks, Scheduling is non-preemptive.)\newline

\textbf{Algorithm: }Task with earliest deadline is processed first. (Arrival times are equal for all tasks,tasks are independent, Scheduling is non-preemptive.)\newline

\textbf{Jackson's Rule: }Given a set of $n$ independent tasks. Processing in order of non-decreasing deadlines is optimal with respect to minimizing the maximum lateness. \newline

\ownsubsection{Latest Deadline First (Lawler's Rule)}

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@@ -76,6 +76,7 @@ A set of tasks is \textcolor{red}{schedulable} if there exists an algorithm that

\begin{itemize}

\item tasks with precedence relations

\item synchronous arrival times

\item non-preemptive

\end{itemize}

\textbf{Algorithm:}

\begin{itemize}

...

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@@ -85,8 +86,12 @@ A set of tasks is \textcolor{red}{schedulable} if there exists an algorithm that

\end{itemize}

\ownsubsection{Earliest Deadline First (Horn's Rule) (6-22)}

\textbf{Algorithm:} Task with earliest deadline is processed first. If new task with earlier deadline arrives, current task is preempted. \newline

\textbf{Horn's Rule: }Given a set of $n$ independent tasks with arbitrary arrival times. An algorithm that at any instant executes the task with the earliest absolute among the ready tasks is optimal with respect to minimizing maximum lateness. \newline

\textbf{Algorithm:} Task with earliest deadline is processed first. If new task with earlier deadline arrives, current task is preempted. \vspace{2mm}

\textbf{Optimization goal:}

It is is optimal in sense of feasibility (it minimizes the maximum lateness under following assumptions: scheduling algorithm is preemptive, the tasks are independent and may have different arrival times)\vspace{2mm}

\textbf{Horn's Rule: }Given a set of $n$ independent tasks with arbitrary arrival times. An algorithm that at any instant executes the task with the earliest absolute deadline among the ready tasks is optimal with respect to minimizing the maximum lateness. \newline

\textbf{Acceptance test:}\\

worst case finishing time of task i: $f_i = t +\sum_{k=1}^i c_k(t)$\\

The following holds for the optimal energy consumption $u(t)$:

\begin{itemize}

\item If the battery is neither full nor empty, $u(t)$ stays constant.

\item If the battery is \textbf{empty}, $u(t)$\textbf{increases}

\item If the battery is \textbf{full}, $u(t)$\textbf{decreases}

\end{itemize}

Since the perfect use function $u(t)$ was chosen with knowledge of all harvested energy for all times, the battery level will drop to 0\% only at times, when the harvesting functions starts delivering more energy than we currently use. \\

The energy consumption will then be chosen, such that the battery is full, when the harvesting function is decreasing, thus after the battery is fully charged, the use function should decrease. \\