add new repoHEADmaster

1 files changed, 132 insertions, 0 deletions

diff --git a/Master/Masterarbeit/thesis/tex/app-schedtest.tex b/Master/Masterarbeit/thesis/tex/app-schedtest.tex
new file mode 100644
index 0000000..7a94f1b
--- /dev/null
+++ b/Master/Masterarbeit/thesis/tex/app-schedtest.tex
@@ -0,0 +1,132 @@
+Zur besseren Lesbarkeit entfällt die Angabe der Zeiteinheit $\mu s$. Die Ausgangswerte für die folgenden Berechnungen sind Tabelle \ref{tab:res:startvalues} zu entnehmen.

+\section*{Berechnungen für $m_1$}

+\[ U_1=\frac{C_1}{T_1} =\frac{135}{1000}=0,135<1 \]

+\[ t^1_1=B_1+\lceil\frac{t^0_1+J_1}{T_1}\rceil C_1 =135+\lceil\frac{135+0}{1000}\rceil 135 =135+1*135=270 \]

+\[ t^2_1=B_1+\lceil\frac{t^1_1+J_1}{T_1}\rceil C_1 =135+\lceil\frac{270+0}{1000}\rceil 135 =135+1*135=270 \]

+\[ t_1=270 \]

+\[ Q_1=\lceil\frac{t_1+J_1}{T_1}\rceil = \lceil\frac{270+0}{1000}\rceil = 1 \]

+\[ \omega^0_1\left( 0\right)=B_1=135 \]

+\[ \omega^1_1\left( 0\right)=B_1+0*C_1= 135+0*135=135\]

+\[ \omega_1\left( 0\right)=135\]

+\[ R_1\left( 0\right)=J_1+ \omega_1\left( 0\right)-0*T_1+C_1=0+135-0+135=270 \]

+\[ R_1=\max\limits_{q=0\dots 1-1}\left( \{R_1\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{270\} \right)=270 \]

+\section*{Berechnungen für $m_2$}

+\[ U_2=\frac{C_1}{T_1}+\frac{C_2}{T_2} =\frac{135}{1000}+\frac{135}{1000}=0,270<1 \]

+\[ t^1_2=B_2+\lceil\frac{t^0_2+J_1}{T_1}\rceil C_1 +\lceil\frac{t^0_2+J_2}{T_2}\rceil C_2 \]

+Da in diesem Beispiel $J_1=J_2\dots =J_7$, $T_1=T_2\dots =T_7$ und $C_1=C_2\dots =C_7$, lässt sich einfacher schreiben

+\[ t^1_2=B_2+\left(\lceil\frac{t^0_2+J_2}{T_2}\rceil C_2 \right)*2 \]

+\[ t^1_2=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*2=135+1*135*2=405 \]

+\[ t^2_2=B_2+\left(\lceil\frac{t^1_2+J_2}{T_2}\rceil C_2\right)*2 =135+\left(\lceil\frac{405+0}{1000}\rceil 135\right)*2 =135+1*135*2=405 \]

+\[ t_2=405 \]

+\[ Q_2=\lceil\frac{t_2+J_2}{T_2}\rceil = \lceil\frac{405+0}{1000}\rceil = 1 \]

+\[ \omega^0_2\left( 0\right)=B_2=135 \]

+\[ \omega^1_2\left( 0\right)=B_2+0*C_2+\lceil\frac{\omega^0_2\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1= 135+0*135+\lceil\frac{135+0+1}{1000}\rceil *135=135+1*135=270\]

+\[ \omega^2_2\left( 0\right)=B_2+0*C_2+\lceil\frac{\omega^1_2\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1= 135+0*135+\lceil\frac{270+0+1}{1000}\rceil *135=135+1*135=270\]

+\[ \omega_2\left( 0\right)=270\]

+\[ R_2\left( 0\right)=J_2+ \omega_2\left( 0\right)-0*T_2+C_2=0+270-0+135=405 \]

+\[ R_2=\max\limits_{q=0\dots 1-1}\left( \{R_2\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{405\} \right)=405 \]

+\section*{Berechnungen für $m_3$}

+\[ U_3=\frac{C_1}{T_1}+\frac{C_2}{T_2}+\frac{C_3}{T_3} =\frac{135}{1000}*3=0,405<1 \]

+\[ t^1_3=B_3+\left(\lceil\frac{t^0_3+J_3}{T_3}\rceil C_3 \right)*3 \]

+\[ t^1_3=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*3=135+1*135*3=540 \]

+\[ t^2_3=B_3+\left(\lceil\frac{t^1_3+J_3}{T_3}\rceil C_3\right)*3 =135+\left(\lceil\frac{540+0}{1000}\rceil 135\right)*3 =135+1*135*3=540 \]

+\[ t_3=540 \]

+\[ Q_3=\lceil\frac{t_3+J_3}{T_3}\rceil = \lceil\frac{540+0}{1000}\rceil = 1 \]

+\[ \omega^0_3\left( 0\right)=B_3=135 \]

+\[ \omega^1_3\left( 0\right)=B_3+0*C_3+\lceil\frac{\omega^0_3\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1+\lceil\frac{\omega^0_3\left( 0\right)+J_2+\tau_{bit}}{T_2}\rceil C_2 \] 

+Da in diesem Beispiel $J_1=J_2\dots =J_7$, $T_1=T_2\dots =T_7$ und $C_1=C_2\dots =C_7$, lässt sich auch hier einfacher schreiben

+\[ \omega^1_3\left( 0\right)=B_3+0*C_3+\left(\lceil\frac{\omega^0_3\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*2 \] 

+\[ \omega^1_3\left( 0\right)=135+0*135+\left(\lceil\frac{135+0+1}{1000}\rceil 135\right)*2 = 135+1*135*2=405\] 

+\[

+\begin{split}

+ \omega^2_3\left( 0\right)=B_3+0*C_3+\left(\lceil\frac{\omega^1_3\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*2=\\ 135+0*135+\left(\lceil\frac{270+0+1}{1000}\rceil *135\right)*2=135+1*135*2=405 

+\end{split}

+\]

+\[ \omega_3\left( 0\right)=405\]

+\[ R_3\left( 0\right)=J_3+ \omega_3\left( 0\right)-0*T_3+C_3=0+405-0+135=540 \]

+\[ R_3=\max\limits_{q=0\dots 1-1}\left( \{R_3\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{540\} \right)=540 \]

+\section*{Berechnungen für $m_4$}

+\[ U_4=\frac{C_1}{T_1}*4 =\frac{135}{1000}*4=0,540<1 \]

+\[ t^1_4=B_4+\left(\lceil\frac{t^0_4+J_1}{T_1}\rceil C_1 \right)*4 \]

+\[ t^1_4=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*4=135+1*135*4=675 \]

+\[ t^2_4=B_4+\left(\lceil\frac{t^1_4+J_1}{T_1}\rceil C_1\right)*4 =135+\left(\lceil\frac{675+0}{1000}\rceil 135\right)*4 =135+1*135*4=675 \]

+\[ t_4=675 \]

+\[ Q_4=\lceil\frac{t_4+J_4}{T_4}\rceil = \lceil\frac{675+0}{1000}\rceil = 1 \]

+\[ \omega^0_4\left( 0\right)=B_4=135 \]

+\[ \omega^1_4\left( 0\right)=B_4+0*C_4+\left(\lceil\frac{\omega^0_4\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*3 \] 

+\[ \omega^1_4\left( 0\right)=135+0*135+\left(\lceil\frac{135+0+1}{1000}\rceil 135\right)*3 = 135+1*135*3=540 \] 

+\[

+\begin{split}

+\omega^2_4\left( 0\right)=B_4+0*C_4+\left(\lceil\frac{\omega^1_4\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*3=\\ 135+0*135+\left(\lceil\frac{540+0+1}{1000}\rceil *135\right)*3=135+1*135*3=540

+\end{split}

+\]

+\[ \omega_4\left( 0\right)=540\]

+\[ R_4\left( 0\right)=J_4+ \omega_4\left( 0\right)-0*T_4+C_4=0+540-0+135=675 \]

+\[ R_4=\max\limits_{q=0\dots 1-1}\left( \{R_4\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{675\} \right)=675 \]

+\section*{Berechnungen für $m_5$}

+\[ U_5=\frac{C_1}{T_1}*5 =\frac{135}{1000}*5=0,675<1 \]

+\[ t^1_5=B_5+\left(\lceil\frac{t^0_5+J_1}{T_1}\rceil C_1 \right)*5 \]

+\[ t^1_5=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*5=135+1*135*5=810 \]

+\[ t^2_5=B_5+\left(\lceil\frac{t^1_5+J_1}{T_1}\rceil C_1\right)*5 =135+\left(\lceil\frac{810+0}{1000}\rceil 135\right)*5 =135+1*135*5=810 \]

+\[ t_5=810 \]

+\[ Q_5=\lceil\frac{t_5+J_5}{T_5}\rceil = \lceil\frac{810+0}{1000}\rceil = 1 \]

+\[ \omega^0_5\left( 0\right)=B_5=135 \]

+\[ \omega^1_5\left( 0\right)=B_5+0*C_5+\left(\lceil\frac{\omega^0_5\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*4 \] 

+\[ \omega^1_5\left( 0\right)=135+0*135+\left(\lceil\frac{135+0+1}{1000}\rceil 135\right)*4 = 135+1*135*4=675 \] 

+\[

+\begin{split}

+\omega^2_5\left( 0\right)=B_5+0*C_5+\left(\lceil\frac{\omega^1_5\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*4=\\ 135+0*135+\left(\lceil\frac{675+0+1}{1000}\rceil *135\right)*4=135+1*135*4=675

+\end{split}

+\]

+\[ \omega_5\left( 0\right)=675\]

+\[ R_5\left( 0\right)=J_5+ \omega_5\left( 0\right)-0*T_5+C_5=0+675-0+135=810 \]

+\[ R_5=\max\limits_{q=0\dots 1-1}\left( \{R_5\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{810\} \right)=810 \]

+\section*{Berechnungen für $m_6$}

+\[ U_6=\frac{C_1}{T_1}*6 =\frac{135}{1000}*6=0,810<1 \]

+\[ t^1_6=B_6+\left(\lceil\frac{t^0_6+J_1}{T_1}\rceil C_1 \right)*6 \]

+\[ t^1_6=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*6=135+1*135*6=945 \]

+\[ t^2_6=B_6+\left(\lceil\frac{t^1_6+J_1}{T_1}\rceil C_1\right)*6 =135+\left(\lceil\frac{945+0}{1000}\rceil 135\right)*6 =135+1*135*6=945 \]

+\[ t_6=945 \]

+\[ Q_6=\lceil\frac{t_6+J_6}{T_6}\rceil = \lceil\frac{945+0}{1000}\rceil = 1 \]

+\[ \omega^0_6\left( 0\right)=B_6=135 \]

+\[ \omega^1_6\left( 0\right)=B_6+0*C_6+\left(\lceil\frac{\omega^0_6\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*5 \] 

+\[ \omega^1_6\left( 0\right)=135+0*135+\left(\lceil\frac{135+0+1}{1000}\rceil 135\right)*5 = 135+1*135*5=810 \] 

+\[

+\begin{split}

+\omega^2_6\left( 0\right)=B_6+0*C_6+\left(\lceil\frac{\omega^1_6\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*5=\\ 135+0*135+\left(\lceil\frac{810+0+1}{1000}\rceil *135\right)*5=135+1*135*5=810

+\end{split}

+\]

+\[ \omega_6\left( 0\right)=810\]

+\[ R_6\left( 0\right)=J_6+ \omega_6\left( 0\right)-0*T_6+C_6=0+810-0+135=945 \]

+\[ R_6=\max\limits_{q=0\dots 1-1}\left( \{R_6\left( 0\right) \} \right) = \max\limits_{q=0\dots 0}\left( \{945\} \right)=945 \]

+\section*{Berechnungen für $m_7$}

+\[ U_7=\frac{C_1}{T_1}*7 =\frac{135}{1000}*7=0,945<1 \]

+\[ t^1_7=B_7+\left(\lceil\frac{t^0_7+J_1}{T_1}\rceil C_1 \right)*7 \]

+\[ t^1_7=135+\left(\lceil\frac{135+0}{1000}\rceil 135 \right)*7=135+1*135*7=1080 \]

+\[ t^2_7=B_7+\left(\lceil\frac{t^1_7+J_1}{T_1}\rceil C_1\right)*7 =135+\left(\lceil\frac{1080+0}{1000}\rceil 135\right)*7 =135+2*135*7=2025 \]

+\[ t^3_7=B_7+\left(\lceil\frac{t^2_7+J_1}{T_1}\rceil C_1\right)*7 =135+\left(\lceil\frac{2025+0}{1000}\rceil 135\right)*7 =135+3*135*7=2970 \]

+\[ t^4_7=B_7+\left(\lceil\frac{t^3_7+J_1}{T_1}\rceil C_1\right)*7 =135+\left(\lceil\frac{2970+0}{1000}\rceil 135\right)*7 =135+3*135*7=2970 \]

+\[ t_7=2970 \]

+\[ Q_7=\lceil\frac{t_7+J_7}{T_7}\rceil = \lceil\frac{2970+0}{1000}\rceil = 3 \]

+\[ \omega^0_7\left( 0\right)=B_7=0 \]

+\[ \omega^1_7\left( 0\right)=0+0*C_7+\left(\lceil\frac{\omega^0_7\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*6 \] 

+\[ \omega^1_7\left( 0\right)=0+0*135+\left(\lceil\frac{0+0+1}{1000}\rceil 135\right)*6 = 0+1*135*6=810 \] 

+\[ \omega^2_7\left( 0\right)=0+0*C_7+\left(\lceil\frac{\omega^1_7\left( 0\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*6= 0+0*135+\left(\lceil\frac{810+0+1}{1000}\rceil *135\right)*5=0+1*135*6=810\]

+\[ \omega_7\left( 0\right)=810\]

+\[ R_7\left( 0\right)=J_7+ \omega_7\left( 0\right)-0*T_7+C_7=0+810-0+135=945 \]

+

+\[ \omega^0_7\left( 1\right)=\omega_7\left( 0\right)+C_7=810+135=945 \]

+\[ \omega^1_7\left( 1\right)=0+1*C_7+\left(\lceil\frac{\omega^0_7\left( 1\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*6 \] 

+\[ \omega^1_7\left( 1\right)=0+1*135+\left(\lceil\frac{945+0+1}{1000}\rceil 135\right)*6 = 1*135+1*135*6=945 \] 

+\[ \omega_7\left( 1\right)=945\]

+\[ R_7\left( 1\right)=J_7+ \omega_7\left( 1\right)-1*T_7+C_7=0+945-1000+135=80 \]

+

+\[ \omega^0_7\left( 2\right)=\omega_7\left( 1\right)+C_7=945+135=1080 \]

+\[ \omega^1_7\left( 2\right)=0+2*C_7+\left(\lceil\frac{\omega^0_7\left( 2\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*6 \] 

+\[ \omega^1_7\left( 2\right)=0+2*135+\left(\lceil\frac{1080+0+1}{1000}\rceil 135\right)*6 = 2*135+2*135*6=1890 \] 

+\[ \omega^2_7\left( 2\right)=0+2*C_7+\left(\lceil\frac{\omega^1_7\left( 2\right)+J_1+\tau_{bit}}{T_1}\rceil C_1\right)*6 \] 

+\[ \omega^2_7\left( 2\right)=0+2*135+\left(\lceil\frac{1890+0+1}{1000}\rceil 135\right)*6 = 2*135+2*135*6=1890 \] 

+\[ \omega_7\left( 2\right)=1890\]

+\[ R_7\left( 2\right)=J_7+ \omega_7\left( 2\right)-2*T_7+C_7=0+1890-2000+135=25 \]

+

+\[ R_7=\max\limits_{q=0\dots 3-1}\left( \{R_7\left( 0\right);R_7\left( 1\right);R_7\left( 2\right) \} \right) = \max\limits_{q=0\dots 2}\left( \{945;80;25\} \right)=945 \]
\ No newline at end of file