From d83e54822fdb8ef6f07a0f8c59ea61012261eaff Mon Sep 17 00:00:00 2001 From: rylon Date: Sat, 17 Aug 2013 02:07:18 +0200 Subject: [PATCH] thesis --- .../Bachelor Thesis/thesis_ug/TUDthesis.aux | 66 +-- .../Bachelor Thesis/thesis_ug/TUDthesis.ist | 2 +- .../Bachelor Thesis/thesis_ug/TUDthesis.log | 325 +++++++------- .../Bachelor Thesis/thesis_ug/TUDthesis.pdf | Bin 17126423 -> 17137601 bytes .../thesis_ug/TUDthesis.synctex.gz | Bin 406136 -> 442555 bytes .../thesis_ug/ext/KreuzungA104.pdf | Bin 139112 -> 144313 bytes .../thesis_ug/pic/osm_overview.png | Bin 0 -> 586464 bytes .../Bachelor Thesis/thesis_ug/tex/anhang.tex | 418 +++++++++++++----- .../thesis_ug/tex/berechnung.tex | 30 +- .../thesis_ug/tex/datengrund.tex | 52 +-- .../Bachelor Thesis/thesis_ug/tex/glossar.tex | 5 +- .../Bachelor Thesis/thesis_ug/tex/modell.tex | 64 +-- 12 files changed, 589 insertions(+), 373 deletions(-) create mode 100644 ss2013/Bachelor Thesis/thesis_ug/pic/osm_overview.png diff --git a/ss2013/Bachelor 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{43}{\ignorespaces Verkehrszhlung vom 30.7.2013.}}{74}{figure.43}} \@writefile{lof}{\contentsline {figure}{\numberline {44}{\ignorespaces Verkehrszhlung vom 5.8.2013.}}{75}{figure.44}} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.ist b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.ist index 848c86a6..99d5e46d 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.ist +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.ist @@ -1,5 +1,5 @@ % makeindex style file created by the glossaries package -% for document 'TUDthesis' on 2013-8-16 +% for document 'TUDthesis' on 2013-8-17 actual '?' encap '|' level '!' diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log index e5fd9b11..04ec81c4 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log @@ -1,7 +1,7 @@ -This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.8.13) 16 AUG 2013 19:08 +This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.8.13) 17 AUG 2013 02:04 entering extended mode **TUDthesis.tex -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.tex" +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.tex" LaTeX2e <2009/09/24> Babel and hyphenation patterns for english, afrikaans, ancientgreek, ar abic, armenian, assamese, basque, bengali, bokmal, bulgarian, catalan, coptic, @@ -956,7 +956,7 @@ File: lstlang1.sty 2013/06/27 1.5pre1 listings language file LaTeX Warning: Unused global option(s): [article,colorback,accentcolor=tud9d]. -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux" +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux" LaTeX Warning: Label `problem:6' multiply defined. @@ -1062,8 +1062,8 @@ LaTeX Info: Redefining \ref on input line 24. LaTeX Info: Redefining \pageref on input line 24. LaTeX Info: Redefining \nameref on input line 24. -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.out") -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.out") +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.out") +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.out") \@outlinefile=\write6 @@ -1208,7 +1208,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 33--33 [0 -] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/danke.tex") +] ("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/danke.tex") [1 @@ -1222,8 +1222,8 @@ File: t15sf.fd 2008/06/23 Fontinst v1.927 font definitions for T1/5sf. ] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/glossar.tex") -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/uebersicht.tex" +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/glossar.tex") +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/uebersicht.tex" Underfull \hbox (badness 10000) in paragraph at lines 3--9 [] @@ -1241,7 +1241,7 @@ l.20 \newpage [1 ]) -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.toc"pdfTeX +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.toc"pdfTeX warning (ext4): destination with the same identifier (name{page.2}) has been a lready used, duplicate ignored @@ -1250,7 +1250,7 @@ l.50 ...e {11}Quellcodeverzeichnis}{33}{section.8} [2]) \tf@toc=\write7 [3] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/einleitung.tex" +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/einleitung.tex" LaTeX Font Info: Font shape `OT1/mdbch/m/n' will be (Font) scaled to size 7.87204pt on input line 2. 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(scrartcl) `scrartcl' soon, so it should not be used on input lin e 73. -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.lol") +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.lol") \tf@lol=\write8 -[33] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/anhang.tex" +[33] ("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/anhang.tex" -pdfTeX warning: pdflatex.exe (file C:/Daten/source/college/ss2013/Bachelor Thes +pdfTeX warning: pdflatex.exe (file C:/daten/source/college/ss2013/Bachelor Thes is/thesis_ug/ext/overviewmap.pdf): PDF inclusion: found PDF version <1.6>, but at most version <1.5> allowed @@ -1771,10 +1771,10 @@ File: ext/MessgruppentabelleNord-2013-01-08.pdf Graphic file (type pdf) File: ext/MessgruppentabelleSued-2013-01-08.pdf Graphic file (type pdf) - [34] [35 ] [36 [34] [35 ] [36 ] [37 ] [37 ] File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) [38 @@ -1784,168 +1784,167 @@ File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) File: ext/KreuzungA3.pdf Graphic file (type pdf) -File: ext/KreuzungA4.pdf Graphic file (type pdf) - - -File: ext/KreuzungA5.pdf Graphic file (type pdf) - - - -File: ext/KreuzungA12.pdf Graphic file (type pdf) - - -File: ext/KreuzungA23.pdf Graphic file (type pdf) - - -File: ext/KreuzungA28.pdf Graphic file (type pdf) - - - -File: ext/KreuzungA29.pdf Graphic file (type pdf) - - - -File: ext/KreuzungA46.pdf Graphic file (type pdf) - - - -File: ext/KreuzungA59.pdf Graphic file (type pdf) - - - -File: ext/KreuzungA104.pdf Graphic file (type pdf) - - [40 - -] [41 ] [42] [43 ] [44 ] [45] [46 ] [47 ] [48 ] [49 ] -[50 ] + File: ext/A3_Uebersetzungstabelle.pdf Graphic file (type pdf) - -File: ext/A4_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A5_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A12_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A23_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A28_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A29_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A46_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A59_Uebersetzungstabelle.pdf Graphic file (type pdf) - - - -File: ext/A104_Uebersetzungstabelle.pdf Graphic file (type pdf) - - [51 - -] [52 ] [53 ] -[54 ] [55 ] [56 ] [57 ] [58 ] [59 ] [60 ] [61 ] - + File: ext/DA_A_3_L4.pdf Graphic file (type pdf) - +File: ext/KreuzungA4.pdf Graphic file (type pdf) + + +File: ext/A4_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_4_L3.pdf Graphic file (type pdf) - + +File: ext/KreuzungA5.pdf Graphic file (type pdf) + + + +File: ext/A5_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_5_L3.pdf Graphic file (type pdf) - -File: ext/DA_A_12.pdf Graphic file (type pdf) + + +File: ext/KreuzungA12.pdf Graphic file (type pdf) - + + +File: ext/A12_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + +File: ext/DA_A_12.pdf Graphic file (type pdf) + +[40 + +] [41 ] [42 ] [43 ] [44] [45 ] [46 ] [47 ] [48 ] +[49 ] [50 ] +File: ext/KreuzungA23.pdf Graphic file (type pdf) + + +File: ext/A23_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_23_L1.pdf Graphic file (type pdf) - + +File: ext/KreuzungA28.pdf Graphic file (type pdf) + + + +File: ext/A28_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_28_L1.pdf Graphic file (type pdf) - + +File: ext/KreuzungA29.pdf Graphic file (type pdf) + + + +File: ext/A29_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_29_L2.pdf Graphic file (type pdf) - + +File: ext/KreuzungA46.pdf Graphic file (type pdf) + + + +File: ext/A46_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_46_L1.pdf Graphic file (type pdf) - -File: ext/DA_A_59.pdf Graphic file (type pdf) + [51] [52 ] [53 ] [54] [55 ] +[56 ] [57 ] [58 ] [59 ] [60 ] [61 ] [62 ] + +File: ext/KreuzungA59.pdf Graphic file (type pdf) - - + + +File: ext/A59_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + +File: ext/DA_A_59.pdf Graphic file (type pdf) + + +File: ext/KreuzungA104.pdf Graphic file (type pdf) + + + +File: ext/A104_Uebersetzungstabelle.pdf Graphic file (type pdf) + + + File: ext/DA_A_104_L1.pdf Graphic file (type pdf) - [62 - -] [63 ] [64 ] [65 ] [66 ] [67 ] [68 ] [69 ] [70 ] [71 ] [72 ] - + [63] [64 ] [65 ] [66 ] [67 ] [68 +] [69 ] [70 ] [71 ] [72 ] + File: ext/verkehrszaehlung.pdf Graphic file (type pdf) - + File: ext/verkehrszaehlung_08_05.pdf Graphic file (type pdf) ) Package atveryend Info: Empty hook `BeforeClearDocument' on input line 76. [73 -] [74 ] [75 ] [75 ] Package atveryend Info: Empty hook `AfterLastShipout' on input line 76. -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux") +("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux") Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 76. Package rerunfilecheck Info: File `TUDthesis.out' has not changed. (rerunfilecheck) Checksum: B826E0EFF58CC00B8C38E3338BCD91D0;3798. @@ -1958,10 +1957,10 @@ LaTeX Warning: There were multiply-defined labels. ) Here is how much of TeX's memory you used: - 17114 strings out of 494019 - 260727 string characters out of 3145626 + 17124 strings out of 494019 + 260845 string characters out of 3145626 468106 words of memory out of 3000000 - 19586 multiletter control sequences out of 15000+200000 + 19596 multiletter control sequences out of 15000+200000 156504 words of font info for 117 fonts, out of 3000000 for 9000 714 hyphenation exceptions out of 8191 65i,13n,77p,1460b,1138s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -1979,9 +1978,9 @@ chr7t.pfb> -Output written on TUDthesis.pdf (79 pages, 17126423 bytes). +Output written on TUDthesis.pdf (79 pages, 17137601 bytes). 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zm>{5>*Y~Cn|IPldM9b2hV0G4xGnVe$tcu?bqF?2fiKav;S)*+F1h{Yi_Xrs1(TO6j z5L#$qAKM5IYohN4*72}REG(ub*9zXCai?v@aRqH#>l=g5p!HkHkC>dQjueZA`oCkl z6Ax2NHdQ#Lu1x0UB08m#5gF3y41$r#NXg&$dQlX=j+i&;xLL6ctXNdPMgmUedZoH) zqz2MGv?Z)?;jwf)X7RPjeKiZHe^=JbLDn4#uc zZAI>(XQXPf03-2Ql1TizkdN-Hv4-m1lR?wir-q;vw26R~|f0qmo`$R>B;nhHH`sof* z6(kXPuusRFJRlQDKJR5tTAjM8DsPmeMH`Vr-)5AlZ z(Bq^}(ebMX2-fnTEMU@GaCs$siVvTgT`~HENORdZ(Y4W%81@^7kk};&f#4TR@+5ync@4VVw$j#4&fy?*(4}?i(S`oMWhPY5XXLZDdfnII^K5udA_ zak&W6sok*NvvvrA4(dyAW!rrPQP}%A-i~-p+K721VonDUIp&(??oBy6^SA6zGL?^f z1T7^(Hmdi0-wuJy+a#G5YwO@=w F{}-pHHxmE= literal 0 HcmV?d00001 diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/anhang.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/anhang.tex index 42b6210f..a89fe53f 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/anhang.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/anhang.tex @@ -29,174 +29,378 @@ \end{figure} \clearpage -\subsection*{Kreuzungsbilder} +\subsection*{Kreuzung A3}\label{anhang:a3} +Ausgangsmatrix der Kreuzung A3:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c} + & D11 & D12 & D13 & D21 & D22 & D23 & D31 & D32 & D33 & V41 & V42 & D43\\ + \hline + A4 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0\\ + \hline + A104 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A3:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c} + & D11 & D12 & D13 & D21 & D22 & D23 & D31 & D32 & D33 & V41 & V42 & D43\\ + \hline + A4 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ + \hline + A104 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A3:\\ \begin{figure} \centering \fbox{\includegraphics[angle={90},width=0.90\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA3}} \caption{Kreuzung A3} \end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA4}} - \caption{Kreuzung A4} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA5}} - \caption{Kreuzung A5} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA12}} - \caption{Kreuzung A12} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} - \caption{Kreuzung A23} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA28}} - \caption{Kreuzung A28} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA29}} - \caption{Kreuzung A29} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA46}} - \caption{Kreuzung A46} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA59}} - \caption{Kreuzung A59} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA104}} - \caption{Kreuzung A104} -\end{figure} -\clearpage - -\subsection*{"Ubersetzungstabellen} +"Ubersetzungstabelle der Kreuzung A3:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.85\textwidth-2\fboxsep-2\fboxrule]{ext/A3_Uebersetzungstabelle}} \caption{bersetzungstabelle fr Kreuzung A3} \end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A4_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A4} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A5_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A5} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A12_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A12} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A23_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A23} -\end{figure} -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A28_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A28} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A29_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A29} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A46_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A46} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A59_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A59} -\end{figure} - -\begin{figure} - \centering - \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A104_Uebersetzungstabelle}} - \caption{bersetzungstabelle fr Kreuzung A104} -\end{figure} -\clearpage - - -\subsection*{CAD-Zeichnungen der Kreuzungen} +CAD-Zeichnung der Kreuzung A3:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.85\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_3_L4}} \caption{CAD Zeichnung der Kreuzung A3} \end{figure} + +\subsection*{Kreuzung A4}\label{anhang:a4} +Ausgangsmatrix der Kreuzung A4:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c} + & D10 & D11 & D12 & D13 & IR21 & D30 & D31 & D32 & D33 & D34 & D40 & D41 & D42 & D43 & D44\\ + \hline + A3 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + \hline + A5 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0\\ + \hline + A23 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A4:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c} + & D10 & D11 & D12 & D13 & IR21 & D30 & D31 & D32 & D33 & D34 & D40 & D41 & D42 & D43 & D44\\ + \hline + A3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1\\ + \hline + A5 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + \hline + A23 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A4:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA4}} + \caption{Kreuzung A4} +\end{figure} +"Ubersetzungstabelle der Kreuzung A4:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A4_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A4} +\end{figure} +CAD-Zeichnung der Kreuzung A4:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_4_L3}} \caption{CAD Zeichnung der Kreuzung A4} \end{figure} + +\subsection*{Kreuzung A5}\label{anhang:a5} +Ausgangsmatrix der Kreuzung A5:\\ +\begin{tabular}{c|c|c|c|c|c|c|c} + & D11 & D12 & D21 & D31 & D41 & D42 & D43\\ + \hline + A4 & 1 & 0 & 1 & 0 & 0 & 0 & 0\\ + \hline + A28 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A5:\\ +\begin{tabular}{c|c|c|c|c|c|c|c} + & D11 & D12 & D21 & D31 & D41 & D42 & D43\\ + \hline + A4 & 0 & 0 & 0 & 0 & 1 & 1 & 1\\ + \hline + A28 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A5:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA5}} + \caption{Kreuzung A5} +\end{figure} +"Ubersetzungstabelle der Kreuzung A5:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A5_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A5} +\end{figure} +CAD-Zeichnung der Kreuzung A5:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_5_L3}} \caption{CAD Zeichnung der Kreuzung A5} \end{figure} + +\subsection*{Kreuzung A12}\label{anhang:a12} +Ausgangsmatrix der Kreuzung A12:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c} + & D11 & D12 & D13 & D21 & D22 & D31 & D32 & D33 & D41 & D42\\ + \hline + A23 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1\\ + \hline + A46 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\\ + \hline + A59 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A12:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c} + & D11 & D12 & D13 & D21 & D22 & D31 & D32 & D33 & D41 & D42\\ + \hline + A23 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0\\ + \hline + A46 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ + \hline + A59 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A12:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA12}} + \caption{Kreuzung A12} +\end{figure} +"Ubersetzungstabelle der Kreuzung A12:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A12_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A12} +\end{figure} +CAD-Zeichnung der Kreuzung A12:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_12}} \caption{CAD Zeichnung der Kreuzung A12} \end{figure} + +\subsection*{Kreuzung A23}\label{anhang:a23} +Ausgangsmatrix der Kreuzung A23:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ + \hline + A4 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + \hline + A12 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\ + \hline + A104 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A23:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ + \hline + A4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0\\ + \hline + A12 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + \hline + A104 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A23:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} + \caption{Kreuzung A23} +\end{figure} +"Ubersetzungstabelle der Kreuzung A23:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A23_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A23} +\end{figure} +CAD-Zeichnung der Kreuzung A23:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_23_L1}} \caption{CAD Zeichnung der Kreuzung A23} \end{figure} + +\subsection*{Kreuzung A28}\label{anhang:a28} +Ausgangsmatrix der Kreuzung A28:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c} + & D11 & D12 & V21 & V22 & V23 & V24 & D31 & D32\\ + \hline + A5 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0\\ + \hline + A23 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1\\ + \hline + A59 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A28:\\ +\begin{tabular}{c|c|c|c|c|c|c|c|c} + & D11 & D12 & V21 & V22 & V23 & V24 & D31 & D32\\ + \hline + A5 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ + \hline + A23 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + \hline + A59 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A28:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA28}} + \caption{Kreuzung A28} +\end{figure} +"Ubersetzungstabelle der Kreuzung A28:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A28_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A28} +\end{figure} +CAD-Zeichnung der Kreuzung A28:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_28_L1}} \caption{CAD Zeichnung der Kreuzung A28} \end{figure} + +\subsection*{Kreuzung A29}\label{anhang:a29} +Ausgangsmatrix der Kreuzung A29:\\ +\begin{tabular}{c|c|c} + & D11 & D12\\ + \hline + A28 & 1 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A29:\\ +\begin{tabular}{c|c|c} + & D11 & D12\\ + \hline + A28 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A29:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA29}} + \caption{Kreuzung A29} +\end{figure} +"Ubersetzungstabelle der Kreuzung A29:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A29_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A29} +\end{figure} +CAD-Zeichnung der Kreuzung A29:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_29_L2}} \caption{CAD Zeichnung der Kreuzung A29} \end{figure} + +\subsection*{Kreuzung A46}\label{anhang:a46} +Ausgangsmatrix der Kreuzung A46:\\ +\begin{tabular}{c|c|c|c|c|c|c|c} + & D11 & D12 & D21 & D31 & D32 & D41 & D42\\ + \hline + A12 & 0 & 1 & 0 & 1 & 0 & 1 & 0\\ + \hline + A104 & 1 & 1 & 0 & 0 & 0 & 1 & 0\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A46:\\ +\begin{tabular}{c|c|c|c|c|c|c|c} + & D11 & D12 & D21 & D31 & D32 & D41 & D42\\ + \hline + A12 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ + \hline + A104 & 0 & 0 & 0 & 1 & 1 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A46:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA46}} + \caption{Kreuzung A46} +\end{figure} +"Ubersetzungstabelle der Kreuzung A46:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A46_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A46} +\end{figure} +CAD-Zeichnung der Kreuzung A46:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_46_L1}} \caption{CAD Zeichnung der Kreuzung A46} \end{figure} + +\subsection*{Kreuzung A59}\label{anhang:a59} +Ausgangsmatrix der Kreuzung A59:\\ +\begin{tabular}{c|c|c|c|c} + & D21 & D51 & D81 & D111\\ + \hline + A12 & 1 & 1 & 1 & 0\\ + \hline + A28 & 1 & 1 & 0 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A59:\\ +\begin{tabular}{c|c|c|c|c} + & D21 & D51 & D81 & D111\\ + \hline + A12 & 0 & 0 & 0 & 1\\ + \hline + A28 & 0 & 0 & 1 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A59:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA59}} + \caption{Kreuzung A59} +\end{figure} +"Ubersetzungstabelle der Kreuzung A59:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A59_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A59} +\end{figure} +CAD-Zeichnung der Kreuzung A59:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_59}} \caption{CAD Zeichnung der Kreuzung A59} \end{figure} + +\subsection*{Kreuzung A104}\label{anhang:a104} +Ausgangsmatrix der Kreuzung A104:\\ +\begin{tabular}{c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6\\ + \hline + A3 & 1 & 1 & 1 & 1 & 0 & 0\\ + \hline + A46 & 0 & 0 & 1 & 0 & 1 & 1\\ +\end{tabular}\\ +Eingangsmatrix der Kreuzung A104:\\ +\begin{tabular}{c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6\\ + \hline + A3 & 0 & 0 & 0 & 0 & 1 & 1\\ + \hline + A46 & 1 & 1 & 0 & 0 & 0 & 0\\ +\end{tabular}\\ +Modellierung der Kreuzung A104:\\ +\begin{figure} + \centering + \fbox{\includegraphics[angle={90},width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA104}} + \caption{Kreuzung A104} +\end{figure} +"Ubersetzungstabelle der Kreuzung A104:\\ +\begin{figure} + \centering + \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/A104_Uebersetzungstabelle}} + \caption{bersetzungstabelle fr Kreuzung A104} +\end{figure} +CAD-Zeichnung der Kreuzung A104:\\ \begin{figure} \centering \fbox{\includegraphics[width=0.95\textwidth-2\fboxsep-2\fboxrule]{ext/DA_A_104_L1}} \caption{CAD Zeichnung der Kreuzung A104} \end{figure} \clearpage - \subsection*{Verkehrszhlungen} \begin{figure} \centering diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex index f5a5a4c4..03bf6749 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex @@ -8,12 +8,12 @@ Es galt folgende Herausforderung zu l"osen: \item{Validierung von Sensorwerten, mithilfe von Validierungssensoren}\label{problem:2} \item{Verkehrswerte f"ur Seitenstraßen ohne Sensoren}\label{problem:5} \item{Fl"ussen zwischen den Kreuzungen}\label{problem:6} - \item{Verkehrswerte für einen Zeitpunkt in der Zuknunft berechnen,}\label{problem:6} + \item{Verkehrswerte f"ur einen Zeitpunkt in der Zuknunft berechnen,}\label{problem:6} \end{enumerate} Es wurden im Rahmen dieser Arbeit mehrere Berechnungsans"atze daraufhin "uberpr"uft, ob sie eines der gegebenen Problem l"osen kann. Die beschriebenen Ans"atze sind 'Hidden Markow Modell', 'Wegfindungsalorithmen' wie A* und 'lineares Gleichungssystem'. \\ \\ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erste Ziel, welche zu erreichen galt. Da virtuelle Sensoren in dem entwickelten Verkehrsmodell ausschließlich Aus- und Eing"ange modellieren, w"urden damit ebenfalls die Herausforderung einen Verkehrswert f"ur die jeweiligen Kreuzungsein- und -ausg"ange zu berechnen gel"ost werden. \subsection{L"osungsansatz: Hidden Markow Modell}\label{sec:berechnung:hmm} - Das Hidden Markow Modell(HMM) ist ein Modell zur Beschreibung von Systemen mit versteckten Zust"anden. Es ist nach dem russischen Mathematiker Andrei Andrejewitsch Markow benannt. Es schien ein geignetes Modell zu sein, da es vermag sowohl bekannte als auch unbekannte Einheiten zu modellieren, in Verbindung einer Übergangswahrscheinlichkeit. [ref] Im Folgendem werden die Grundlagen von Hidden Marokw Modellen umrissen. + Das Hidden Markow Modell(HMM) ist ein Modell zur Beschreibung von Systemen mit versteckten Zust"anden. Es ist nach dem russischen Mathematiker Andrei Andrejewitsch Markow benannt. Es schien ein geignetes Modell zu sein, da es vermag sowohl bekannte als auch unbekannte Einheiten zu modellieren, in Verbindung einer "Ubergangswahrscheinlichkeit. [ref] Im Folgendem werden die Grundlagen von Hidden Marokw Modellen umrissen. \subsubsection{Grundlagen} \subsubsection{HMM f"ur eine Kreuzung} @@ -25,12 +25,12 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst au"serdem entspricht das Verfahren durch den "zufall" eher besserem Raten. \subsection{L"osungsansatz: Wegfindungsalgorithmen}\label{sec:berechnung:astar} - Um den Weg eines Autos zu simulieren bieten sich Wegfindungsalgorithmen an, da sie den k"urzesten Weg zum Ziel finden und das dem Verhalten des Menschen "ahnelt. Die Idee die Anzahl der Autos anhand der Sensorwerte zu bestimmen und diese durch das Straßennetz zu ihrem Ziel fahren zu lassen erschien als eine gute L"osung. Aus dem Studium bekannte Algorithmen wie der A* k"onnen ein solches Wegfindungsproblem l"osen. Insbesondere die Möglichkeit einen Graphen direkt zur Berechnung zu verwenden, ließen diesen Ansatz erfolgsversprechend aussehen. Die Absch"atzung f"ur die Distanz zweier Knoten w"are dabei die Luftlinie zwischen ihnen. Da keine Werte "uber einzelne Autos, sondern nur Messwerte "uber eine Minute zur Verf"ugung standen musste nicht nur ein einzelnes Auto, sondern eine Autokolonne simuliert werden.\\ \\ + Um den Weg eines Autos zu simulieren bieten sich Wegfindungsalgorithmen an, da sie den k"urzesten Weg zum Ziel finden und das dem Verhalten des Menschen "ahnelt. Die Idee die Anzahl der Autos anhand der Sensorwerte zu bestimmen und diese durch das Straßennetz zu ihrem Ziel fahren zu lassen erschien als eine gute L"osung. Aus dem Studium bekannte Algorithmen wie der A* k"onnen ein solches Wegfindungsproblem l"osen. Insbesondere die M"oglichkeit einen Graphen direkt zur Berechnung zu verwenden, ließen diesen Ansatz erfolgsversprechend aussehen. Die Absch"atzung f"ur die Distanz zweier Knoten w"are dabei die Luftlinie zwischen ihnen. Da keine Werte "uber einzelne Autos, sondern nur Messwerte "uber eine Minute zur Verf"ugung standen musste nicht nur ein einzelnes Auto, sondern eine Autokolonne simuliert werden.\\ \\ Allerdings stellte sich heraus das keinerlei Daten "uber das Ziel der Autofahrer in der Stadt Darmstadt bekannt oder gemessen wurden. Eine Erhebung war ebenfalls nicht m"oglich, da eine Vielzahl von Ausg"angen aus der 'Ministadt' untersucht werden m"ussten. Da kein Wegfindungsalgorithmus ohne Ziel funktionieren kann wurden Wegfindungsalgorithmen als L"osungsansatz verworfen. \subsection{L"osungsansatz: Lineares Gleichungssystem}\label{sec:berechnung:lgs} - Das in Kapitel \autoref{sec:modell} beschriebene Modell erlaubt es mithilfe von linearen Gleichungssystemen einen Wert f"ur jeden Kreuzungsein- und Ausgang zu berechnen. Vorraussetzung daf"ur ist, dass alle Kreuzungseing"ange auf jeder Spur mit Sensoren best"uckt sind, sowie dass alle Verkehrsteilnehmer sich an die Straßenverkehrsordnung halten. Insbesodere das Einhalten der Spurrichtung ist Vorraussetzung f"ur eine korrekte Berechnung. In Kapitel \autoref{sec:modell} werden die Einschränkungen des Modells näher erläutert.\\ \\ - Durch Addition derjenigen Sensorwerte, welche auf den jeweiligen Ausgang zeigen, kann ein Wert f"ur diesen ausgerechnet werden. F"ur Mischspursensoren werden daf"ur Abbiegewahrscheinlichkeiten ben"otigt, um den Sensorwert entsprechend dem Abbiegeverhalten der Verkehrsteilnehmer auf die Ausg"ange zu verteilen. Die Abbiegewahrscheinlichkeit gibt dabei an, wieviel Prozent des Verkehrs, welcher "uber den Sensor fließt dem jeweiligen Ausgangsknoten zugeordnet werden kann. Der Sensorwert wird entsprechend mit der jeweiligen Abbiegewahrscheinlichkeit multipliziert und auf den Ausgang addiert. Einspursensoren k"onnen dagegen direkt auf den Ausgang addiert werden ohne das Abbiegewahrscheinlichkeiten von N"oten sind. Um das Berechnungsmodell einheitlich zu halten wurde bei der Matrizenrechnung eine Abbiegewahrscheinlichkeit von 1.0 für Einspursensoren angegeben.\\ \\ + Das in Kapitel \autoref{sec:modell} beschriebene Modell erlaubt es mithilfe von linearen Gleichungssystemen einen Wert f"ur jeden Kreuzungsein- und Ausgang zu berechnen. Vorraussetzung daf"ur ist, dass alle Kreuzungseing"ange auf jeder Spur mit Sensoren best"uckt sind, sowie dass alle Verkehrsteilnehmer sich an die Straßenverkehrsordnung halten. Insbesodere das Einhalten der Spurrichtung ist Vorraussetzung f"ur eine korrekte Berechnung. In Kapitel \autoref{sec:modell} werden die Einschr"ankungen des Modells n"aher erl"autert.\\ \\ + Durch Addition derjenigen Sensorwerte, welche auf den jeweiligen Ausgang zeigen, kann ein Wert f"ur diesen ausgerechnet werden. F"ur Mischspursensoren werden daf"ur Abbiegewahrscheinlichkeiten ben"otigt, um den Sensorwert entsprechend dem Abbiegeverhalten der Verkehrsteilnehmer auf die Ausg"ange zu verteilen. Die Abbiegewahrscheinlichkeit gibt dabei an, wieviel Prozent des Verkehrs, welcher "uber den Sensor fließt dem jeweiligen Ausgangsknoten zugeordnet werden kann. Der Sensorwert wird entsprechend mit der jeweiligen Abbiegewahrscheinlichkeit multipliziert und auf den Ausgang addiert. Einspursensoren k"onnen dagegen direkt auf den Ausgang addiert werden ohne das Abbiegewahrscheinlichkeiten von N"oten sind. Um das Berechnungsmodell einheitlich zu halten wurde bei der Matrizenrechnung eine Abbiegewahrscheinlichkeit von 1.0 f"ur Einspursensoren angegeben.\\ \\ Im Folgendem werden die Grundlagen von linearen Gleichungssystemen umrissen, woraufhin die entwickelte Berechnungsmethodik f"ur Kreuzungen und zwischen Kreuzungen genauer untersucht wird. \subsubsection{Grundlagen}\label{sec:berechnung:lgs:grund} Ein lineares Gleichungssystem ist ein System linearer Gleichungen. Ein solches System hat n Unbekannte und m Gleichungen. Eine allgemeine Darstellungsform ist die folgende:\\ @@ -42,7 +42,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst a_{m1} x_1 + a_{m2} x_2 \, + & \cdots & +\, a_{mn} x_n & = & b_m\\ \end{matrix} \end{equation} - Ein lineares Gleichungssystem ist l"osbar, wenn alle Gleichungen erf"ullbar sind. Ist dies nicht der Fall spricht man von einem unl"osbaren Gleichungssystem. L"osbare Systeme lassen sich nochmals in die 'eindeutig L"osbaren' und 'nicht eindeutig L"osbaren' unterteilen. F"ur ein eindeutig l"osbares Gleichungssystem kann eine numerische L"osung f"ur $x_1$ bis $x_n$ gefunden werden, im Gegensatz zu nicht eindeutig L"osbaren System, f"ur welche eine L"osung nur in Abh"angigkeit von einem oder mehreren Parametern angeben werden kann. Ein lineares Gleichungssystem ist genau dann eindeutig lösbar wenn R(rang)...[]\\ \\ + Ein lineares Gleichungssystem ist l"osbar, wenn alle Gleichungen erf"ullbar sind. Ist dies nicht der Fall spricht man von einem unl"osbaren Gleichungssystem. L"osbare Systeme lassen sich nochmals in die 'eindeutig L"osbaren' und 'nicht eindeutig L"osbaren' unterteilen. F"ur ein eindeutig l"osbares Gleichungssystem kann eine numerische L"osung f"ur $x_1$ bis $x_n$ gefunden werden, im Gegensatz zu nicht eindeutig L"osbaren System, f"ur welche eine L"osung nur in Abh"angigkeit von einem oder mehreren Parametern angeben werden kann. Ein lineares Gleichungssystem ist genau dann eindeutig l"osbar wenn R(rang)...[]\\ \\ Eine g"angige Art der Darstellung von linearen Gleichungssystemen ist die Matrixdarstellung. Das System zerf"allt dabei in drei Teile. Die Koeffizientenmatrix enth"alt die Werte $a_{11}$ bis $a_{nm}$. Die Unbekannten $x_1$ bis $x_n$ werden in einer einspaltigen Matrize zusammengefasst, ebenso wie die Ergebniswerte $b_1$ bis $b_m$. \begin{equation} \begin{pmatrix} @@ -66,11 +66,11 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst b_n \\ \end{pmatrix} \end{equation} - Für ein solches Gleichungssystem existieren verschiedene Lösungsverfahren. Ein Beispiel ist der Gaus-Algorithmus. + F"ur ein solches Gleichungssystem existieren verschiedene L"osungsverfahren. Ein Beispiel ist der Gaus-Algorithmus. [gaus] - Neben dem Gaus-Algorithmus existieren viele weitere Lösungsalgorithmen, einschließlich numerische Verfahren. Die Qualität der Lösung hängt dabei von dem gewählten Lösungsverfahren und dem vorliegenden Gleichungssystem ab. + Neben dem Gaus-Algorithmus existieren viele weitere L"osungsalgorithmen, einschließlich numerische Verfahren. Die Qualit"at der L"osung h"angt dabei von dem gew"ahlten L"osungsverfahren und dem vorliegenden Gleichungssystem ab. \subsubsection{Lineares Gleichungssystem einer Kreuzung}\label{sec:berechnung:lgs:xr} - Die Beziehungen zwischen Induktionsschleifensensoren und Kreuzungsein- und Ausg"angen kann durch eine lineares Gleichungssystem ausgedr"uckt werden. Der Wert f"ur den Ausgang errechnet sich aus der Summe aller, diesem Kreuzungseingang zugeordneten, Sensoren. Ein Kreuzungsausgang errechnet sich aus den Werten derjenigen Sensoren, wessen Spur dem Verkehr erlauben diesen Kreuzungsausgang zu bedienen. Dabei muss zwischen Einspursensoren und Mischspursensoren unterschieden werden. Einspursensoren k"onnen direkt auf den Ausgang addiert werden, w"ahrend f"ur Mischspursensoren eine Abbiegewahrscheinlichkeit ben"otigt wird, die angibt, wie viel Verkehr in die entsprechende Richtung fließt. Durch Multiplikation des Sensorwertes mit der Abbiegewahrscheinlichkeit erh"alt man den gesuchten Teil des Verkehrs und kann diesen auf den Ausgang addieren. Für den Kreuzungseingang werden keine Abbiegewahrscheinlichkeiten benötigt und können direkt, unerheblich ob nun Misch- oder Einzelspursensor, auf den Eingang addiert werden.\\ \\ + Die Beziehungen zwischen Induktionsschleifensensoren und Kreuzungsein- und Ausg"angen kann durch eine lineares Gleichungssystem ausgedr"uckt werden. Der Wert f"ur den Ausgang errechnet sich aus der Summe aller, diesem Kreuzungseingang zugeordneten, Sensoren. Ein Kreuzungsausgang errechnet sich aus den Werten derjenigen Sensoren, wessen Spur dem Verkehr erlauben diesen Kreuzungsausgang zu bedienen. Dabei muss zwischen Einspursensoren und Mischspursensoren unterschieden werden. Einspursensoren k"onnen direkt auf den Ausgang addiert werden, w"ahrend f"ur Mischspursensoren eine Abbiegewahrscheinlichkeit ben"otigt wird, die angibt, wie viel Verkehr in die entsprechende Richtung fließt. Durch Multiplikation des Sensorwertes mit der Abbiegewahrscheinlichkeit erh"alt man den gesuchten Teil des Verkehrs und kann diesen auf den Ausgang addieren. F"ur den Kreuzungseingang werden keine Abbiegewahrscheinlichkeiten ben"otigt und k"onnen direkt, unerheblich ob nun Misch- oder Einzelspursensor, auf den Eingang addiert werden.\\ \\ Allgemein kann der Wert des Kreuzungsein- und Ausgang durch folgende Gleichung ausgedr"uckt werden: \begin{equation} Kreuzungausgang_x = \sum ES_{xi} + \sum MS_{xj}*ABW_{xj} @@ -85,7 +85,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst $ABW_xi$ bezeichnet die Abbiegewahrscheinlichkeit des Mehrspursensors $MS_{xi}$ in Richtung Kreuzung x.\\ $S_x$ bezeichnet alle Sensoren welche direkt nach einem Kreuzungseingang in der Straße verbaut sind und entsprechend eine Verbindung, gegen die Fließrichtung, zu dem Kreuzungseingang x hat.\\ Die Berechnung erfolgt dabei f"ur alle Aus- bzw. Eing"ange mithilfe eines linearen Gleichungssystems, um unbekannte Werte, mithilfe der Abh"angigkeiten der Gleichungen untereinander, zu ermitteln.\\ - Eine allgemeine Form des Gleichungssystem für Ein- bzw. Ausgänge ist in [] beschrieben. + Eine allgemeine Form des Gleichungssystem f"ur Ein- bzw. Ausg"ange ist in [] beschrieben. \begin{equation} \begin{Bmatrix} & S_1 & S_2 & S_3 & \dots & S_n\\ @@ -134,7 +134,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst Out_m\\ \end{Bmatrix} \end{equation} - Zur Erläuterung wird nochmals die A23\ref{abb:a23} betrachtet. Die in Kapitel \autoref{sec:modell} entwickelte Matrixdarstellung erweist sich als hilfreich und kann durch dekorieren mit Abbiegewahrscheinlichkeiten zur Berechnung einer L"osung benutzt werden. Hierf"ur werden Verbindungen zwischen Einspursensoren und dem Aus- bzw. Eingang nach wie vor mit einer '1' markiert, da alle verkehr der "uber diesen Sensor fließt genau einem Ausgang zugeordnet werden kann, kann 100\% des Wertes auf den entsprechenden Ausgang übertragen werden. F"ur Mischspursensoren dagegen werden die Verbindungen durch eine Fließkommazahl ersetzt, welche die jeweilige Abbiegewahrscheinlichkeit repr"asentiert. Durch Multiplikation der Matrix mit den Sensorwerten, kann ein Ergebnis f"ur die Ein- und Ausg"ange berechnet werden, sofern aller, in die Kreuzung einstr"omender, Verkehr von Sensoren erfasst wird. + Zur Erl"auterung wird nochmals die A23\ref{abb:a23} betrachtet. Die in Kapitel \autoref{sec:modell} entwickelte Matrixdarstellung erweist sich als hilfreich und kann durch dekorieren mit Abbiegewahrscheinlichkeiten zur Berechnung einer L"osung benutzt werden. Hierf"ur werden Verbindungen zwischen Einspursensoren und dem Aus- bzw. Eingang nach wie vor mit einer '1' markiert, da alle verkehr der "uber diesen Sensor fließt genau einem Ausgang zugeordnet werden kann, kann 100\% des Wertes auf den entsprechenden Ausgang "ubertragen werden. F"ur Mischspursensoren dagegen werden die Verbindungen durch eine Fließkommazahl ersetzt, welche die jeweilige Abbiegewahrscheinlichkeit repr"asentiert. Durch Multiplikation der Matrix mit den Sensorwerten, kann ein Ergebnis f"ur die Ein- und Ausg"ange berechnet werden, sofern aller, in die Kreuzung einstr"omender, Verkehr von Sensoren erfasst wird. \begin{equation} \begin{Bmatrix} & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10\\ @@ -196,7 +196,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst \end{equation} F"ur die Kreuzung A23 ist es nicht n"otig ein Gleichungssystem zu l"osen, da alle ben"otigten Werte bekannt sind. Dies ist darauf zur"uckzuf"uhren, dass alle Sensorwerte f"ur diese Kreuzung bekannt sind und alle eingehenden Spuren mit Sensoren best"uckt sind. Desweiteren stehen f"ur alle Mischspursensoren Abbiegewahrscheinlichkeiten der Stadt Darmstadt zur Verf"ugung.\\ Im folgenden wird diskutiert in wiefern das Gleichungssystem mit unbekannten Eingangsspuren bzw. unbekannten Abbiegewahrscheinlichkeiten gel"ost werden kann.\\ \\ - Durch hinzufügen es virtuellen Sensors für einen weiteren Kreuzungseingang wird das Gleichungssystem zu einem eben solchen, da nun unbekannte in der Gleichung auftauchen. Dies führt unmittelbar zur Unlösbarkeit des Systems, da Rang[]. Am Beispiel der A23 sei das demonstriert. Hierfür wird der Sensor D10 zu einer virtuellen Sensor, welcher keine Werte liefert. + Durch hinzuf"ugen es virtuellen Sensors f"ur einen weiteren Kreuzungseingang wird das Gleichungssystem zu einem eben solchen, da nun unbekannte in der Gleichung auftauchen. Dies f"uhrt unmittelbar zur Unl"osbarkeit des Systems, da Rang[]. Am Beispiel der A23 sei das demonstriert. Hierf"ur wird der Sensor D10 zu einer virtuellen Sensor, welcher keine Werte liefert. \begin{equation} \begin{Bmatrix} & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & V10 &\\ @@ -226,15 +226,15 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst A104 & A104\\ \end{Bmatrix} \end{equation} - Dieses System ist nicht lösbar, da zu viele Unbekannte in der Gleichung auftauchen. Dies liegt insbesondere an fehlenden Ausgangswerten. Diese können allerdings nicht bestimmt werden.[zeitproblem] + Dieses System ist nicht l"osbar, da zu viele Unbekannte in der Gleichung auftauchen. Dies liegt insbesondere an fehlenden Ausgangswerten. Diese k"onnen allerdings nicht bestimmt werden.[zeitproblem] - Durch Zusätzliche Gleichungen können die Werte weiter eingeschränkt werden. Dies führt allerdings nicht zur Lösbarkeit des Systems. + Durch Zus"atzliche Gleichungen k"onnen die Werte weiter eingeschr"ankt werden. Dies f"uhrt allerdings nicht zur L"osbarkeit des Systems. \begin{enumerate} \item{Abbw addiert = 1} \item{Vallidierungssensoren} \end{enumerate} - Eine weitere Anwendung ist die Berechnung der Abbiegewahrscheinlichkeiten. Unter der Annahme, dass alle Werte der Sensoren bekannt sind, allerdings für einen Mischspursensor die Abbiegewahrscheinlichkeiten nicht bekannt sind. Allerdings ist auch dieses System nicht lösbar, da Ausgangswerte fehlen. + Eine weitere Anwendung ist die Berechnung der Abbiegewahrscheinlichkeiten. Unter der Annahme, dass alle Werte der Sensoren bekannt sind, allerdings f"ur einen Mischspursensor die Abbiegewahrscheinlichkeiten nicht bekannt sind. Allerdings ist auch dieses System nicht l"osbar, da Ausgangswerte fehlen. \subsection{Kreuzungsberechnung am Graphen}\label{sec:berechnung:graph} Da alle modellierten Kreuzungen der 'Ministadt' alle eingehenden Spuren mit Sensoren versehen haben, k"onnen die Gleichungen f"ur die jeweiligen Ausg"ange unabh"angig voneinander gel"ost werden. Dies erlaubt es die Ausg"ange bzw. Eing"ange mithilfe des Graphen zu berechnen.Das entwickelte Verfahren amcht sich zunutze, dass alle Eing"ange mit den Ausg"angen einer Kreuzung "uber genau einen bekannten Sensor miteinander verbunden sind.\\ \\ diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex index c10de504..97a6ce70 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex @@ -1,12 +1,12 @@ \section{Datenbasis und Grundlagen}\label{sec:datengrund} In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung beschrieben, sowie die Verkehrsdaten welchen f"ur diese Arbeit zur Verf"ugung standen und wie diese aufbereitet wurden. Die Aufbereitung der Daten dient der Modellierung des Verkehrssystems welches im Kapitel \autoref{sec:modell} n"aher beschrieben wird. \subsection {Induktionsschleifen}\label{sec:datengrund:induct} - Eine Induktionsschleife ist ein, in die Fahrbahndecke integrierter, Sensor welcher dem Messen des Verkehr dient. Er macht sich das Prinzip der elektromagnetischen Induktion zur Nutze, um metallische Objekte zu detektieren. Hierf"ur werden Kabelschleifen in die Fahrbahndecke eingelassen, parallel zu einem Kondensator geschaltet und mit einem Oszillator verbunden. Die Konstruktion aus Kondensator und Spule, der Induktionsschleife, wird Schwingkreis genannt. Durch Anlegen eines konstanten Gleichstroms erzeugen die Kabelschleifen ein Magnetfeld auf der Stra"se, welches sich ver"andert, wenn ein Auto darauf steht oder dar"uber f"ahrt. Diese Änderung ist an einer geänderten Resonanzfrequenz mithilfe des Oszillators messbar. Die Resonanzfrequenz berechnet sich dabei aus der Induktivität der Induktionsschleife und der Kapazität des Kondensators nach folgender Formel: + Eine Induktionsschleife ist ein, in die Fahrbahndecke integrierter, Sensor welcher dem Messen des Verkehr dient. Er macht sich das Prinzip der elektromagnetischen Induktion zur Nutze, um metallische Objekte zu detektieren. Hierf"ur werden Kabelschleifen in die Fahrbahndecke eingelassen, parallel zu einem Kondensator geschaltet und mit einem Oszillator verbunden. Die Konstruktion aus Kondensator und Spule, der Induktionsschleife, wird Schwingkreis genannt. Durch Anlegen eines konstanten Gleichstroms erzeugen die Kabelschleifen ein Magnetfeld auf der Stra"se, welches sich ver"andert, wenn ein Auto darauf steht oder dar"uber f"ahrt. Diese "Anderung ist an einer ge"anderten Resonanzfrequenz mithilfe des Oszillators messbar. Die Resonanzfrequenz berechnet sich dabei aus der Induktivit"at der Induktionsschleife und der Kapazit"at des Kondensators nach folgender Formel: \begin{equation} f_0 = \frac1{2 \pi \sqrt{L C}} \end{equation} - $L$ bezeichnet die Induktivität der Induktionsschleife, $C$ die Kapazität des Kondensators. - Die Elektronik der Induktionsschleife werte die gemessene Resonanzfrequenz aus und übermittelt aufbereitete Werte, welche von einer adaptiven Ampel benutzt werden kann, um den Verkehr zu steuern. So können Werte für die Anzahl der Autos, welche den Sensor passiert haben bestimmt werden, sowie die Belegungszeit des Sensors. In Abbildung \ref{abb:2} ist eine in die Fahrbahndecke verbaute Kabelschleife zu sehen, in Abbildung \ref{abb:3} ist der schematische Aufbau einer Induktionsschleife beschrieben.\\ \\ + $L$ bezeichnet die Induktivit"at der Induktionsschleife, $C$ die Kapazit"at des Kondensators. + Die Elektronik der Induktionsschleife werte die gemessene Resonanzfrequenz aus und "ubermittelt aufbereitete Werte, welche von einer adaptiven Ampel benutzt werden kann, um den Verkehr zu steuern. So k"onnen Werte f"ur die Anzahl der Autos, welche den Sensor passiert haben bestimmt werden, sowie die Belegungszeit des Sensors. In Abbildung \ref{abb:2} ist eine in die Fahrbahndecke verbaute Kabelschleife zu sehen, in Abbildung \ref{abb:3} ist der schematische Aufbau einer Induktionsschleife beschrieben.\\ \\ \begin{figure} \centering \subfigure[Induktionsschleife mit Kabel nach Abfr"asen der Fahrbahn. Quelle: wikipedia.org]{\includegraphics[width=0.3\textwidth-2\fboxsep-2\fboxrule]{pic/800px-Induktionsschleife}} @@ -14,15 +14,15 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \subfigure[Schematischer Aubau einer Induktionsschleife \cite{thesis:mazur}.]{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{pic/induktionsschleife-schema}} \label{abb:3} \end{figure} - Wie bei jedem Sensor sind die Messungen unter Vorbehalt des Fehlers zu betrachten. In der Arbeit von \cite{thesis:lehnhoff} wurden die Induktionsschleifen des Stadtgebiets von Hannover untersucht und festgestellt, das es sehr starke Unterschiede der Messgenauigkeit unter den Sensoren gibt, so wird festgestellt, dass bei nur einem drittel der Sensoren eine Messgenauigkeit von 90\% erreicht wird während ein gleichgroßer andere Teil eine Genauigkeit von unter 40\% aufweist. Messfehler werden dabei laut dem Merkblatt zu Detektoren für den Straßenverkehr\cite{merk:street} zwischen vier Fehlertypen unterschieden: + Wie bei jedem Sensor sind die Messungen unter Vorbehalt des Fehlers zu betrachten. In der Arbeit von \cite{thesis:lehnhoff} wurden die Induktionsschleifen des Stadtgebiets von Hannover untersucht und festgestellt, das es sehr starke Unterschiede der Messgenauigkeit unter den Sensoren gibt, so wird festgestellt, dass bei nur einem drittel der Sensoren eine Messgenauigkeit von 90\% erreicht wird w"ahrend ein gleichgroßer andere Teil eine Genauigkeit von unter 40\% aufweist. Messfehler werden dabei laut dem Merkblatt zu Detektoren f"ur den Straßenverkehr\cite{merk:street} zwischen vier Fehlertypen unterschieden: \begin{enumerate} \item{Zeitlich bedinge Messfehler} - \item{Räumliche Messfehler} + \item{R"aumliche Messfehler} \item{Lage- und formbedingte Messfehler} \item{Umfeldbedingte Messfehler} \end{enumerate} - Zeitliche Fehler wirken sich dabei auf die Belegzeitmessung aus. Da diese nicht innerhalb dieser Arbeit betrachtet wird, hat dieser Fehlertyp keine Auswirkungen auf die verwendeten Daten. Räumlich Messfehler beziehen sich ebenfalls auf die Belegzeitmessung und können zu Problemen mit der Bestimmung des Fahrzeugtypes führen, da für gleich lange Fahrzeuge verschiedene Belegzeiten gemessen werden können. Lage- und formbedingte Fehler wirken sich auf den, in dieser Arbeit benutzten, Autozählwert aus. Diese treten auf, wenn ein Fahrzeug der, mit einem Sensor bestückten, Nachbarspur zu nahe kommt und fälschlicher weise ein Auto für diese gezählt wird. Umfeldbedingte Fehler sind am schwersten festzustellen. Es handelt sich dabei um Fehler, die durch magnetische Störquellen in der Umgebung oder schlechte Isolation der Induktionsschleife auftreten.\\ - Über die Fehlerh"aufigkeit liegen keine Daten der Stadt Darmstadt vor. Die G"ultigkeit der Induktionsschleifenwerte wird in dem Kapitel \autoref{sec:validierung} genauer behandelt.\\ \\ + Zeitliche Fehler wirken sich dabei auf die Belegzeitmessung aus. Da diese nicht innerhalb dieser Arbeit betrachtet wird, hat dieser Fehlertyp keine Auswirkungen auf die verwendeten Daten. R"aumlich Messfehler beziehen sich ebenfalls auf die Belegzeitmessung und k"onnen zu Problemen mit der Bestimmung des Fahrzeugtypes f"uhren, da f"ur gleich lange Fahrzeuge verschiedene Belegzeiten gemessen werden k"onnen. Lage- und formbedingte Fehler wirken sich auf den, in dieser Arbeit benutzten, Autoz"ahlwert aus. Diese treten auf, wenn ein Fahrzeug der, mit einem Sensor best"uckten, Nachbarspur zu nahe kommt und f"alschlicher weise ein Auto f"ur diese gez"ahlt wird. Umfeldbedingte Fehler sind am schwersten festzustellen. Es handelt sich dabei um Fehler, die durch magnetische St"orquellen in der Umgebung oder schlechte Isolation der Induktionsschleife auftreten.\\ + "Uber die Fehlerh"aufigkeit liegen keine Daten der Stadt Darmstadt vor. Die G"ultigkeit der Induktionsschleifenwerte wird in dem Kapitel \autoref{sec:validierung} genauer behandelt.\\ \\ Induktionsschleifen m"ussen zus"atzlich in zwei Sensortypen unterschieden werden, da sie eine unterschiedliche Behandlungsweise erfordern. Dabei gibt es keinen Unterschied zwischen der verbauten Sensorelektronik oder -Installation. Der Sensortyp bestimmt sich aus der Fahrspur auf der er in die Stra"sendecke eingelassen ist: \begin{enumerate} \item{Einspursensor: Ein Auto auf dieser Spur kann die Kreuzung nur in eine Richtung verlassen.} @@ -31,9 +31,9 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be Diese Unterscheidung ist wichtig, da Mischspursensoren neben den Induktionsschleifenwerte noch sog. Abbiegewahrscheinlichkeiten ben"otigen, um Kreuzungszusammenh"ange zu berechnen. Die Verwendung der Abbiegewahrscheinlichkeiten ist im Kapitel \autoref{sec:berechnung} beschrieben. \subsection{Adaptive Steuerung von Ampelanlagen}\label{sec:datengrund:adapt} Mit der Zunahme des motorisierten Verkehrs erhielten Anfang des 20. Jahrhunderts sog. Verkehrspolizisten die Aufgabe den Verkehr an Kreuzungen zu regeln. 1924 wurde Potzdamer Platz die erste Ampel errichtet, um die Personalkosten zu reduzieren. In den folgenden Jahren wurde die Ampeltechnik weiter verbessert, an der manuellen Steuerung durch Verkehrspolizisten wurde allerdings festgehalten.\\ - Die erste verkehrsabhängige Steuerung wurde 1928 von Charles Adler jr. entwickelt und in Baltimore,Maryland das erste mal eingesetzt\cite{paper:adaptiv}[direct cite]. Bevor allerdings diese Technik Einzug in den alltäglichen Kreuzungsverkehr fand vergingen allerdings noch etwa 40 Jahre. Die meisten der eingesetzten verkehrsbahängigen Ampelsteuerungen setzen sog. Ablauflogiken ein, die es erlauben zu prüfen, ob eine zeitliche oder logische Bedingung der Kreuzung verletzt ist. Im Rahmen dieser Bedingungen kann die Umlaufzeit, Versatzzeit, Phasenfolge und/oder die Freigabezeit dynamisch dem Verkehr angepasst werden. Um den Bedarf an Freigabezeit zu berechnen kommen die oben beschriebenen Induktionsschleifen zum Einsatz um den Verkehr zu messen. Wird ein Auto auf einem Sensor erkannt, so kann die Ampelphase verl"angert oder die entsprechende Verkehrsrichtung freigeschaltet werden. Diese verkehrsabh"angige Steuerung von Lichtanlagen wird 'adaptive Steuerung' genannt. Der Begriff leitet sich dabei aus der Tatsache her, dass sich die Ampelsteuerung dem Verkehrsaufkommen anpasst.\\ \\ - Durch eine solche Ampelsteuerung verk"urzt sich die Haltezeiten von Autos und sorgt f"ur einen fl"ussigeren Verkehr, im Vergleich zu einer statischen Ampelschaltung. Dies begr"undet sich darin, dass die Ampelschaltung eine Spur nur freischaltet, wenn diese von einem Fahrzeug, detektiert über den Sensor in der Straße, benötigt wird. Es besteht außerdem die M"oglichkeit die Ampelphase so lange zu verl"angern, bis eine L"ucke in der Fahrzeugkolonne erkannt wird um ein Zug von Autos über die Kreuzung zu lassen. Werden die Induktionsschleifen an den Haltelinien einer Kreuzung verbaut, k"onnen sie au"serdem verwendet werden um Rotlichtverst"o"se automatisch erkannt werden.\\ \\ - Die Steuerung der Ampelanlagen ist ein Teil der Verkehrsmanagement\autoref{abb:verkehrsmanagement} und ist für viele andere Bereiche der Verkehrstechnik von großem Interesse, da die Ampeln Sensordaten liefern, die vielfältig verwendet werden können. Ein Beispiel der Verwendung ist diese Arbeit, die aus den erfassten Induktionsschleifenwerten Verkehrsflüsse berechnet. + Die erste verkehrsabh"angige Steuerung wurde 1928 von Charles Adler jr. entwickelt und in Baltimore,Maryland das erste mal eingesetzt\cite{paper:adaptiv}[direct cite]. Bevor allerdings diese Technik Einzug in den allt"aglichen Kreuzungsverkehr fand vergingen allerdings noch etwa 40 Jahre. Die meisten der eingesetzten verkehrsbah"angigen Ampelsteuerungen setzen sog. Ablauflogiken ein, die es erlauben zu pr"ufen, ob eine zeitliche oder logische Bedingung der Kreuzung verletzt ist. Im Rahmen dieser Bedingungen kann die Umlaufzeit, Versatzzeit, Phasenfolge und/oder die Freigabezeit dynamisch dem Verkehr angepasst werden. Um den Bedarf an Freigabezeit zu berechnen kommen die oben beschriebenen Induktionsschleifen zum Einsatz um den Verkehr zu messen. Wird ein Auto auf einem Sensor erkannt, so kann die Ampelphase verl"angert oder die entsprechende Verkehrsrichtung freigeschaltet werden. Diese verkehrsabh"angige Steuerung von Lichtanlagen wird 'adaptive Steuerung' genannt. Der Begriff leitet sich dabei aus der Tatsache her, dass sich die Ampelsteuerung dem Verkehrsaufkommen anpasst.\\ \\ + Durch eine solche Ampelsteuerung verk"urzt sich die Haltezeiten von Autos und sorgt f"ur einen fl"ussigeren Verkehr, im Vergleich zu einer statischen Ampelschaltung. Dies begr"undet sich darin, dass die Ampelschaltung eine Spur nur freischaltet, wenn diese von einem Fahrzeug, detektiert "uber den Sensor in der Straße, ben"otigt wird. Es besteht außerdem die M"oglichkeit die Ampelphase so lange zu verl"angern, bis eine L"ucke in der Fahrzeugkolonne erkannt wird um ein Zug von Autos "uber die Kreuzung zu lassen. Werden die Induktionsschleifen an den Haltelinien einer Kreuzung verbaut, k"onnen sie au"serdem verwendet werden um Rotlichtverst"o"se automatisch erkannt werden.\\ \\ + Die Steuerung der Ampelanlagen ist ein Teil der Verkehrsmanagement\autoref{abb:verkehrsmanagement} und ist f"ur viele andere Bereiche der Verkehrstechnik von großem Interesse, da die Ampeln Sensordaten liefern, die vielf"altig verwendet werden k"onnen. Ein Beispiel der Verwendung ist diese Arbeit, die aus den erfassten Induktionsschleifenwerten Verkehrsfl"usse berechnet. \begin{figure} \label{abb:verkehrsmanagement} \centering \includegraphics[width=0.5\textwidth]{pic/verkehrsmanagement} @@ -42,22 +42,22 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \subsection{Macro- und microskopische Modellierung von Verkehr}\label{sec:macromicro} In der Verkehrstechnik wird zwischen verschiedenen Arten der Verkehrsmodellierung unterschieden. Dabei kann ein Modell nach seinem Verwendungszweck klassifiziert werden. Es wird zwischen vier verschiedenen Arten des Verwendungszwecks unterschieden\cite{lect:simumod}: \begin{enumerate} - \item{Erklärungsmodell: dient dazu reale Phänomen oder deren Entstehung zu erklären.} + \item{Erkl"arungsmodell: dient dazu reale Ph"anomen oder deren Entstehung zu erkl"aren.} \item{Prognosemodelle: dient der Vorhersage verschiedenster Verkehrsparameter.} - \item{Gestaltungsmodelle: dient der Voraussage von Veränderungen des Verkehrsverhaltens bei (infrastruckturellen) Maßnahmen.} + \item{Gestaltungsmodelle: dient der Voraussage von Ver"anderungen des Verkehrsverhaltens bei (infrastruckturellen) Maßnahmen.} \item{Optimierungsmodelle: dient der Optimierung von Verkehr.} \end{enumerate} - Desweiteren wird zwischen den Genauigkeitsstufen des Modells unterschieden. Dies trifft insbesondere auf Flussmodelle zu, da diese auf verschiedenen Ebenen modelliert werden können. Es wird zwischen vier Genauigkeitsstufen unterschieden\cite{lect:simumod}: + Desweiteren wird zwischen den Genauigkeitsstufen des Modells unterschieden. Dies trifft insbesondere auf Flussmodelle zu, da diese auf verschiedenen Ebenen modelliert werden k"onnen. Es wird zwischen vier Genauigkeitsstufen unterschieden\cite{lect:simumod}: \begin{itemize} \item{makroskopisch: Modellierung auf Basis von Fahrzeugkollektiven} \item{mesoskopisch: Modelliert auf Basis von Fahrzeugkollektiven, betrachtet allerdings auch einzelne Fahrzeuge} \item{microskopisch: Modelliert auf Basis von einzelnen Fahrzeugen} \item{submicroskopisch: } \end{itemize} - Macroskopische Modelle zeichnen sich dabei besonders durch Simplizität und hohe Recheneffizienz aus. Allerdings ist die Auflösung eines macroskopischen Modells gering. Ein microskopisches Modell betrachtet dagegen einzelne Fahrzeuge. Während das Macroskopische Modell Größen wie die Durchschnittsgeschwindigkeit oder die Verkehrsdichte betrachtet, werden in microskopischen Modellen Größen wie die Individualgeschwindigkeit eines Fahrzeugs oder dessen Reaktion auf andere Fahrzeuge untersucht. Ein mesoskopisches Modell ist dabei eine Mischung aus beiden Ansätzen. Ein submicroskopisches Modell untersucht noch kleinere Einheiten wie z.B. den Zusammenhang zwischen Fahrer und Fahrzeug oder Fahrer und Fahrassistenten.\\ \\ - Der in dieser Arbeit betrachtete Ansatz ist der macroskopischen Modellierung zuzuordnen. Dies begründet sich an den vorliegenden Messdaten, welche einen Rückschluss auf die einzelne Autos nicht zulässt. Die zur Verfügung stehenden Daten werden auf den folgenden Seiten beschrieben. + Macroskopische Modelle zeichnen sich dabei besonders durch Simplizit"at und hohe Recheneffizienz aus. Allerdings ist die Aufl"osung eines macroskopischen Modells gering. Ein microskopisches Modell betrachtet dagegen einzelne Fahrzeuge. W"ahrend das Macroskopische Modell Gr"oßen wie die Durchschnittsgeschwindigkeit oder die Verkehrsdichte betrachtet, werden in microskopischen Modellen Gr"oßen wie die Individualgeschwindigkeit eines Fahrzeugs oder dessen Reaktion auf andere Fahrzeuge untersucht. Ein mesoskopisches Modell ist dabei eine Mischung aus beiden Ans"atzen. Ein submicroskopisches Modell untersucht noch kleinere Einheiten wie z.B. den Zusammenhang zwischen Fahrer und Fahrzeug oder Fahrer und Fahrassistenten.\\ \\ + Der in dieser Arbeit betrachtete Ansatz ist der macroskopischen Modellierung zuzuordnen. Dies begr"undet sich an den vorliegenden Messdaten, welche einen R"uckschluss auf die einzelne Autos nicht zul"asst. Die zur Verf"ugung stehenden Daten werden auf den folgenden Seiten beschrieben. \subsection{Induktionsschleifenwerte}\label{sec:inductvalues} - F"ur die Untersuchungen dieser Arbeit stellte die Stadt Darmstadt\footnote{\url{http://www.darmstadt.de/}} die Werte der in der Stadt verbauten Induktionsschleifen zur Verfügung. Die Daten werden 'live' gemessen, und f"ur die adaptive Ampelsteuerung eingesetzt. F"ur diese Arbeit standen allerdings nur Daten zur Verf"ugung, welche "uber einen Zeitraum von einer Minute gemessen wurden. Die Induktionsschleifen liefern die Werte 'count' und 'load' welche Auskunft "uber die Anzahl der Autos gibt, welche den Sensor innerhalb des Messintervalls von einer Minute passiert haben und wie lange dieser Sensor innerhalb des Intervalls belegt war. Die Induktionsschleifen sind dabei fast ausschlie"slich an den Kreuzungseing"angen in den Stra"sen verbaut. Daten werden "uber ein fest definiertes Intervall von einer Minute erhoben.\\ \\ + F"ur die Untersuchungen dieser Arbeit stellte die Stadt Darmstadt\footnote{\url{http://www.darmstadt.de/}} die Werte der in der Stadt verbauten Induktionsschleifen zur Verf"ugung. Die Daten werden 'live' gemessen, und f"ur die adaptive Ampelsteuerung eingesetzt. F"ur diese Arbeit standen allerdings nur Daten zur Verf"ugung, welche "uber einen Zeitraum von einer Minute gemessen wurden. Die Induktionsschleifen liefern die Werte 'count' und 'load' welche Auskunft "uber die Anzahl der Autos gibt, welche den Sensor innerhalb des Messintervalls von einer Minute passiert haben und wie lange dieser Sensor innerhalb des Intervalls belegt war. Die Induktionsschleifen sind dabei fast ausschlie"slich an den Kreuzungseing"angen in den Stra"sen verbaut. Daten werden "uber ein fest definiertes Intervall von einer Minute erhoben.\\ \\ Der 'load'-Wert gibt dabei an, wie viel Prozent des Messintervalls der Sensor als belegt erkannt wurde. Es handelt sich folglich um einen Floatingpoint-Wert zwischen 0 und 1. Der 'count'-Wert repr"asentiert die Anzahl der Autos, welche den Sensor innerhalb des Messintervalls passiert haben. Es handelt sich folglich um eine ganze nat"urlich Zahl, einschlie"slich der Null.\\ \\ W"urde ein Sensor einen 'load' von 0.3 und einen 'count' von 5 melden, bedeutet das, dass dieser Sensor 30 Prozent einer Minute (18 Sekunden) belegt war und 5 Autos ihn passiert haben.\\ \\ Die Daten werden von der Stadt Darmstadt als CSV-Dateien zur Verf"ugung gestellt und wurden im Rahmen der Arbeit \cite{thesis:mueller} "offentlich gemacht\footnote{Die Induktionsschleifenwerte sind und \url{http://www.da-sense.de/trafficdata/} zu finden}. @@ -92,20 +92,20 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \caption{CSV-Datei Ausschnitt von[] } \end{figure} Sensorspalten, welche auf Z enden, bezeichnen den 'count'-Wert des jeweiligen Sensors, solche die auf B enden den 'load'-Wert. Jede Zeile in der CSV-Datei repr"asentiert dabei eine Kreuzung zu dem gegebenen Zeitpunkt. F"ur eine Kreuzung k"onnen dabei bis zu 64 Sensoren in der CSV bereitgestellt werden. - Um die Zuordnung von CSV-Spalte zu dem ta"achlichen Sensornamen der CAD-Zeichnungen[gls:cad] herzustellen, werden sog. "Ubersetzungstabellen ben"otigt. Diese ordnen einer CSV-Sensorspalte (1-64) einen kreuzungsspezifischen Sensornamen zu. In der Praxis wird eine solche "Ubersetzungstabelle durch einen Offset auf der CSV-Datei im Computer nachgebildet. Für die in diese Arbeit modellierten Kreuzungen sind Übersetzungstabellen sowie die CAD-Zeichnung im Anhang zu finden\autoref{abb}. + Um die Zuordnung von CSV-Spalte zu dem ta"achlichen Sensornamen der CAD-Zeichnungen[gls:cad] herzustellen, werden sog. "Ubersetzungstabellen ben"otigt. Diese ordnen einer CSV-Sensorspalte (1-64) einen kreuzungsspezifischen Sensornamen zu. In der Praxis wird eine solche "Ubersetzungstabelle durch einen Offset auf der CSV-Datei im Computer nachgebildet. F"ur die in diese Arbeit modellierten Kreuzungen sind "Ubersetzungstabellen sowie die CAD-Zeichnung im Anhang zu finden\autoref{abb}. \subsubsection{MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}\label{sec:datengrund:inductvalues:mysql} - Im Rahmen der Arbeit von \cite{thesis:mueller}, wurde eine JEE6\footnote{todo} Anwendung entwickelt, welche die aufbereiteten Verkehrsdaten der Stadt Darmstadt bereit stellt. Hierfür wurden die CSV-Dateien geparsed und in eine MYSQL-Datenbank überführt. Die dort gesammelten Sensordaten wurden bereits mit Geoinformation des OpenStreetMap Projektes verknüpft und erlauben eine Positionierung von Kreuzungs- und Sensorknoten mithilfe der bereitgestellten Latidue und Longitude Werte. + Im Rahmen der Arbeit von \cite{thesis:mueller}, wurde eine JEE6\footnote{todo} Anwendung entwickelt, welche die aufbereiteten Verkehrsdaten der Stadt Darmstadt bereit stellt. Hierf"ur wurden die CSV-Dateien geparsed und in eine MYSQL-Datenbank "uberf"uhrt. Die dort gesammelten Sensordaten wurden bereits mit Geoinformation des OpenStreetMap Projektes verkn"upft und erlauben eine Positionierung von Kreuzungs- und Sensorknoten mithilfe der bereitgestellten Latidue und Longitude Werte. [ER Diagramm] - Aus dieser Datenbank wurden alle Sensorwerte und Positionsangaben, welche im Rahmen dieser Arbeit benötigten wurden, entnommen. Die gesuchten Daten sind dabei auf drei Tabellen verteilt: + Aus dieser Datenbank wurden alle Sensorwerte und Positionsangaben, welche im Rahmen dieser Arbeit ben"otigten wurden, entnommen. Die gesuchten Daten sind dabei auf drei Tabellen verteilt: \begin{enumerate} \item{jee\_crmodel\_CrossroadDim: In dieser Tabelle werden Kreuzungsname und -Position abgespeichert.} \item{jee\_crmodel\_SensorDim: In dieser Tabelle werden Sensorname und -Position, sowie die Kreuzung auf der der Sensor verbaut ist, gespeichert. Ein CSV-Offset identifiziert den Sensor bez"uglich seiner Position in der CSV-Datei.} \item{jee\_trafficlight\_rawevents: In dieser Tabelle werden die eingelesenen CSV-Dateien der Stadt gespeichert. Dies umfasst neben den Werten 'load' und 'count' und Messdatum, die zugeh"orige Kreuzung. Ein Sensor kann anhand des gespeicherten CSV-Offsets mit jee\_crmodel\_SensorDim identifiziert und lokalisiert werden.} \end{enumerate} - Um die Daten für eigene Zwecke verwenden zu können, wurden die benötigten Teile extrahiert und in einem eigenen Datenbankschema abgespeichert. Mehr Informationen zu dem entwickelten Datenbankmodell sind im Kapitel \autoref{sec:berechnung} zu finden. Desweiteren wurden verschiedene SQL-Abfragen entwickelt, um die benötigten Informationen zu extrahieren. \\ \\ - Um die gespeicherte Sensorposition zu ermitteln wurde eine SQL-Abfrage\ref{lst:sql_sensorquery} entwickelt, welche Kreuzungs- und Sensornamen, sowie dessen jeweiligen Latitude und Longitude zur"uckgibt. Die Auswahl ist dabei auf die zehn untersuchten Kreuzungen beschr"ankt. Das Feld 'VALIDTO' in der Kreuzungstabelle bestimmt dabei, ob die Kreuzung noch in Betrieb/gültig ist. Sensornamen werden ebenfalls gefiltert, da ausschließlich Werte für Sensoren mit einem führenden 'D' vorliegen. + Um die Daten f"ur eigene Zwecke verwenden zu k"onnen, wurden die ben"otigten Teile extrahiert und in einem eigenen Datenbankschema abgespeichert. Mehr Informationen zu dem entwickelten Datenbankmodell sind im Kapitel \autoref{sec:berechnung} zu finden. Desweiteren wurden verschiedene SQL-Abfragen entwickelt, um die ben"otigten Informationen zu extrahieren. \\ \\ + Um die gespeicherte Sensorposition zu ermitteln wurde eine SQL-Abfrage\ref{lst:sql_sensorquery} entwickelt, welche Kreuzungs- und Sensornamen, sowie dessen jeweiligen Latitude und Longitude zur"uckgibt. Die Auswahl ist dabei auf die zehn untersuchten Kreuzungen beschr"ankt. Das Feld 'VALIDTO' in der Kreuzungstabelle bestimmt dabei, ob die Kreuzung noch in Betrieb/g"ultig ist. Sensornamen werden ebenfalls gefiltert, da ausschließlich Werte f"ur Sensoren mit einem f"uhrenden 'D' vorliegen. \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} \begin{lstlisting}[caption={[abc] Die Stra"senklasse ST}, label={lst:sql_sensorquery}, captionpos=bsec] SELECT CD.REALNAME AS CR_NAME, @@ -121,7 +121,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be AS sensors \end{lstlisting} \end{minipage} - Eine weitere Abfrage dient dem Ermitteln der Sensorwerte "uber einen bestimmten Zeitraum. Zu Identifizierung des Sensors wird der CSV-Offset benutzt. Die extrahierten Daten entsprechen dem Inhalt einer CSV-Datei der Stadt Darmstadt. Die Abfrage aus \autoref{lst:sql_sensorquery} wird dabei mit einer Abfrage auf der Tabelle 'jee\_trafficlight\_rawevents kombiniert. Auf diese Weise erhält man Sowohl die Sensor und Kreuzungsinformationen, als auch die Zählwerte der Induktionsschleifen. Ein Filter auf der Spalte DATETIME der Ampelrohevents erlaubt eine Auswahl des Zeitpunktes. Dabei ist zu beachten, dass die Zeitangaben in UTC-Zeitformat angegeben werden müssen. + Eine weitere Abfrage dient dem Ermitteln der Sensorwerte "uber einen bestimmten Zeitraum. Zu Identifizierung des Sensors wird der CSV-Offset benutzt. Die extrahierten Daten entsprechen dem Inhalt einer CSV-Datei der Stadt Darmstadt. Die Abfrage aus \autoref{lst:sql_sensorquery} wird dabei mit einer Abfrage auf der Tabelle 'jee\_trafficlight\_rawevents kombiniert. Auf diese Weise erh"alt man Sowohl die Sensor und Kreuzungsinformationen, als auch die Z"ahlwerte der Induktionsschleifen. Ein Filter auf der Spalte DATETIME der Ampelrohevents erlaubt eine Auswahl des Zeitpunktes. Dabei ist zu beachten, dass die Zeitangaben in UTC-Zeitformat angegeben werden m"ussen. \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} \begin{lstlisting}[caption={[abc] Die Stra"senklasse ST}, label={listing1}, captionpos=bsec] SELECT * FROM (SELECT CD.REALNAME AS CR_NAME, @@ -154,7 +154,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \item{Seitenstra"sen: Seitenstra"sen ohne Sensorik.} \item{Validierungssensoren: Sensoren, welche die Sensorwerte anderer Sensoren (teilweise) best"atigen.} \end{enumerate} - Die Einbahnstraße verläuft dabei von Kreuzung A29 nach A104. Sie verspricht eine einfachere Berechnung von Verkehrswerten, da eine Kreuzung mit einer Einbahnstraße nur drei Kreuzungsein- und -Ausgänge hat, im Gegensatz zu einer 'normalen' Kreuzung mit jeweils vier Ein- und Ausgängen. Mischspuren sind dagegen hinderlich für die Berechnung, da ihr gemessener Wert, im Gegensatz zu Einspursensoren, nicht direkt einem Ausgang zugeordnet werden kann. + Die Einbahnstraße verl"auft dabei von Kreuzung A29 nach A104. Sie verspricht eine einfachere Berechnung von Verkehrswerten, da eine Kreuzung mit einer Einbahnstraße nur drei Kreuzungsein- und -Ausg"ange hat, im Gegensatz zu einer 'normalen' Kreuzung mit jeweils vier Ein- und Ausg"angen. Mischspuren sind dagegen hinderlich f"ur die Berechnung, da ihr gemessener Wert, im Gegensatz zu Einspursensoren, nicht direkt einem Ausgang zugeordnet werden kann. \subsection{CAD-Zeichnungen der Kreuzungen}\label{sec:datengrund:cad} Es stehen au"serdem die CAD-Zeichnungen[gls:cad] der Kreuzungen von der Stadt Darmstadt zur Verf"ugung. Diese CADs wurden im Rahmen der Kooperation des Projekts \cite{thesis:mueller} und der Stadt Darmstadt der TU-Darmstadt zur Verf"ugung gestellt\footnote{Die CAD-Bilder sind unter \url{http://www.da-sense.de/trafficdata/information.php} zu erhalten}. Sie geben Aufschluss, an welcher Stelle ein Sensor in der Stra"sendecke verbaut ist und weist dessen kreuzungsinternen Namen aus, welcher zu Identifizierung des Sensors ben"otigt wird. Die CAD-Zeichnungen dienen der manuellen Modellierung des Stra"senmodells, sowie der Identifizierung der Sensoren sowie der Zuordnung ihrer Sensor-Klasse und -Typs. So sind in den CAD-Zeichnungen die Fahrspuren und deren erlaubte Flie"srichtung markiert. Aufgrund dessen konnte eine Zuordnung von Sensoren nach ihrer Klasse, Einspursensor oder Mischspursensor vorgenommen werden. @@ -162,8 +162,8 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \subsection{Abbiegewahrscheinlichkeiten}\label{sec:datengrund:abbw} Von der Stadt Darmstadt wurden neben den Sensorwerten, gemittelte Abbiegewahrscheinlichkeiten f"ur einige der Induktionsschleifen zur Verf"ugung gestellt, welche f"ur die Berechnung von Verkehrsfl"ussen bei Mischspursensoren ben"otigt werden. Die Abbiegewahrscheinlichkeiten eines Sensors beschreiben dabei wie viel Prozent des Verkehrs, welcher "uber den Sensor flie"st, zu den jeweiligen Ausgang der Kreuzung flie"sen darf. N"aheres ist im Kapitel \autoref{sec:berechnung} zu finden. Diese Daten wurden mithilfe von Video"uberwachung der zu untersuchenden Kreuzungen, f"ur die Planungsabteilung des Verkehrsamtes der Stadt ermittelt. Alle Werte sind dabei "uber alle Messungen eines Tages gemittelt und liegen in PDF-Format vor \ref{abb:5}\ref{abb:6}.\\ \\ \cite{thesis:michael} hat im Rahmen seiner Bachelorarbeit diese Daten in eine MYSQL-Datenbank "ubertragen. Desweiteren berechnet er genauere Abbiegewahrscheinlichkeiten f"ur die einzelnen Knoten, indem mithilfe einer Mittelung die Ausgangswerte einer Kreuzung in Beziehung zu einem Wert am benachbarten Kreuzungseingang gesetzt werden. Diese Daten lagen allerdings noch nicht vor und konnten aus diesem Grund im Rahmen dieser Arbeit nicht untersucht werden.\\ \\ - Die Abbiegewahrscheinlichkeiten der Stadt liegen in der Form (Kreuzung, Sensor, Links, Rechts, Geradeaus) vor. Die Werte für Links, Rechts und Geradeaus sind dabei in einer komplexen Form angegeben und müssen zur Verwendung auf eine Gleitkommazahl reduziert werden. Desweiteren gilt es die Richtung vom Sensor unabhängig zu machen, da die Angaben Links, Rechts und Geradeaus sich auf die Fahrtrichtung des Verkehrs über den Sensor beziehen.\\ \\ - Zu Reduzierung der Werte auf Gleitkommazahlen wurden die Daten manuell bearbeitet. Die CAD-Zeichnungen dienen dabei als Hilfe, um die kreuzungsspezifischen Angaben interpretieren zu können. + Die Abbiegewahrscheinlichkeiten der Stadt liegen in der Form (Kreuzung, Sensor, Links, Rechts, Geradeaus) vor. Die Werte f"ur Links, Rechts und Geradeaus sind dabei in einer komplexen Form angegeben und m"ussen zur Verwendung auf eine Gleitkommazahl reduziert werden. Desweiteren gilt es die Richtung vom Sensor unabh"angig zu machen, da die Angaben Links, Rechts und Geradeaus sich auf die Fahrtrichtung des Verkehrs "uber den Sensor beziehen.\\ \\ + Zu Reduzierung der Werte auf Gleitkommazahlen wurden die Daten manuell bearbeitet. Die CAD-Zeichnungen dienen dabei als Hilfe, um die kreuzungsspezifischen Angaben interpretieren zu k"onnen. [BSP] -- berechnung? Neben der Reduktion auf Prozentwerte, m"ussen die Richtungsangaben 'Straight', 'Left und 'Right' auf globale Werte umgerechnet werden, da diese Richtungsangaben von der Position des Sensors abh"angt. Hierf"ur m"ussen die drei Richtungsangaben auf Kreuzungsnamen umgerechnet werden, welche auf den Ausgang der betrachteten Kreuzung folgen. @@ -199,7 +199,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be } \end{enumerate} \subsection{Herausforderungen} - Während der Datenanalyse und Aufbereitung wurden einige Herausforderungen erkannt, die es zu lösen gilt, da sie andernfalls die Lösungsmöglichkeiten einschränken. Zum einen ist das das Zeitproblem, welches eine Verbindung von Sensorwerten von zwei Kreuzungen nicht zulässt, zum anderen das Abbiegeproblem, welches beschreibt, das die Abbiegewahrscheinlichkeit nicht mithilfe der Sensorwerte gemessen werden kann. + W"ahrend der Datenanalyse und Aufbereitung wurden einige Herausforderungen erkannt, die es zu l"osen gilt, da sie andernfalls die L"osungsm"oglichkeiten einschr"anken. Zum einen ist das das Zeitproblem, welches eine Verbindung von Sensorwerten von zwei Kreuzungen nicht zul"asst, zum anderen das Abbiegeproblem, welches beschreibt, das die Abbiegewahrscheinlichkeit nicht mithilfe der Sensorwerte gemessen werden kann. \subsubsection{Das Zeitproblem}\label{sec:datengrund:probtime} Die Daten der Induktionsschleifen sind die Werte der Sensoren "uber die letzte Minute. Sie zeigen eine Art summierte Momentaufnahme des Verkehrs an den Messpunkten. Das macht es allerdings schwer zwei Messungen in eine Beziehung zu stellen. Bildlich gesprochen kann man nicht trivial bestimmen, wie lange ein Auto von der einen zur anderen Kreuzung ben"otigt. Da die Daten nur f"ur bestimmte Zeitpunkte zur Verf"ugung stehen, kann nicht mehr festgetsllt werden wann ein Auto, welches an Kreuzung A "uber den Sensor gefahren ist, an Kreuzung B ankommt und dort "uber den Sensor f"ahrt. Eine 'Verfolgung' eines Autos ist somit nicht m"oglich, da nicht festgestellt werden kann, wie weit es bis zur n"achsten Momentaufnahme gekommen ist. diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/glossar.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/glossar.tex index 432bb4ca..f892237f 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/glossar.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/glossar.tex @@ -11,4 +11,7 @@ lkw pkw cad -hmm \ No newline at end of file +hmm +jgrapht +jgraph +jdbm driver \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex index a1d8971a..47844899 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex @@ -1,10 +1,10 @@ \section{Verkehrsmodell}\label{sec:modell} In diesem Kapitel werden zwei Modellierungen der zehn untersuchten Kreuzungen, der 'Ministadt', vorgestellt und erkl"art. Die 'Ministadt' weist eine große Anzahl an verbauten Sensoren in ihrem Gebiet auf und eignet sich aus diesem Grund f"ur eine Modellierung. Die beiden diskutierten Modelle sind die Darstellung als Matrix und die als Graph. Diese beiden Darstellungen sind untereinander kompatibel, k"onnen deshalb ineinander "uberf"uhrt werden. Der Graph ist ein n"utzliches Werkzeug der Visualisierung w"ahrend die Matrixdarstellung der Berechnung dient. Als Grundlage f"ur die Modellierung dienen die in Kapitel \autoref{Daten} beschriebenen Daten.\\ \\ -In der Industrie eingesetzte Software zur Berechnung und Modellierung von Verkehrsfl"ussen, verwenden meistens ein sog. Micro Modell(VISUM), um die Interaktion der einzelnen Verkehrsteilnehmer modellieren zu k"onnen. Da die Sensorwerte, welche zur Verf"ugung stehen allerdings "uber einen Zeitraum von einer Minute aufgenommen werden, eignet sich eine Micromodellierung des Verkehrs nicht. F"ur einen solchen Modellierungsansatz sind genauere und mehr Daten notwendig. Es stehen allerdings lediglich Messwerte von 89 Sensoren zur Verf"ugung. Eine Modellierung einzelner Autos erscheint deshalb, allein anhand der Induktionsschleifen, nicht möglich zu sein\\ \\ +In der Industrie eingesetzte Software zur Berechnung und Modellierung von Verkehrsfl"ussen, verwenden meistens ein sog. Micro Modell(VISUM), um die Interaktion der einzelnen Verkehrsteilnehmer modellieren zu k"onnen. Da die Sensorwerte, welche zur Verf"ugung stehen allerdings "uber einen Zeitraum von einer Minute aufgenommen werden, eignet sich eine Micromodellierung des Verkehrs nicht. F"ur einen solchen Modellierungsansatz sind genauere und mehr Daten notwendig. Es stehen allerdings lediglich Messwerte von 89 Sensoren zur Verf"ugung. Eine Modellierung einzelner Autos erscheint deshalb, allein anhand der Induktionsschleifen, nicht m"oglich zu sein\\ \\ In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches f"ur Kreuzungen eine genauere Modellierung auf Sensorebene zul"asst, w"ahrend es zwischen den Kreuzungen ein ungenauere Modellierung vornimmt. Dies ist sinnvoll, da nur im Kreuzungsbereich Sensoren zur Verf"ugung stehen, w"ahrend kleinere Kreuzungen und Straßenz"uge nicht mit Sensoren best"uckt sind und aus diesem Grund keine qualifiziert Aussage "uber diese gemacht werden kann.\\ -Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die Stra"senverkehrsordnung halten, da nur verkehrsg"ultige Verbindungen von Kreuzungen, Knoten und Sensoren modelliert werden. Die beschriebene Modellierung kann dabei nicht jedes Verkehrsverhalten beschreiben. So kann beispielsweise der R"uckfluss von Autos, welche eine sog. 'U-Turn' an einer Kreuzung vollf"uhren, nicht mit dem entwickelten Modell modelliert werden. Eine genaue Beschreibung der Einschränkungen und Voraussetzungen ist am Ende dieses Kapitels zu finden.\\ \\ +Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die Stra"senverkehrsordnung halten, da nur verkehrsg"ultige Verbindungen von Kreuzungen, Knoten und Sensoren modelliert werden. Die beschriebene Modellierung kann dabei nicht jedes Verkehrsverhalten beschreiben. So kann beispielsweise der R"uckfluss von Autos, welche eine sog. 'U-Turn' an einer Kreuzung vollf"uhren, nicht mit dem entwickelten Modell modelliert werden. Eine genaue Beschreibung der Einschr"ankungen und Voraussetzungen ist am Ende dieses Kapitels zu finden.\\ \\ \subsection{Modell der Ministadt}\label{sec:modell:ministadt} - Die 'Ministadt' enth"alt zehn, mit Sensoren best"uckte, Kreuzungen. Diese Kreuzungen werden mit A3, A4, A5, A12, A23, A28, A29, A46, A59 und A104 bezeichnet. Die Bezeichnung stammt dabei aus der CAD-Übersichtskarte\ref{abb:caddarmstadt} der Stadt Darmstadt,. Eine genaue Beschreibung des gewählten geographischen Ausschnitts Daten ist in Kapitel \autoref{sec:datengrund} zu finden.\\ \\ + Die 'Ministadt' enth"alt zehn, mit Sensoren best"uckte, Kreuzungen. Diese Kreuzungen werden mit A3, A4, A5, A12, A23, A28, A29, A46, A59 und A104 bezeichnet. Die Bezeichnung stammt dabei aus der CAD-"Ubersichtskarte\ref{abb:caddarmstadt} der Stadt Darmstadt,. Eine genaue Beschreibung des gew"ahlten geographischen Ausschnitts Daten ist in Kapitel \autoref{sec:datengrund} zu finden.\\ \\ F"ur das hier entwickelte Stra"senmodell wurde das Straßennetz in sieben Objekte unterteilt: \begin{enumerate} \item{Stra"se: Eine Stra"se, auf der Autos fahren d"urfen. Sie ist nicht mit Sensoren best"uckt und hat eine Fließrichtung.} @@ -22,8 +22,8 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/Kreuzungsuebersicht}} \caption{Kreuzungs"ubersicht 'Ministadt'in der Stadt Darmstadt} \end{figure} - Um eine Übersicht "uber die zu betrachtenden Kreuzungen zu erhalten wurden manuell Zeichnungen von den zehn Kreuzungen angefertigt. Die gew"ahlte intuitive Modellierung entspricht in etwa der, welche sp"ater im Computer entsteht. Die Grundlage f"ur diese Modellierung sind die CAD-Zeichnungen der Kreuzungen der Stadt Darmstadt. Sie werden im Kapitel \autoref{sec:datengrund} genauer beschrieben.\\ \\ - In der Kreuzungs"ubersicht entfallen sehr viele Details, da keine Daten f"ur zwischen xen Kreuzungen vorhanden sind. Dagegen k"onnen die modellierten Kreuzungen wesentlich genauer dargestellt werden und lassen sich sehr gut auf Sensorebene modellieren. Neben den realen Sensoren erh"alt jede Kreuzung jeweils bis zu vier Ein- und Ausg"ange, modelliert als 'virtuelle Sensoren'. Die Sensoren werden dabei nach den jeweiligen Kreuzungseing"angen platziert, auf dem sie in der Realit"at in der Straße verbaut sind. Validierungssensoren sind solche welche R"uckschl"usse auf andere Sensoren der Kreuzung zulassen. Sie werden in der manuellen Modellierung aufgezeigt. In der Matrixdarstellung findet sich allerdings keinen Platz f"ur diese, da diese für die Berechnung notwendig sind und diese von der Grundannahme ausgeht, dass ein Sensor direkt mit einem Kreuzungsein- und Ausgang, ohne Zwischenknoten, verbunden ist. Wie anhand des entwickelten Modells Verkehrsströme berechnet werden können und wie sich Sensoren mit Validierungssensoren validieren lassen wird im Kapitel \autoref{sec:berechnung} genauer behandelt.\\ \\ + Um eine "Ubersicht "uber die zu betrachtenden Kreuzungen zu erhalten wurden manuell Zeichnungen von den zehn Kreuzungen angefertigt. Die gew"ahlte intuitive Modellierung entspricht in etwa der, welche sp"ater im Computer entsteht. Die Grundlage f"ur diese Modellierung sind die CAD-Zeichnungen der Kreuzungen der Stadt Darmstadt. Sie werden im Kapitel \autoref{sec:datengrund} genauer beschrieben.\\ \\ + In der Kreuzungs"ubersicht entfallen sehr viele Details, da keine Daten f"ur zwischen xen Kreuzungen vorhanden sind. Dagegen k"onnen die modellierten Kreuzungen wesentlich genauer dargestellt werden und lassen sich sehr gut auf Sensorebene modellieren. Neben den realen Sensoren erh"alt jede Kreuzung jeweils bis zu vier Ein- und Ausg"ange, modelliert als 'virtuelle Sensoren'. Die Sensoren werden dabei nach den jeweiligen Kreuzungseing"angen platziert, auf dem sie in der Realit"at in der Straße verbaut sind. Validierungssensoren sind solche welche R"uckschl"usse auf andere Sensoren der Kreuzung zulassen. Sie werden in der manuellen Modellierung aufgezeigt. In der Matrixdarstellung findet sich allerdings keinen Platz f"ur diese, da diese f"ur die Berechnung notwendig sind und diese von der Grundannahme ausgeht, dass ein Sensor direkt mit einem Kreuzungsein- und Ausgang, ohne Zwischenknoten, verbunden ist. Wie anhand des entwickelten Modells Verkehrsstr"ome berechnet werden k"onnen und wie sich Sensoren mit Validierungssensoren validieren lassen wird im Kapitel \autoref{sec:berechnung} genauer behandelt.\\ \\ Alle Sensoren wurde neben der Unterteilung nach Einspursensor und Mischspursensor nochmals in Subklassen unterschieden. Einspursensoren unterteilen sich dabei in drei Subklassen:\\ \begin{enumerate} \item{Einspur - Geradeaus} @@ -46,21 +46,21 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \caption{Kreuzung A23} \end{figure} Wie in Figur \autoref{abb:9} zu erkennen sind in der Kreuzung A23 zwei Validierungssensoren verbaut. Die manuelle Modellierung verbindet diese mit den entsprechenden Eingangssensoren. Dies ist zwar korrekt, aber erwies sich f"ur die Berechnung als hinderlich. Aus diesem Grund werden bei der computergest"utzten Modellierung die Eingangssensoren direkt mit den jeweiligen Ausg"angen verbunden.\\ \\ - Diese intuitive Modellierung auf zwei Ebenen hat sich sowohl aus "Ubersichtsgr"unden, als auch f"ur die Berechnung als sinnvoll erwiesen. W"ahrend ein Kreuzungsbild eine wesentlich genauere Abbildung der Realit"at ist, so ist im Vergleich die Kreuzungs"ubersicht relativ ungenau, da Seitenstra"sen nicht modelliert werden und alle Kreuzungen als gleich weit voneinander entfernt betrachtet werden. Die gew"ahlte Modellierung hat folglich zwei Genauigkeitsstufen. Die "Ubersicht "uber die Kreuzungen gew"ahrt einen Blick auf die Gesammtverkehrssituation. Sie dient wie der Name schon sagt, der "Ubersicht. Ein wesentliches Ziel ist es Verkehrsdaten f"ur dieses Modell zu errechnen oder abzusch"atzen, da zwar Informationen "uber die einzelnen Kreuzungen zur Verf"ugung stehen, allerdings diese noch nicht auf ein Gesamtbild des Verkehrs "ubertragen werden können. + Diese intuitive Modellierung auf zwei Ebenen hat sich sowohl aus "Ubersichtsgr"unden, als auch f"ur die Berechnung als sinnvoll erwiesen. W"ahrend ein Kreuzungsbild eine wesentlich genauere Abbildung der Realit"at ist, so ist im Vergleich die Kreuzungs"ubersicht relativ ungenau, da Seitenstra"sen nicht modelliert werden und alle Kreuzungen als gleich weit voneinander entfernt betrachtet werden. Die gew"ahlte Modellierung hat folglich zwei Genauigkeitsstufen. Die "Ubersicht "uber die Kreuzungen gew"ahrt einen Blick auf die Gesammtverkehrssituation. Sie dient wie der Name schon sagt, der "Ubersicht. Ein wesentliches Ziel ist es Verkehrsdaten f"ur dieses Modell zu errechnen oder abzusch"atzen, da zwar Informationen "uber die einzelnen Kreuzungen zur Verf"ugung stehen, allerdings diese noch nicht auf ein Gesamtbild des Verkehrs "ubertragen werden k"onnen. \subsection{Modell als Graph}\label{sec:modell:graph} Ein naheliegender Modellierungsansatz ist es, das Stra"sennetz als Graph zu modellieren. Dies eignet sich nicht nur, da Graphen sehr gut erforscht und viele Algorithmen auf ihnen zur Verf"ugung stehen, sonder auch, weil die intuitiv gew"ahlte manuelle Modellierung sich als Graph darstellen l"asst. Aus diesem Grund wurden Graphen als Basis der computergest"utzten Modellierung gew"ahlt. Insbesondere die M"oglichkeit Graphen in Matrizen zu "uberf"uhren, oder Matrizen-Rechnungen an Graphen zu vollf"uhren erweist sich als n"utzlich. Da Einbahnstra"sen und Verkehr mit einer Flussrichtung modelliert werden m"ussen, w"ahlt man einen gerichteten Graphen. Da sich die Zweistufenmodellierung als n"utzlich erwiesen hat, wird auch diese als Graph im Computer abgebildet. Daf"ur m"ussen zwei verschiedenen Graphen aufgebaut werden. Der einer Kreuzung, mit Sensoren und virtuellen Sensoren als Knoten, sowie Stra"sen als Kanten. Der Graph der Kreuzungs"ubersicht dagegen hat Kreuzungen als Knoten und ebenfalls Stra"sen als Kanten.\\ \\ Zur Modellierung am Computer wird auf die Java Bibliothek JGraphT zur"uckgegriffen. Sie erlaubt es, dank moderner 'Templatisierung'[], Graphen mit belieben Klassen als Knoten aufzubauen. Das selbe gilt f"ur Kanten mit wenigen Einschr"ankungen. Desweiteren erlaubt JGraphT eine Konvertierung zu der weit verbreiteten Bibliothek JGraph, welche eine Visualisierungschnittstelle f"ur Graphen mitbringt. Es soll dabei die Knoten des Kreuzungs"ubersichtsgraphen die Graphen der einzelnen Kreuzungen enthalten um den Zusmmenhalt des Modells zu gew"ahrleisten.\\ \\ - Es folgt eine kurze Übersicht über Graphen, woraufhin computergestützte Modellierung des Kreuzungsgraph und Kreuzungsübersichtsgraphen beschrieben wird. + Es folgt eine kurze "Ubersicht "uber Graphen, woraufhin computergest"utzte Modellierung des Kreuzungsgraph und Kreuzungs"ubersichtsgraphen beschrieben wird. \subsubsection{Grundlagen}\label{sec:modell:graph:grund} - Ein Graph ist eine Struktur, welche Objekte und deren Verbindung untereinander abbildet. Die Objekte werden dabei Knoten, die Verbindungen Kanten genannt. Eine Kante verbindet dabei genau zwei Knoten. Graphen lassen sich besonders gut visualisieren, indem Knoten als Punkte oder Kästen und Kanten als Linien zwischen diesen dargestellt werden.\\ \\ + Ein Graph ist eine Struktur, welche Objekte und deren Verbindung untereinander abbildet. Die Objekte werden dabei Knoten, die Verbindungen Kanten genannt. Eine Kante verbindet dabei genau zwei Knoten. Graphen lassen sich besonders gut visualisieren, indem Knoten als Punkte oder K"asten und Kanten als Linien zwischen diesen dargestellt werden.\\ \\ Ein Graph kann als Tupel $(V, E)$ beschrieben werden. $V$ bezeichnet dabei Menge von Knoten, - $E$ eine Menge von Kanten. Die Menge der möglichen Kannten hängt dabei von dem gewählten Typ des Graphen ab. + $E$ eine Menge von Kanten. Die Menge der m"oglichen Kannten h"angt dabei von dem gew"ahlten Typ des Graphen ab. Es wird zwischen folgenden Typen von Graphen unterschieden: \begin{itemize} \item{ungerichter Graph} \item{gerichteter Graph} \end{itemize} - Ein ungerichteter Graph kann dabei genau eine Kante zwischen zwei Knoten haben. Ein gerichteter Graph dagegen kann bis zu zwei Kanten zwischen zwei Knoten haben, einen für jeder Richtung. Diese Einschränkung gilt hingegen nicht für Graphen, welche Mehrfachkanten erlauben. Mehrfachkanten sind solche welche zwei oder mehr Kanten zwischen zwei Knoten zulassen. + Ein ungerichteter Graph kann dabei genau eine Kante zwischen zwei Knoten haben. Ein gerichteter Graph dagegen kann bis zu zwei Kanten zwischen zwei Knoten haben, einen f"ur jeder Richtung. Diese Einschr"ankung gilt hingegen nicht f"ur Graphen, welche Mehrfachkanten erlauben. Mehrfachkanten sind solche welche zwei oder mehr Kanten zwischen zwei Knoten zulassen. \begin{figure} \centering \subfigure[Ungerichteter Graph. Quelle: wikipedia.org] {\includegraphics[width=0.3\textwidth-2\fboxsep-2\fboxrule]{pic/120px-Graph_ungerichtet}} @@ -85,10 +85,10 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{itemize} [Klassendiagramm] Die Klasse SE kann dabei Sensorname, Position in Latitude und Longitude, sowie die Kreuzung, welche den Sensor beinhaltet, speichern. Das Feld 'sensorType' erlaubt dabei die Unterscheidung von virtuellen und realen Sensoren. - Desweiteren stehen drei Felder zur Verknüpfung mit anderen Sensoren zur Verfügung. Das Feld 'multipleOutputDirections' erlaubt es zu bestimmen, ob es sich um einen Mehr- oder Einspursensor handelt. Sollte es sich um einen virtuellen Ein- oder Ausgang einer Kreuzung handeln, so werden in den Feldern 'outXR' und 'inXR' die Namen der benachbarten Kreuzungen gespeichert. Zusätzlich zu den Verknüpfungs- und Typinformationen können noch ein 'value' und ein 'test\_value' gespeichert werden. Value wird dabei zur Berechnung eingesetzt, während der Testwert zur Überprüfung eines berechneten Ergebnis dient. Wer und Testwert sind dabei von der Klasse VL.\\ \\ - Die Klasse VL kann die beiden Werte der Induktionsschleifen 'load' und 'count' halten, sowie eine Sensor ID, welche eine Zuordnung zu einem Sensor ermöglicht. Ein Zeitstempel bestimmt dabei den Zeitpunkt der Messung der Werte. Zur Überprüfung eines Wertes mit einem Testwert wird ein gemessener Wert als Testwert gespeichert. Eine Berechnung soll nun einen Wert berechnen. Durch Vergleich von gemessem Testwert und berechnetem Wert kann bestimmt werden wie genau die Berechnung ist.\\ \\ - Die Klasse ST modelliert eine Straße. Sie kann die Namen der Knoten, welche sie verbindet speichern, um den Graphen nicht ständig nach den Namen der Nachbarn abzusuchen zu müssen. Diese beiden Werte dienen lediglich der Visualisierung. Desweiteren kann eine Gleitkommazahl gespeichert werden, welche die Abbiegewahrscheinlichkeit von einem Sensor, entlang dieser Kante, repräsentiert.\\ \\ - Um den Graph mit der JGraphT-Bibliothek zu modellieren wurde die Klasse ListableDirectedGraph benutzt\autoref{lst:sensorgraph}. Diese Klasse des Frameworks erlaubt gerichtete Graphen aufzubauen und diese später zu visualisieren.\\ + Desweiteren stehen drei Felder zur Verkn"upfung mit anderen Sensoren zur Verf"ugung. Das Feld 'multipleOutputDirections' erlaubt es zu bestimmen, ob es sich um einen Mehr- oder Einspursensor handelt. Sollte es sich um einen virtuellen Ein- oder Ausgang einer Kreuzung handeln, so werden in den Feldern 'outXR' und 'inXR' die Namen der benachbarten Kreuzungen gespeichert. Zus"atzlich zu den Verkn"upfungs- und Typinformationen k"onnen noch ein 'value' und ein 'test\_value' gespeichert werden. Value wird dabei zur Berechnung eingesetzt, w"ahrend der Testwert zur "Uberpr"ufung eines berechneten Ergebnis dient. Wer und Testwert sind dabei von der Klasse VL.\\ \\ + Die Klasse VL kann die beiden Werte der Induktionsschleifen 'load' und 'count' halten, sowie eine Sensor ID, welche eine Zuordnung zu einem Sensor erm"oglicht. Ein Zeitstempel bestimmt dabei den Zeitpunkt der Messung der Werte. Zur "Uberpr"ufung eines Wertes mit einem Testwert wird ein gemessener Wert als Testwert gespeichert. Eine Berechnung soll nun einen Wert berechnen. Durch Vergleich von gemessem Testwert und berechnetem Wert kann bestimmt werden wie genau die Berechnung ist.\\ \\ + Die Klasse ST modelliert eine Straße. Sie kann die Namen der Knoten, welche sie verbindet speichern, um den Graphen nicht st"andig nach den Namen der Nachbarn abzusuchen zu m"ussen. Diese beiden Werte dienen lediglich der Visualisierung. Desweiteren kann eine Gleitkommazahl gespeichert werden, welche die Abbiegewahrscheinlichkeit von einem Sensor, entlang dieser Kante, repr"asentiert.\\ \\ + Um den Graph mit der JGraphT-Bibliothek zu modellieren wurde die Klasse ListableDirectedGraph benutzt\autoref{lst:sensorgraph}. Diese Klasse des Frameworks erlaubt gerichtete Graphen aufzubauen und diese sp"ater zu visualisieren.\\ \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} \begin{lstlisting}[caption={[abc] Die Kreuzungsklasse XR}, label={lst:sensorgraph}, captionpos=bsec] public ListenableDirectedGraph sensorGraph @@ -96,14 +96,14 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{lstlisting} \end{minipage} \subsubsection{Kreuzungs"ubersicht}\label{sec:modell:graph:overview} - Auch hier ist eine Reduktion auf Knoten und Kanten notwendig, um die Kreuzungs"ubersicht als Graph darstellen zu k"onnen. Folgende Festlegung wurde hierfür getroffen: + Auch hier ist eine Reduktion auf Knoten und Kanten notwendig, um die Kreuzungs"ubersicht als Graph darstellen zu k"onnen. Folgende Festlegung wurde hierf"ur getroffen: \begin{itemize} \item{Stra"se: Eine Straße sei eine Kante} \item{Kreuzung: Eine Kreuzung sei ein Knoten} \end{itemize} [klassendiagramm] - Eine Kreuzung wird hierfür mit der Klasse XR modelliert. Sie enthält den, in Listing \autoref{lst:sensorgraph} gezeigten, Sensorgraph. Desweiteren werden auch für die Kreuzungen eine Position in Latitude und Longitude abgespeichert, sowie alle verbundenen eingehnden Kreuzungen, sowie allen Ausgehenden Kreuzungen. Das Speichern von beiden, Vorgänger und Nachfolgerkreuzung ist zum Aufbaue des Graphen nicht nötig. Dafür würden entweder Ein- oder Ausgänge ausreichen. Um Visualisierung und Berechnung zu vereinfachen wurden allerdings beide definiert. - Eine Straße wird, wie in der Kreuzungsmodellierung mit der Klasse ST beschrieben. Das Feld für die Abbiegewahrscheinlichkeit kann allerdings nicht gefüllt werden, da keine Abbiegewahrscheinlichkeiten zu Seitenstraßen bekannt sind. Das Feld wird späterhin zum Speichern von Flüssen zwischen den Kreuzungen benutzt. + Eine Kreuzung wird hierf"ur mit der Klasse XR modelliert. Sie enth"alt den, in Listing \autoref{lst:sensorgraph} gezeigten, Sensorgraph. Desweiteren werden auch f"ur die Kreuzungen eine Position in Latitude und Longitude abgespeichert, sowie alle verbundenen eingehnden Kreuzungen, sowie allen Ausgehenden Kreuzungen. Das Speichern von beiden, Vorg"anger und Nachfolgerkreuzung ist zum Aufbaue des Graphen nicht n"otig. Daf"ur w"urden entweder Ein- oder Ausg"ange ausreichen. Um Visualisierung und Berechnung zu vereinfachen wurden allerdings beide definiert. + Eine Straße wird, wie in der Kreuzungsmodellierung mit der Klasse ST beschrieben. Das Feld f"ur die Abbiegewahrscheinlichkeit kann allerdings nicht gef"ullt werden, da keine Abbiegewahrscheinlichkeiten zu Seitenstraßen bekannt sind. Das Feld wird sp"aterhin zum Speichern von Fl"ussen zwischen den Kreuzungen benutzt. \subsection{Modell als Matrix}\label{sec:modell:matrix} Als Grundlage f"ur die Berechnung wurde eine Matrixdarstellung f"ur Kreuzungen entwickelt. Der oben entwickelte Graph l"asst sich dabei in eine Matrixform "uberf"uhren. Matrizen bieten z.b. durch Matrixmultiplikation die M"oglichkeit komplexe Zusammenh"ange durch einfache Rechenschritte auszurechnen.\\ \\ Um den Graph einer Kreuzung zu beschreiben ist es n"otig die Verbindungen von Sensoren zu deren m"oglichen Ausg"angen bzw. Eing"angen zu modellieren. F"ur Kreuzungen mit sog. Validierungssensoren ist dies nicht m"oglich, da die Validierungssensoren zwischen Sensor und Ausgang in dem Graphen liegen. Aus diesem Grund werden f"ur die Matrixdarstellung die Valliderungssensoren nicht mit abgebildet. Im Kapitel \autoref{sec:berechnung} wird nochmals n"aher darauf eingegangen, wie diese Sensoren zur L"osung eines Gleichungssystems, um Verkehrsfl"usse auf einer Kreuzung zu berechnen, verwendet werden k"onnen. Da fast alle betrachteten Kreuzungen der Stadt Darmstadt nur einen Sensor zwischen Ein- und entsprechenden Ausgang haben sind die entwickelten Matrizen auf fast alle Kreuzungen, ohne das Weglassen von Sensoren, direkt anzuwenden.\\ \\ @@ -120,7 +120,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St Out_4 & 0/1 & 0/1 & \dots & 0/1\\ \end{Bmatrix} \end{equation} - $Out_1$ bis $Out_4$ bezeichnen dabei die Ausg"ange einer Kreuzung. Je nach Kreuzung können dies auch lediglich drei Ausgänge sein. $S_1$ bis $S_n$ bezeichnen die einzelnen Sensoren, einschließlich der virtuellen Sensoren f"ur Kreuzungseingangsspuren ohne Sensor. Da alle modellierten Kreuzungen der Stadt Darmstadt auf jeder Eingangsspur mit Sensoren bestückt ist, sind keine virtuellen Sensoren fpr Eingangsspuren notwendig. Die Werte der Matrize bestimmen ob eine Verbindung zwischen Sensor und jeweiligem Kreuzungsausgang besteht. Einspursensoren besitzen nur eine Verbindung, Mischspursensoren besitzen dagegen mehr als eine.\\ \\ + $Out_1$ bis $Out_4$ bezeichnen dabei die Ausg"ange einer Kreuzung. Je nach Kreuzung k"onnen dies auch lediglich drei Ausg"ange sein. $S_1$ bis $S_n$ bezeichnen die einzelnen Sensoren, einschließlich der virtuellen Sensoren f"ur Kreuzungseingangsspuren ohne Sensor. Da alle modellierten Kreuzungen der Stadt Darmstadt auf jeder Eingangsspur mit Sensoren best"uckt ist, sind keine virtuellen Sensoren fpr Eingangsspuren notwendig. Die Werte der Matrize bestimmen ob eine Verbindung zwischen Sensor und jeweiligem Kreuzungsausgang besteht. Einspursensoren besitzen nur eine Verbindung, Mischspursensoren besitzen dagegen mehr als eine.\\ \\ \begin{figure}[htbp!]\label{abb:a23} \centering \fbox{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} @@ -149,7 +149,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{Bmatrix} \end{equation} $In_1$ bis $In_4$ bezeichnen dabei die Eing"ange einer Kreuzung. $S_1$ bis $S_n$ bezeichnen die einzelnen Sensoren, einschließlich der virtuellen Sensoren f"ur Kreuzungseingangsspuren ohne Sensor. Die Werte der Matrize bestimmen ob eine Verbindung zwischen Sensor und jeweiligem Kreuzungseingang besteht.\\ \\ - Hier im Beispiel die Eingangsmatrix von Kreuzung A23\ref{abb:a23}. Wieder sind nur drei Eing"ange verzeichnet, was sich mit der Einbahnstraße begr"undet, welche über die Kreuzung verläuft. + Hier im Beispiel die Eingangsmatrix von Kreuzung A23\ref{abb:a23}. Wieder sind nur drei Eing"ange verzeichnet, was sich mit der Einbahnstraße begr"undet, welche "uber die Kreuzung verl"auft. \begin{equation} \begin{Bmatrix} & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ @@ -158,7 +158,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St A4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0\\ \end{Bmatrix} \end{equation} - Ein- und Ausgangsmatrix zusammen beschreiben den gesamten Graphen ohne Validierungssensoren. Im Kapitel \autoref{sec:berechnung} wird näher auf eine mögliche Verwendung der Validierungssensoren eingegangen. + Ein- und Ausgangsmatrix zusammen beschreiben den gesamten Graphen ohne Validierungssensoren. Im Kapitel \autoref{sec:berechnung} wird n"aher auf eine m"ogliche Verwendung der Validierungssensoren eingegangen. \subsection{Datenbankmodell}\label{sec:modell:dbmodell} Um mit einem Programm schneller und einfacher auf die, in Kapitel \autoref{sec:datengrund}, extrahierten Daten zuzugreifen, bietet es sich an diese in einem Datenbank Server abzuspeichern. Hierf"ur wurde eine Datenbankschema erstellt, um alle Informationen, die von dem entwickelten Modell zur Visualisierung und Berechnung ben"otigte Informationen zu speichern vermag.\\ \\ Folgende Informationen wurden in der Datenbank abgespeichert: @@ -168,26 +168,26 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \item{Die Abbiegewahrscheinlichkeit welche der richtigen Verbindungen zwischen Sensor und entsprechendem virtuellen Kreuzungsausgang zugordnet ist.} \end{enumerate} [ER diagramm] - Für Sensoren werden dafür folgende Daten gespeichert: + F"ur Sensoren werden daf"ur folgende Daten gespeichert: \begin{itemize} \item{Eindeutige ID des Sensors} \item{Name des Sensors} \item{Position des Sensors als Latitude und Longitude Werte} - \item{Die zu dem Sensor gehörige Kreuzung} + \item{Die zu dem Sensor geh"orige Kreuzung} \item{Der Sensortyp} \item{Die Verbindungen des Sensor zu bis zu drei Sensoren.} \item{Typ der Spur - Misch- oder Einzelspur} - \item{Für virtuelle Sensoren der Aus- und Eingänge, der Name der vorhergehenden bzw. nachfolgenden Kreuzung.} + \item{F"ur virtuelle Sensoren der Aus- und Eing"ange, der Name der vorhergehenden bzw. nachfolgenden Kreuzung.} \end{itemize} - Dabei ist eine ID ein eindeutiges Merkmahl des Sensors. Der Sensorname dagegen ist nur innerhalb einer Kreuzung eindeutig. So ist auf Kreuzung [] ein Sensor [] zu finden, sowie auf [] einen mit dem selben Namen. Dementsprechend sind Verkn"upfungen unter den Sensoren "uber die Sensorid identifiziert. Diese Verkn"upfungen werden "uber die Felder 'toSensorLeftID', 'toSensorStraightID' und 'toSensorRightID' modelliert und erlauben es den Graphen aufzubauen. Verbindungen zwischen Knoten werden dabei in Verkehrsflussrichtung gespeichert. In der Spalte 'sensorType' wird der Type des Sensors gespeichert. Eine zus"atzliche Tabelle erlaubt es Einzelheiten zu den einzelnen Sensoretypen zu definieren. In dieser Arbeit wird nur auf die beiden Sensortypen 'virtueller Sensor' und 'realer Sensor' zurückgegriffen. Die Datenbankstruktur erlaubt es allerdings durch hinzuf"ugen einer Zeile in der Tabelle 'bt\_sensor\_types' einen neuen Sensortyp zu definieren, auf den ein Algorithmus, welcher auf dem Graphen rechnet, anders als auf die anderen beiden Sensortypen reagieren kann.\\ \\ - Die Definition f"ur Kreuzungen ist dagegen deutlich einfacher. Da jede Kreuzung, die Modelliert wurde h"ochsten vier Ausg"ange hat, m"ussen jeweils 4 Ausg"ange sowie 4 Eing"ange modelliert werden. Auch hier werden Latitude und Logitude ben"otigt, um die Kreuzung auf einer Karte, oder realativ zu anderen Objekten der Modellierung, darstellen zu k"onnen. Die Kreuzungsnamen sind in der Stadt Darmstadt eindeutig, weshalb es keine ID für eine Identifikation von Kreuzungen bedarf.\\ \\ - Die Tabelle Values enth"alt aufbereitete Induktionsschleifenwerte. Diese werden mit den Abfragen, welche in \autoref{sec:datengrund} beschrieben sind, aus der MYSQL-Datenbank der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten extrahiert, um das manuelle Parsen der CSV-Dateien zu umgehen. Sensoren werden hierf"ur mit ihrer eindeutigen ID identifiziert. Ein Zeitstempel der Sensordaten erlaubt es mehrere Datensätze von verschiedenen Zeiten zu speichern. Ein Filter auf dem Zeitstempel erlaubt es Daten eines gewählten Zeitpunktes erneut zu extrahieren. Gespeichert werden dafür die Werte 'load' und 'count' der Induktionschleifen, zusammen mit der eindeutigen Sensor ID und dem entsprechen Zeitstempel.\\ \\ - Die Tabelle FlowStatistics h"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. Da diese Werte dieser Tabelle aus der Abbiegewahrscheinlichkeitstabelle der Stadt Darmstadt entnommen wurden, werden Sensoren "uber Kreuzungs- und Sensorname identifiziert und nicht über eine eindeutige Sensor ID. Dies ist möglich, obwohl Sensornamen nicht eindeutig sind, da sie innerhalb einer Kreuzung eine eindeutige Identifikation über den Namen zulässt. Eine Kombination aus dem eindeutigem Kreuzungsnamen und der innerhalb der Kreuzung eindeutigen Sensornamens, kann ein Sensor eindeutig bestimmt werden. Für die Abbiegewahrscheinlichkeitentabelle werden neben dem Kreuzungs- und Sensornamen, bis zu drei verschiedenen Abbiegewahrscheinlichkeiten angegeben. Die Wahrscheinlichkeit, das ein verkehrsteilnehmer, welcher über den Sensor fährt rechts, links oder geradeaus die Kreuzung verlässt. Zusätzlich wird der nächste Sensorknoten, diesmal identifiziert über die Sensorid, für jede Richtung mit angegeben. Wie die Zuordnung von Links, Rechts und Geradeaus zu einem Knoten erfolgt, wird im Kapitel \autoref{sec:berechnung} beschrieben.\\ - Neben den Abbiegewahrscheinlichkeiten kann in der Abbiegewahrscheinlichkeitstabelle ebenfalls ein Zeitstempel und eine Intervalllänge zu jedem Datensatz abgespeichert werden. Dies erlaubt es genauere, zeitspezifische, Abbiegewahrscheinlichkeiten abzuspeichern. Für diese Arbeit lagen allerdings ausschließlich die Werte der Stadt Darmstadt vor, welche über alle Messungen gemittelt sind. + Dabei ist eine ID ein eindeutiges Merkmahl des Sensors. Der Sensorname dagegen ist nur innerhalb einer Kreuzung eindeutig. So ist auf Kreuzung [] ein Sensor [] zu finden, sowie auf [] einen mit dem selben Namen. Dementsprechend sind Verkn"upfungen unter den Sensoren "uber die Sensorid identifiziert. Diese Verkn"upfungen werden "uber die Felder 'toSensorLeftID', 'toSensorStraightID' und 'toSensorRightID' modelliert und erlauben es den Graphen aufzubauen. Verbindungen zwischen Knoten werden dabei in Verkehrsflussrichtung gespeichert. In der Spalte 'sensorType' wird der Type des Sensors gespeichert. Eine zus"atzliche Tabelle erlaubt es Einzelheiten zu den einzelnen Sensoretypen zu definieren. In dieser Arbeit wird nur auf die beiden Sensortypen 'virtueller Sensor' und 'realer Sensor' zur"uckgegriffen. Die Datenbankstruktur erlaubt es allerdings durch hinzuf"ugen einer Zeile in der Tabelle 'bt\_sensor\_types' einen neuen Sensortyp zu definieren, auf den ein Algorithmus, welcher auf dem Graphen rechnet, anders als auf die anderen beiden Sensortypen reagieren kann.\\ \\ + Die Definition f"ur Kreuzungen ist dagegen deutlich einfacher. Da jede Kreuzung, die Modelliert wurde h"ochsten vier Ausg"ange hat, m"ussen jeweils 4 Ausg"ange sowie 4 Eing"ange modelliert werden. Auch hier werden Latitude und Logitude ben"otigt, um die Kreuzung auf einer Karte, oder realativ zu anderen Objekten der Modellierung, darstellen zu k"onnen. Die Kreuzungsnamen sind in der Stadt Darmstadt eindeutig, weshalb es keine ID f"ur eine Identifikation von Kreuzungen bedarf.\\ \\ + Die Tabelle Values enth"alt aufbereitete Induktionsschleifenwerte. Diese werden mit den Abfragen, welche in \autoref{sec:datengrund} beschrieben sind, aus der MYSQL-Datenbank der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten extrahiert, um das manuelle Parsen der CSV-Dateien zu umgehen. Sensoren werden hierf"ur mit ihrer eindeutigen ID identifiziert. Ein Zeitstempel der Sensordaten erlaubt es mehrere Datens"atze von verschiedenen Zeiten zu speichern. Ein Filter auf dem Zeitstempel erlaubt es Daten eines gew"ahlten Zeitpunktes erneut zu extrahieren. Gespeichert werden daf"ur die Werte 'load' und 'count' der Induktionschleifen, zusammen mit der eindeutigen Sensor ID und dem entsprechen Zeitstempel.\\ \\ + Die Tabelle FlowStatistics h"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. Da diese Werte dieser Tabelle aus der Abbiegewahrscheinlichkeitstabelle der Stadt Darmstadt entnommen wurden, werden Sensoren "uber Kreuzungs- und Sensorname identifiziert und nicht "uber eine eindeutige Sensor ID. Dies ist m"oglich, obwohl Sensornamen nicht eindeutig sind, da sie innerhalb einer Kreuzung eine eindeutige Identifikation "uber den Namen zul"asst. Eine Kombination aus dem eindeutigem Kreuzungsnamen und der innerhalb der Kreuzung eindeutigen Sensornamens, kann ein Sensor eindeutig bestimmt werden. F"ur die Abbiegewahrscheinlichkeitentabelle werden neben dem Kreuzungs- und Sensornamen, bis zu drei verschiedenen Abbiegewahrscheinlichkeiten angegeben. Die Wahrscheinlichkeit, das ein verkehrsteilnehmer, welcher "uber den Sensor f"ahrt rechts, links oder geradeaus die Kreuzung verl"asst. Zus"atzlich wird der n"achste Sensorknoten, diesmal identifiziert "uber die Sensorid, f"ur jede Richtung mit angegeben. Wie die Zuordnung von Links, Rechts und Geradeaus zu einem Knoten erfolgt, wird im Kapitel \autoref{sec:berechnung} beschrieben.\\ + Neben den Abbiegewahrscheinlichkeiten kann in der Abbiegewahrscheinlichkeitstabelle ebenfalls ein Zeitstempel und eine Intervalll"ange zu jedem Datensatz abgespeichert werden. Dies erlaubt es genauere, zeitspezifische, Abbiegewahrscheinlichkeiten abzuspeichern. F"ur diese Arbeit lagen allerdings ausschließlich die Werte der Stadt Darmstadt vor, welche "uber alle Messungen gemittelt sind. \subsection{Einschr"ankungen und Schw"achen des Modell}\label{sec:modell:limits} Das entwickelte Modell kann nicht alle Verkehrsverhalten modellieren. In diesem Abschnitt wird behandelt, welche Einschr"ankungen das Modell mitbringt und welche Reduktionen des Detailgrades vorgenommen wurden.\\ \\ - Das Modell kann sog. 'U-Turns', nicht modellieren. Als 'U-Turn' bezeichnet man dasjenige Verkehrsmanöver, welches den Verkehrsteilnehmer von dem Kreuzungseingang einer Kreuzung zu dem Ausgang, welcher in die Richtung zeigt, aus der er kommt. Dieses Verkehrsverhalten ist selten zu beobachten und wurde aus diesem nicht modelliert. Desweiteren würde eine Modellierung dieses Manövers eine 'U-Turn-Wahrscheinlichkeit' erfordern, welche nicht vorliegt.\\ \\ - Ein weitere, sehr elementare Schwäche des Modells ist die Abstraktion der Sensorposition. Wie in den manuell angefertigten Kreuzungszeichnungen wird die Position eines Sensors innerhalb des Graphenmodells einem Eingang zugeordnet. Die Latitude und Longitude Werte des Sensors werden nur zur Visualisierung benutzt. Dies erlaubt allerdings einen Spurwechsel, nach dem Überfahren eines Sensors, nicht zu modellieren. Die Genauigkeit des Modells hängt folglich direkt mit der Entfernung des Sensors von der Kreuzung ab. Ist der Sensor weit entfernt, so kann ein Auto die Spur nochmals wechseln. Ist der Sensor direkt vor der Haltelinie verbaut, kann die Spur nicht mehr gewechselt werden.\\ \\ - Neben diesen Einschränkungen wird nur gültiges Verkehrsverhalten modelliert. So können Verkehrsteilnehmer, welche zwar auf einer Rechtabbiegerspur stehen, allerdings geradeaus fahren nicht von dem Modell modelliert werden.\\ \\ - Es ist allerdings denkbar das Modell durch U-Turn-, Spurwechsel- und Falschfahrwahrscheinlichkeiten zu dekorieren und somit die Menge der modellierbaren Kreuzungszustände und -Übergänge zu vergrößern und ein realistischeres Bild des Verkehrs zu berechnen. Allerdings lagen keine Daten über das Verhalten der Verkehrsteilnehmer vor. + Das Modell kann sog. 'U-Turns', nicht modellieren. Als 'U-Turn' bezeichnet man dasjenige Verkehrsman"over, welches den Verkehrsteilnehmer von dem Kreuzungseingang einer Kreuzung zu dem Ausgang, welcher in die Richtung zeigt, aus der er kommt. Dieses Verkehrsverhalten ist selten zu beobachten und wurde aus diesem nicht modelliert. Desweiteren w"urde eine Modellierung dieses Man"overs eine 'U-Turn-Wahrscheinlichkeit' erfordern, welche nicht vorliegt.\\ \\ + Ein weitere, sehr elementare Schw"ache des Modells ist die Abstraktion der Sensorposition. Wie in den manuell angefertigten Kreuzungszeichnungen wird die Position eines Sensors innerhalb des Graphenmodells einem Eingang zugeordnet. Die Latitude und Longitude Werte des Sensors werden nur zur Visualisierung benutzt. Dies erlaubt allerdings einen Spurwechsel, nach dem "Uberfahren eines Sensors, nicht zu modellieren. Die Genauigkeit des Modells h"angt folglich direkt mit der Entfernung des Sensors von der Kreuzung ab. Ist der Sensor weit entfernt, so kann ein Auto die Spur nochmals wechseln. Ist der Sensor direkt vor der Haltelinie verbaut, kann die Spur nicht mehr gewechselt werden.\\ \\ + Neben diesen Einschr"ankungen wird nur g"ultiges Verkehrsverhalten modelliert. So k"onnen Verkehrsteilnehmer, welche zwar auf einer Rechtabbiegerspur stehen, allerdings geradeaus fahren nicht von dem Modell modelliert werden.\\ \\ + Es ist allerdings denkbar das Modell durch U-Turn-, Spurwechsel- und Falschfahrwahrscheinlichkeiten zu dekorieren und somit die Menge der modellierbaren Kreuzungszust"ande und -"Uberg"ange zu vergr"oßern und ein realistischeres Bild des Verkehrs zu berechnen. Allerdings lagen keine Daten "uber das Verhalten der Verkehrsteilnehmer vor. \newpage \ No newline at end of file

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