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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 2013-8-13 +% for document 'TUDthesis' on 2013-8-14 actual '?' encap '|' level '!' diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log index 9c81446e..9a426419 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) 13 AUG 2013 23:13 +This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.8.13) 14 AUG 2013 18:08 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> 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("C:\Program Files (x86)\MiKTeX\tex\latex\mathdesign\mdbcmr.fd" File: mdbcmr.fd ) -LaTeX Font Info: ... okay on input line 22. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 22. -LaTeX Font Info: ... okay on input line 22. -LaTeX Font Info: Try loading font information for T1+5ch on input line 22. +LaTeX Font Info: ... okay on input line 24. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 24. +LaTeX Font Info: ... okay on input line 24. +LaTeX Font Info: Try loading font information for T1+5ch on input line 24. ("C:\Program Files\tuddesign\texmf\tex\latex\tex-tudfonts\softmake\charter\t15c h.fd" @@ -1052,7 +1052,7 @@ File: t15ch.fd 2008/06/23 Fontinst v1.927 font definitions for T1/5ch. \TUD@part@topskip=\skip123 \c@lstlisting=\count180 -Package hyperref Info: Link coloring OFF on input line 22. +Package hyperref Info: Link coloring OFF on input line 24. 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LaTeX Font Info: Font shape `OML/mdput/m/it' will be -(Font) scaled to size 5.546pt on input line 31. +(Font) scaled to size 5.546pt on input line 33. \@TUD@titlelines=\count182 - + File: tud_logo.pdf Graphic file (type pdf) File: tud_logo.pdf Graphic file (type pdf) @@ -1208,18 +1208,18 @@ Non-PDF special ignored! Non-PDF special ignored!{C:/Users/Rylon/AppData/Local/MiKTeX/2.9/pdftex/config/ pdftex.map} ] -Underfull \hbox (badness 10000) in paragraph at lines 31--31 +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 ] -LaTeX Font Info: Try loading font information for T1+5sf on input line 37. +LaTeX Font Info: Try loading font information for T1+5sf on input line 39. 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Thesis/thesis_ug/TUDthesis.out b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out index a173472b..0dbb27b6 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out @@ -1,47 +1,49 @@ \BOOKMARK [1][-]{section.1}{\334bersicht}{}% 1 \BOOKMARK [1][-]{section.2}{Einleitung}{}% 2 -\BOOKMARK [2][-]{subsection.2.1}{Zielsetzung}{section.2}% 3 -\BOOKMARK [1][-]{section.3}{Related Work}{}% 4 -\BOOKMARK [1][-]{section.4}{Datenbasis und Grundlagen}{}% 5 -\BOOKMARK [2][-]{subsection.4.1}{Induktionsschleifen}{section.4}% 6 -\BOOKMARK [2][-]{subsection.4.2}{adaptive Steuerung von Ampelanlagen}{section.4}% 7 -\BOOKMARK [2][-]{subsection.4.3}{Macro- und microskopische Modellierung von Verkehr}{section.4}% 8 -\BOOKMARK [2][-]{subsection.4.4}{Induktionsschleifenwerte}{section.4}% 9 -\BOOKMARK [3][-]{subsubsection.4.4.1}{CSV-Daten der Stadt Darmstadt}{subsection.4.4}% 10 -\BOOKMARK [3][-]{subsubsection.4.4.2}{MYSQL-Daten des Projektes Verkehrsvisualisierung}{subsection.4.4}% 11 -\BOOKMARK [2][-]{subsection.4.5}{Geographischer Ausschnitt der Daten}{section.4}% 12 -\BOOKMARK [2][-]{subsection.4.6}{CAD-Zeichnungen der Kreuzungen}{section.4}% 13 -\BOOKMARK [2][-]{subsection.4.7}{Abbiegewahrscheinlichkeiten}{section.4}% 14 -\BOOKMARK [2][-]{subsection.4.8}{Das Zeitproblem}{section.4}% 15 -\BOOKMARK [2][-]{subsection.4.9}{Das Abbiegeproblem}{section.4}% 16 -\BOOKMARK [1][-]{section.5}{Verkehrsmodell}{}% 17 -\BOOKMARK [2][-]{subsection.5.1}{Modell der Ministadt}{section.5}% 18 -\BOOKMARK [2][-]{subsection.5.2}{Modell als Graph}{section.5}% 19 -\BOOKMARK [3][-]{subsubsection.5.2.1}{Kreuzungsgraph}{subsection.5.2}% 20 -\BOOKMARK [3][-]{subsubsection.5.2.2}{Kreuzungs\374bersicht}{subsection.5.2}% 21 -\BOOKMARK [2][-]{subsection.5.3}{Modell als Matrix}{section.5}% 22 -\BOOKMARK [3][-]{subsubsection.5.3.1}{Ausgangsmatrix}{subsection.5.3}% 23 -\BOOKMARK [3][-]{subsubsection.5.3.2}{Eingangsmatrix}{subsection.5.3}% 24 -\BOOKMARK [3][-]{subsubsection.5.3.3}{Sonderfall: Vallidierungssensor}{subsection.5.3}% 25 -\BOOKMARK [2][-]{subsection.5.4}{Datenbankmodell}{section.5}% 26 -\BOOKMARK [3][-]{subsubsection.5.4.1}{Datenbank Schema}{subsection.5.4}% 27 -\BOOKMARK [1][-]{section.6}{L\366sungsans\344tze}{}% 28 -\BOOKMARK [2][-]{subsection.6.1}{L\366sungsansatz: Hidden Markow Modell}{section.6}% 29 -\BOOKMARK [2][-]{subsection.6.2}{L\366sungsansatz: Wegfindungsalgorithmen}{section.6}% 30 -\BOOKMARK [2][-]{subsection.6.3}{L\366sungsansatz: Lineares Gleichungssystem}{section.6}% 31 -\BOOKMARK [3][-]{subsubsection.6.3.1}{Grundlagen}{subsection.6.3}% 32 -\BOOKMARK [3][-]{subsubsection.6.3.2}{Lineares Gleichungssystem einer Kreuzung}{subsection.6.3}% 33 -\BOOKMARK [2][-]{subsection.6.4}{Lineares Gleichungssystem am Graph}{section.6}% 34 -\BOOKMARK [3][-]{subsubsection.6.4.1}{Verkehrsfluss zwischen Kreuzungen}{subsection.6.4}% 35 -\BOOKMARK [1][-]{section.7}{Visualisierung}{}% 36 -\BOOKMARK [2][-]{subsection.7.1}{Visualisierung des Graphen mit Geoinformationen}{section.7}% 37 -\BOOKMARK [2][-]{subsection.7.2}{Visualisierung des JGraphT-Graphen}{section.7}% 38 -\BOOKMARK [1][-]{section.8}{Validierung}{}% 39 -\BOOKMARK [2][-]{subsection.8.1}{Testdatenmenge}{section.8}% 40 -\BOOKMARK [2][-]{subsection.8.2}{Verkehrsz\344hlung}{section.8}% 41 -\BOOKMARK [2][-]{subsection.8.3}{Validierung der Verkehrsaufkommensvorhersage}{section.8}% 42 -\BOOKMARK [1][-]{section.9}{Ausblick}{}% 43 -\BOOKMARK [1][-]{section.9}{Glossar}{}% 44 -\BOOKMARK [1][-]{section.9}{Abbildungsverzeichnis}{}% 45 -\BOOKMARK [1][-]{section.9}{Quellcodeverzeichnis}{}% 46 -\BOOKMARK [1][-]{section.13}{Anhang}{}% 47 +\BOOKMARK [1][-]{section.3}{Datenbasis und Grundlagen}{}% 3 +\BOOKMARK [2][-]{subsection.3.1}{Induktionsschleifen}{section.3}% 4 +\BOOKMARK [2][-]{subsection.3.2}{Adaptive Steuerung von Ampelanlagen}{section.3}% 5 +\BOOKMARK [2][-]{subsection.3.3}{Macro- und microskopische Modellierung von Verkehr}{section.3}% 6 +\BOOKMARK [2][-]{subsection.3.4}{Induktionsschleifenwerte}{section.3}% 7 +\BOOKMARK [3][-]{subsubsection.3.4.1}{CSV-Daten der Stadt Darmstadt}{subsection.3.4}% 8 +\BOOKMARK [3][-]{subsubsection.3.4.2}{MYSQL-Daten des Projektes Verkehrsvisualisierung}{subsection.3.4}% 9 +\BOOKMARK [2][-]{subsection.3.5}{Geographischer Ausschnitt der Daten}{section.3}% 10 +\BOOKMARK [2][-]{subsection.3.6}{CAD-Zeichnungen der Kreuzungen}{section.3}% 11 +\BOOKMARK [2][-]{subsection.3.7}{Abbiegewahrscheinlichkeiten}{section.3}% 12 +\BOOKMARK [2][-]{subsection.3.8}{Das Zeitproblem}{section.3}% 13 +\BOOKMARK [2][-]{subsection.3.9}{Das Abbiegeproblem}{section.3}% 14 +\BOOKMARK [1][-]{section.4}{Verkehrsmodell}{}% 15 +\BOOKMARK [2][-]{subsection.4.1}{Modell der Ministadt}{section.4}% 16 +\BOOKMARK [2][-]{subsection.4.2}{Modell als Graph}{section.4}% 17 +\BOOKMARK [3][-]{subsubsection.4.2.1}{Kreuzungsgraph}{subsection.4.2}% 18 +\BOOKMARK [3][-]{subsubsection.4.2.2}{Kreuzungs\374bersicht}{subsection.4.2}% 19 +\BOOKMARK [2][-]{subsection.4.3}{Modell als Matrix}{section.4}% 20 +\BOOKMARK [3][-]{subsubsection.4.3.1}{Ausgangsmatrix}{subsection.4.3}% 21 +\BOOKMARK [3][-]{subsubsection.4.3.2}{Eingangsmatrix}{subsection.4.3}% 22 +\BOOKMARK [3][-]{subsubsection.4.3.3}{Sonderfall: Vallidierungssensor}{subsection.4.3}% 23 +\BOOKMARK [2][-]{subsection.4.4}{Datenbankmodell}{section.4}% 24 +\BOOKMARK [3][-]{subsubsection.4.4.1}{Datenbank Schema}{subsection.4.4}% 25 +\BOOKMARK [2][-]{subsection.4.5}{Einschr\344nkungen und Voraussetzungen f\374r das Modell}{section.4}% 26 +\BOOKMARK [1][-]{section.5}{L\366sungsans\344tze}{}% 27 +\BOOKMARK [2][-]{subsection.5.1}{L\366sungsansatz: Hidden Markow Modell}{section.5}% 28 +\BOOKMARK [3][-]{subsubsection.5.1.1}{Grundlagen}{subsection.5.1}% 29 +\BOOKMARK [3][-]{subsubsection.5.1.2}{HMM f\374r eine Kreuzung}{subsection.5.1}% 30 +\BOOKMARK [2][-]{subsection.5.2}{L\366sungsansatz: Wegfindungsalgorithmen}{section.5}% 31 +\BOOKMARK [2][-]{subsection.5.3}{L\366sungsansatz: Lineares Gleichungssystem}{section.5}% 32 +\BOOKMARK [3][-]{subsubsection.5.3.1}{Grundlagen}{subsection.5.3}% 33 +\BOOKMARK [3][-]{subsubsection.5.3.2}{Lineares Gleichungssystem einer Kreuzung}{subsection.5.3}% 34 +\BOOKMARK [2][-]{subsection.5.4}{Kreuzungsberechnung am Graphen}{section.5}% 35 +\BOOKMARK [3][-]{subsubsection.5.4.1}{Verkehrsfluss zwischen Kreuzungen}{subsection.5.4}% 36 +\BOOKMARK [1][-]{section.6}{Visualisierung}{}% 37 +\BOOKMARK [2][-]{subsection.6.1}{Visualisierung des Graphen mit Geoinformationen}{section.6}% 38 +\BOOKMARK [2][-]{subsection.6.2}{Visualisierung des JGraphT-Graphen}{section.6}% 39 +\BOOKMARK [1][-]{section.7}{Validierung}{}% 40 +\BOOKMARK [2][-]{subsection.7.1}{Testdatenmenge}{section.7}% 41 +\BOOKMARK [2][-]{subsection.7.2}{Verkehrsz\344hlung}{section.7}% 42 +\BOOKMARK [2][-]{subsection.7.3}{Validierung der Verkehrsaufkommensvorhersage}{section.7}% 43 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zJ|gY3l)JAq1kPFb&h+2gn@onA(}(?2fv5N-)d}~28WMbXraOC}+7#SN1&UFPzN8ZW z_xXHlitprqf3%5c!IGJQ`S?&PzIlHPwfxQdZ4H~p+1&^4FGDhY@O~R)@i`g3prT9J z`>)+^Q)wb(b$#o z{ER9bT3@-}oao6;kJ#(y<#!YHh7iq1CTnGR?+TM=)IF-N!S5#Nt>f1(wC^Twg)+!Q z4H^y)@BMP#SbE=yH{299Kxs9cN*Ml1`sX22D1=FpspPvt)+X6n{cDCK}q|vs1uC11fZ;>ZA0<7!1Jp)5}jk{PGJe z%jFOM_QyZ{{L`QR`nP}j_2-{{`Hx?I*#Gl?etY@hfBo7Rc2)8GE%KY#u0|Ni*l{{urp#HOA3 FCjh2zACUk6 diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.tex b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.tex index 7af01a08..614d52b7 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.tex @@ -18,6 +18,8 @@ } %listing options \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} +%matrix +\setcounter{MaxMatrixCols}{20} \begin{document} %Title etc für TUD Design @@ -46,8 +48,6 @@ \newpage \section{Einleitung}{\input{tex/einleitung}} \newpage - \section{Related Work}{\input{tex/relatedwork}} - \newpage \section{Datenbasis und Grundlagen}{\input{tex/datengrund}} \newpage \section{Verkehrsmodell}{\input{tex/modell}} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc index 405b56d1..4dc89c85 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc @@ -1,47 +1,49 @@ \contentsline {section}{\numberline {1}\active@dq \dq@prtct {U}bersicht}{1}{section.1} \contentsline {section}{\numberline {2}Einleitung}{4}{section.2} -\contentsline {subsection}{\numberline {2.1}Zielsetzung}{5}{subsection.2.1} -\contentsline {section}{\numberline {3}Related Work}{6}{section.3} -\contentsline {section}{\numberline {4}Datenbasis und Grundlagen}{7}{section.4} -\contentsline {subsection}{\numberline {4.1}Induktionsschleifen}{7}{subsection.4.1} -\contentsline {subsection}{\numberline {4.2}adaptive Steuerung von Ampelanlagen}{8}{subsection.4.2} -\contentsline {subsection}{\numberline {4.3}Macro- und microskopische Modellierung von Verkehr}{8}{subsection.4.3} -\contentsline {subsection}{\numberline {4.4}Induktionsschleifenwerte}{8}{subsection.4.4} -\contentsline {subsubsection}{\numberline {4.4.1}CSV-Daten der Stadt Darmstadt}{8}{subsubsection.4.4.1} -\contentsline {subsubsection}{\numberline {4.4.2}MYSQL-Daten des Projektes Verkehrsvisualisierung}{10}{subsubsection.4.4.2} -\contentsline {subsection}{\numberline {4.5}Geographischer Ausschnitt der Daten}{11}{subsection.4.5} -\contentsline {subsection}{\numberline {4.6}CAD-Zeichnungen der Kreuzungen}{11}{subsection.4.6} -\contentsline {subsection}{\numberline {4.7}Abbiegewahrscheinlichkeiten}{12}{subsection.4.7} -\contentsline {subsection}{\numberline {4.8}Das Zeitproblem}{12}{subsection.4.8} -\contentsline {subsection}{\numberline {4.9}Das Abbiegeproblem}{13}{subsection.4.9} -\contentsline {section}{\numberline {5}Verkehrsmodell}{14}{section.5} -\contentsline {subsection}{\numberline {5.1}Modell der Ministadt}{14}{subsection.5.1} -\contentsline {subsection}{\numberline {5.2}Modell als Graph}{16}{subsection.5.2} -\contentsline {subsubsection}{\numberline {5.2.1}Kreuzungsgraph}{17}{subsubsection.5.2.1} -\contentsline {subsubsection}{\numberline {5.2.2}Kreuzungs\active@dq \dq@prtct {u}bersicht}{18}{subsubsection.5.2.2} -\contentsline {subsection}{\numberline {5.3}Modell als Matrix}{18}{subsection.5.3} -\contentsline {subsubsection}{\numberline {5.3.1}Ausgangsmatrix}{19}{subsubsection.5.3.1} -\contentsline {subsubsection}{\numberline {5.3.2}Eingangsmatrix}{19}{subsubsection.5.3.2} -\contentsline {subsubsection}{\numberline {5.3.3}Sonderfall: Vallidierungssensor}{20}{subsubsection.5.3.3} -\contentsline {subsection}{\numberline {5.4}Datenbankmodell}{20}{subsection.5.4} -\contentsline {subsubsection}{\numberline {5.4.1}Datenbank Schema}{21}{subsubsection.5.4.1} -\contentsline {section}{\numberline {6}L\active@dq \dq@prtct {o}sungsans\active@dq \dq@prtct {a}tze}{24}{section.6} -\contentsline {subsection}{\numberline {6.1}L\active@dq \dq@prtct {o}sungsansatz: Hidden Markow Modell}{24}{subsection.6.1} -\contentsline {subsection}{\numberline {6.2}L\active@dq \dq@prtct {o}sungsansatz: Wegfindungsalgorithmen}{24}{subsection.6.2} -\contentsline {subsection}{\numberline {6.3}L\active@dq \dq@prtct {o}sungsansatz: Lineares Gleichungssystem}{24}{subsection.6.3} -\contentsline {subsubsection}{\numberline {6.3.1}Grundlagen}{25}{subsubsection.6.3.1} -\contentsline {subsubsection}{\numberline {6.3.2}Lineares Gleichungssystem einer Kreuzung}{25}{subsubsection.6.3.2} -\contentsline {subsection}{\numberline {6.4}Lineares Gleichungssystem am Graph}{26}{subsection.6.4} -\contentsline {subsubsection}{\numberline {6.4.1}Verkehrsfluss zwischen Kreuzungen}{27}{subsubsection.6.4.1} -\contentsline {section}{\numberline {7}Visualisierung}{28}{section.7} -\contentsline {subsection}{\numberline {7.1}Visualisierung des Graphen mit Geoinformationen}{28}{subsection.7.1} -\contentsline {subsection}{\numberline {7.2}Visualisierung des JGraphT-Graphen}{28}{subsection.7.2} -\contentsline {section}{\numberline {8}Validierung}{29}{section.8} -\contentsline {subsection}{\numberline {8.1}Testdatenmenge}{29}{subsection.8.1} -\contentsline {subsection}{\numberline {8.2}Verkehrsz\active@dq \dq@prtct {a}hlung}{29}{subsection.8.2} -\contentsline {subsection}{\numberline {8.3}Validierung der Verkehrsaufkommensvorhersage}{29}{subsection.8.3} -\contentsline {section}{\numberline {9}Ausblick}{30}{section.9} -\contentsline {section}{\numberline {10}Glossar}{32}{section.9} -\contentsline {section}{\numberline {11}Abbildungsverzeichnis}{33}{section.9} -\contentsline {section}{\numberline {12}Quellcodeverzeichnis}{33}{section.9} -\contentsline {section}{\numberline {13}Anhang}{34}{section.13} +\contentsline {section}{\numberline {3}Datenbasis und Grundlagen}{6}{section.3} +\contentsline {subsection}{\numberline {3.1}Induktionsschleifen}{6}{subsection.3.1} +\contentsline {subsection}{\numberline {3.2}Adaptive Steuerung von Ampelanlagen}{7}{subsection.3.2} +\contentsline {subsection}{\numberline {3.3}Macro- und microskopische Modellierung von Verkehr}{7}{subsection.3.3} +\contentsline {subsection}{\numberline {3.4}Induktionsschleifenwerte}{7}{subsection.3.4} +\contentsline {subsubsection}{\numberline {3.4.1}CSV-Daten der Stadt Darmstadt}{7}{subsubsection.3.4.1} +\contentsline {subsubsection}{\numberline {3.4.2}MYSQL-Daten des Projektes Verkehrsvisualisierung}{9}{subsubsection.3.4.2} +\contentsline {subsection}{\numberline {3.5}Geographischer Ausschnitt der Daten}{10}{subsection.3.5} +\contentsline {subsection}{\numberline {3.6}CAD-Zeichnungen der Kreuzungen}{10}{subsection.3.6} +\contentsline {subsection}{\numberline {3.7}Abbiegewahrscheinlichkeiten}{11}{subsection.3.7} +\contentsline {subsection}{\numberline {3.8}Das Zeitproblem}{11}{subsection.3.8} +\contentsline {subsection}{\numberline {3.9}Das Abbiegeproblem}{12}{subsection.3.9} +\contentsline {section}{\numberline {4}Verkehrsmodell}{13}{section.4} +\contentsline {subsection}{\numberline {4.1}Modell der Ministadt}{13}{subsection.4.1} +\contentsline {subsection}{\numberline {4.2}Modell als Graph}{15}{subsection.4.2} +\contentsline {subsubsection}{\numberline {4.2.1}Kreuzungsgraph}{16}{subsubsection.4.2.1} +\contentsline {subsubsection}{\numberline {4.2.2}Kreuzungs\active@dq \dq@prtct {u}bersicht}{17}{subsubsection.4.2.2} +\contentsline {subsection}{\numberline {4.3}Modell als Matrix}{17}{subsection.4.3} +\contentsline {subsubsection}{\numberline {4.3.1}Ausgangsmatrix}{18}{subsubsection.4.3.1} +\contentsline {subsubsection}{\numberline {4.3.2}Eingangsmatrix}{18}{subsubsection.4.3.2} +\contentsline {subsubsection}{\numberline {4.3.3}Sonderfall: Vallidierungssensor}{19}{subsubsection.4.3.3} +\contentsline {subsection}{\numberline {4.4}Datenbankmodell}{19}{subsection.4.4} +\contentsline {subsubsection}{\numberline {4.4.1}Datenbank Schema}{20}{subsubsection.4.4.1} +\contentsline {subsection}{\numberline {4.5}Einschr\active@dq \dq@prtct {a}nkungen und Voraussetzungen f\active@dq \dq@prtct {u}r das Modell}{22}{subsection.4.5} +\contentsline {section}{\numberline {5}L\active@dq \dq@prtct {o}sungsans\active@dq \dq@prtct {a}tze}{23}{section.5} +\contentsline {subsection}{\numberline {5.1}L\active@dq \dq@prtct {o}sungsansatz: Hidden Markow Modell}{23}{subsection.5.1} +\contentsline {subsubsection}{\numberline {5.1.1}Grundlagen}{23}{subsubsection.5.1.1} +\contentsline {subsubsection}{\numberline {5.1.2}HMM f\active@dq \dq@prtct {u}r eine Kreuzung}{23}{subsubsection.5.1.2} +\contentsline {subsection}{\numberline {5.2}L\active@dq \dq@prtct {o}sungsansatz: Wegfindungsalgorithmen}{23}{subsection.5.2} +\contentsline {subsection}{\numberline {5.3}L\active@dq \dq@prtct {o}sungsansatz: Lineares Gleichungssystem}{24}{subsection.5.3} +\contentsline {subsubsection}{\numberline {5.3.1}Grundlagen}{24}{subsubsection.5.3.1} +\contentsline {subsubsection}{\numberline {5.3.2}Lineares Gleichungssystem einer Kreuzung}{24}{subsubsection.5.3.2} +\contentsline {subsection}{\numberline {5.4}Kreuzungsberechnung am Graphen}{26}{subsection.5.4} +\contentsline {subsubsection}{\numberline {5.4.1}Verkehrsfluss zwischen Kreuzungen}{26}{subsubsection.5.4.1} +\contentsline {section}{\numberline {6}Visualisierung}{27}{section.6} +\contentsline {subsection}{\numberline {6.1}Visualisierung des Graphen mit Geoinformationen}{27}{subsection.6.1} +\contentsline {subsection}{\numberline {6.2}Visualisierung des JGraphT-Graphen}{27}{subsection.6.2} +\contentsline {section}{\numberline {7}Validierung}{28}{section.7} +\contentsline {subsection}{\numberline {7.1}Testdatenmenge}{28}{subsection.7.1} +\contentsline {subsection}{\numberline {7.2}Verkehrsz\active@dq \dq@prtct {a}hlung}{28}{subsection.7.2} +\contentsline {subsection}{\numberline {7.3}Validierung der Verkehrsaufkommensvorhersage}{28}{subsection.7.3} +\contentsline {subsection}{\numberline {7.4}Überprüfung des Modells}{28}{subsection.7.4} +\contentsline {section}{\numberline {8}Ausblick}{29}{section.8} +\contentsline {section}{\numberline {9}Glossar}{31}{section.8} +\contentsline {section}{\numberline {10}Abbildungsverzeichnis}{32}{section.8} +\contentsline {section}{\numberline {11}Quellcodeverzeichnis}{32}{section.8} +\contentsline {section}{\numberline {12}Anhang}{33}{section.12} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex index 0b801e06..4fde0b26 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex @@ -10,4 +10,9 @@ Sollten in einer Stadt fl"achendeckend validierende Ausgangssensoren verbaut sei Die durch Modell und Berechnung gewonnenen Erkenntnisse k"onnen zur Optimierung von Verkehr, als Analysetool oder zur Planung von neuen Kreuzungen eingesetzt werden. Es ist damit zurechnen, dass mehr Sensoren auf die Stra"se gelangen werden. So plant Deutschland in einer gesetzesin [] allen Autofahrern vorzuschreiben eine sog. 'Blackbox' im auto zu verbauen. Diese Blackboxen sollen GPS, Brems- und Beschleunigungsverhalten messen. Stehen diese Daten zur Verf"ugung kann man auf eine Vielzahl von Sensoren zur"uckgreifen und die Verkehrsinformationen werden verl"asslicher. -Dadurch w"urde eine Genauere und bessere Modellierung des Verkehrs m"oglich. \ No newline at end of file +Dadurch w"urde eine Genauere und bessere Modellierung des Verkehrs m"oglich. + +[mehr sensordaten] +[genauere sensordaten] +[genauere abbiegewahrscheinlichkeiten] +[validierungssensoren] \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex index bea1db98..dd158ab9 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex @@ -1,31 +1,40 @@ \label{sec:berechnung} -In diesem Kapitel werden drei Lösungsansätze für die Herausforderungen der Verkehrsflussberechnung anhand des in Kapitel \autoref{sec:modell} beschrieben Modells vorgestellt. Dabei konnten für Kreuzungen ein lineares Gleichungssystem entwickelt werden, welches sowohl die Verkehrswerte für die Ausgänge als auch für die Eingänge der entsprechenden Kreuzung berechnen kann. Anhand der Berechnungen innerhalb von Kreuzungen konnten Verkehrsflusswerte für zwischen den Kreuzungen bestimmt werden.\\ \\ -Es galt folgende Herausforderung zu lösen: +In diesem Kapitel werden drei L"osungsans"atze f"ur die Herausforderungen der Verkehrsflussberechnung anhand des in Kapitel \autoref{sec:modell} beschrieben Modells vorgestellt. Dabei konnten f"ur Kreuzungen ein lineares Gleichungssystem entwickelt werden, welches sowohl die Verkehrswerte f"ur die Ausg"ange als auch f"ur die Eing"ange der entsprechenden Kreuzung berechnen kann. Anhand der Berechnungen innerhalb von Kreuzungen konnten Verkehrsflusswerte f"ur zwischen den Kreuzungen bestimmt werden.\\ \\ +Es galt folgende Herausforderung zu l"osen: \begin{enumerate} - \item{Werte für virtuelle Sensoren}\label{problem:1} - \item{Wie viele Autos verlassen die Kreuzung in Richtung Norden/Süden/Westen/Osten}\label{problem:3} - \item{Wie viele Autos kommen auf die Kreuzung aus Richtung Norden/Süden/Westen/Osten}\label{problem:4} + \item{Werte f"ur virtuelle Sensoren}\label{problem:1} + \item{Wie viele Autos verlassen die Kreuzung in Richtung Norden/S"uden/Westen/Osten}\label{problem:3} + \item{Wie viele Autos kommen auf die Kreuzung aus Richtung Norden/S"uden/Westen/Osten}\label{problem:4} \item{Validierung von Sensorwerten, mithilfe von Validierungssensoren}\label{problem:2} - \item{Verkehrswerte für Seitenstraßen ohne Sensoren}\label{problem:5} + \item{Verkehrswerte f"ur Seitenstraßen ohne Sensoren}\label{problem:5} + \item{Fl"ussen zwischen den Kreuzungen} + \item{Werte f"ur Kreuzungen ohne Sensoren} + \item{Blick in die Zukunft} \end{enumerate} -Es wurden im Rahmen dieser Arbeit mehrere Berechnungsansätze daraufhin überprüft, ob sie eines der gegebenen Problem lösen kann. Die beschriebenen Ansätze sind 'Hidden Markow Modell', 'Wegfindungsalorithmen' wie A* und 'lineares Gleichungssystem'. \\ \\ -Das Ziel für \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 Eingänge modellieren würden damit ebenfalls die Herausforderung einen Verkehrswert für die jeweiligen Kreuzungsein- und -ausgänge zu berechnen gelöst werden. -\subsection{L"osungsansatz: Hidden Markow Modell}{\label{sec:berechnung:hmm} +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. Im Folgendem werden die Grundlagen von Hidden Marokw Modellen umrissen. + \subsubsection{Grundlagen} + + \subsubsection{HMM f"ur eine Kreuzung} + Problem, nicht zyklischer Graph. Ein Verkehrsnetz hat viele Kreise und ein solches Modell ist aus diesen Gr"unden nicht sinnvoll. Als Ansatz kann man ein Markov-Modell auf einen zuf"allig ausgew"ahlten nicht zyklischen Graphen berechnen. Berechnet man nun viele solcher zuf"allig nicht zyklischen Graphen, und mittelt man die Werte f"ur die einzelnen unbekannten Sensoren, k"onnte eine 'gute' L"osung herauskommen.\\ Problem: Es ist nicht gegeben das die Daten dann noch irgend ein Realit"atsbezug haben, 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 kürzesten Weg zum Ziel finden und das dem Verhalten des Menschen ähnelt. 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 Lösung. Aus dem Studium bekannte Algorithmen wie der A* können ein solches Wegfindungsproblem lösen. Die Abschätzung für die Distanz zweier Knoten wäre dabei die Luftlinie. Da keine Werte über einzelne Autos, sondern nur Messwerte über eine Minute zur Verfügung standen musste nicht nur ein einzelnes Auto, sondern eine Autokolonne simuliert werden.\\ \\ - Allerdings stellte sich heraus das keinerlei Daten über das Ziel der Autofahrer in der Stadt Darmstadt bekannt oder gemessen wurden. Eine Erhebung war ebenfalls nicht möglich, da eine Vielzahl von Ausgängen aus der 'Ministadt' untersucht werden müssten. Da kein Wegfindungsalgorithmus ohne Ziel funktionieren kann wurden Wegfindungsalgorithmen verworfen. - } -\subsection{L"osungsansatz: Lineares Gleichungssystem}{\label{sec:berechnung:lgs} - Gehen wir von einem Geregelten, Verkehrsordnung achtenden Verkehr aus, k"onnen wir f"ur jeden Ausgangsknoten durch addition derjenigen Sensorwerte, welche auf den Ausgang zeigen berechnen, wieviele Autos am Ausgangsknoten angekommen sein m"ussen. Das Problem dabei sind die Mischspuren, "uber welche der Verkehr in verschiedene Richtungen flie"sen kann. F"ur diese Sensoren werden Abbiegewahrscheinlichkeiten ben"otigt um zu berechnen, wie viel Prozent der Autos, welche "uber den Sensor Fahren an dem jeweiligen Ausgangsknoten angelangen. Der Sensorwert wird entsprechend mit der jeweiligen Abbiegewahrscheinlichkeit multipliziert und auf den Ausgang addiert.\\ - Da lineare Gleichungssysteme das Ergebnis dieser Arbeit sind ist ihnen ein eigenes Kapitel, um genauer darauf einzugehen. - \subsubsection{Grundlagen}{\label{sec:berechnung:lgs:grund} +\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. Die Absch"atzung f"ur die Distanz zweier Knoten w"are dabei die Luftlinie. 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.\\ \\ + 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.\\ \\ + 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:\\ \begin{equation} \begin{matrix} @@ -34,11 +43,10 @@ Das Ziel für \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst &\vdots&&\vdots&\\ a_{m1} x_1 + a_{m2} x_2 \, + & \cdots & +\, a_{mn} x_n & = & b_m\\ \end{matrix} - \end{equation} - - Ein lineares Gleichungssystem ist lösbar, wenn alle Gleichungen erfüllbar sind. Ist dies nicht der Fall spricht man von einem unlösbaren Gleichungssystem.\\ - Lösbare Systeme lassen sich nochmals in die 'eindeutig Lösbaren' und 'nicht eindeutig Lösbaren' unterteilen. Für ein eindeutig lösbares Gleichungssystem kann eine numerische Lösung für $x_1$ bis $x_n$ gefunden werden, im Gegensatz zu nicht eindeutig Lösbaren System, für welche eine Lösung nur in Abhängigkeit von einem oder mehreren Parametern angeben werden kann.\\ \\ - Eine gängige Art der Darstellung von linearen Gleichungssystemen ist die Matrixdarstellung. Das System zerfällt dabei in drei Teile. Die Koeffizientenmatrix enthält dabei die Werte $a_{11}$ bis $a_{nm}$. Die unbekannten werden in einer einspaltigen Matrize zusammengefasst, ebenso wie die Ergebniswerte $b_1$ bis $b_m$. + \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.\\ \\ + Eine g"angige Art der Darstellung von linearen Gleichungssystemen ist die Matrixdarstellung. Das System zerf"allt dabei in drei Teile. Die Koeffizientenmatrix enth"alt dabei 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} a_{11} & a_{12} & \cdots & a_{1n} \\ @@ -61,13 +69,11 @@ Das Ziel für \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst b_n \\ \end{pmatrix} \end{equation} - Eine solche Gleichung kann mit einem beliebigem Lösungsverfahren wie z.b. dem Gaus-Algorithmus gelöst werden. Die Genauigkeit der Lösung hängt dabei von dem gewählten Verfahren ab. - } + Eine solche Gleichung kann mit einem beliebigem L"osungsverfahren wie z.b. dem Gaus-Algorithmus gel"ost werden. Die Genauigkeit der L"osung h"angt dabei von dem gew"ahlten Verfahren ab. - \subsubsection{Lineares Gleichungssystem einer Kreuzung}{\label{sec:berechnung:lgs:xr} - Die Beziehungen zwischen Induktionsschleifensensoren und Kreuzungsein- und Ausgangängen kann durch eine lineares Gleichungssystem ausgedrückt werden. Der Wert für den Ausgang errechnet sich aus der Summe aller darauffolgenden, 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 under Mischspursensoren unterschieden werden. Einspursensoren können direkt auf den Ausgang addiert werden, während für Mischspursensoren eine Abbiegewahrscheinlichkeit benötigt wird, die Angibt, wie viel Verkehr in die entsprechende Richtung fließt. Durch Multiplikation des Sensorwertes mit der Abbiegewahrscheinlichkeit erhält man den gesuchten Teil des Verkehrs und kann diesen auf den Ausgang addieren. - Für den Ausgang der Kreuzung [] in richtung [] wäre dies folgende: - [Gleichung nur Einspur] + \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.\\ + 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} \end{equation} @@ -77,62 +83,101 @@ Das Ziel für \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst $ES_x$ bezeichnet alle Einspursensoren welche auf den Kreuzungsausgang x zeigen.\\ $MS_x$ bezeichnet alle Mehrspursensoren welche auf den Kreuzungsausgang x zeigen.\\ $ABW_xi$ 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. + $S_x$ 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 l"osen.\\ + Eine allgemeine Form ist die folgende: + [todo] + \begin{equation} + Kreuzungausgang_x = \sum ES_{xi} + \sum MS_{xj}*ABW_{xj} + \end{equation} + \begin{equation} + Kreuzungseingang_x = \sum S_{xi} + \end{equation} - Diese Berechnung erweist sich, da nur Einspursensoren in das Ergebnis einfließen, als trivial. Im Gegensatz zu Mischspursensoren, welche einen Wert für zwei oder mehr Ausgänge liefern. Ein Koeffizient für jede Richtung, in die ein Autofahrer, der den Sensor überfahren hat, bestimmt welcher Anteil des gemessen Verkehrswertes auf den jeweiligen Ausgang übertragen werden muss. Für diese Koeffizienten wurden die im Kapitel [Daten] vorgestellten Abbiegewahrscheinlichkeiten verwendet. Da alle Autos eine der Richtungen, welche ihnen die mit dem Sensor bestückte, Straße vorgibt, wählen müssen, muss die Summe aller Abbiegewahrscheinlichkeiten der verschiedenen Richtungen eins ergeben.\\ \\ + Hierf"ur 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 gnau einem Ausgang zugeordnet werden kann. 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 & D13 & D14\\ + A12 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + A28 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0\\ + \end{Bmatrix} + * + \begin{Bmatrix} + & count\\ + D1 & 1\\ + D2 & 2\\ + D3 & 3\\ + D4 & 4\\ + D5 & 5\\ + D6 & 6\\ + D7 & 7\\ + D8 & 8\\ + D9 & 9\\ + D10 & 0\\ + D13 & 0\\ + D14 & 0\\ + \end{Bmatrix} + = + \begin{Bmatrix} + & count\\ + A12 & 1\\ + A28 & 2\\ + A4 & 3\\ + \end{Bmatrix} + \end{equation} - [Lösbarkeit ohne Abbiegewahrscheinlichkeiten] + \begin{equation} + \begin{Bmatrix} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ + A12 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A4 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A104 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ + \end{Bmatrix} + * + \begin{Bmatrix} + & count\\ + D1 & 1\\ + D2 & 2\\ + D3 & 3\\ + D4 & 4\\ + D5 & 5\\ + D6 & 6\\ + D7 & 7\\ + D8 & 8\\ + D9 & 9\\ + D10 & 0\\ + D13 & 0\\ + D14 & 0\\ + \end{Bmatrix} + = + \begin{Bmatrix} + & count\\ + A12 & 1\\ + AA & 2\\ + A104 & 3\\ + \end{Bmatrix} + \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 auf 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. - Dekoriert man die Matrizen, welche im Kapitel [Modell], beschrieben werden, mit den Abbiegewahrscheinlichkeiten für die Mischspursensoren, lässt sich ein Gleichungssystem der Form - [Form] - aufstellen, welches jedem Kreuzungsaus- sowie -eingang einen Wert zuweist. + [virtuelle spursensoren] + [l"osbarkeit] + [zus"atzlich gleichungen] + [L"osbarkeit ohne Abbiegewahrscheinlichkeiten] + + \subsection{Kreuzungsberechnung am Graphen}{ + 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.\\ \\ + F"ur Eingangsknoten wird ausgehen von diesem alle ausgehenden Kanten des Graphen verfolgt und der Wert aller darauffolgender Knoten aufaddiert. Dies entspricht der in \ref{sec:berechnung:lgs:xr} beschrieben Berechnungsmethode f"ur Eingangsknoten. + [bild mit berechnung] + F"ur Ausgangsknoten einer Kreuzung kann das selbe Verfahren benutzt werden. Allerdings werden alle eingehenden Kanten, entgegen der Verkehrsflussrichtung, + vom Ausgangsknoten ausgehend, aufaddiert. F"ur Mischspursensoren wird dabei der Wert mit der an der Kante annotierten Abbiegewahrscheinlichkeit multipliziert. + [bild mit berechnung] - Zweirichtungeniterration vom Sensor weg. - - W"ahrend oben Verbindungsmatrizen beschrieben werden, welche ausschlie"slich modellieren, ob ein Knoten(virtuell oder Sensor) mit einem anderen verbunden ist, - so kann man bei bekannten Abbiegewahrscheinlichkeiten f"ur die Kreuzung diese direkt in der Ausgangsmatrix verzeichnen: - - \begin{figure}[htbp!] - \centering - \fbox{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} - \caption{Kreuzung A23} - \end{figure} - $\begin{Bmatrix} - & A12 & A4 & A104 \\ - D1 & 0 & 1 & 1 \\ - D2 & 0 & 1 & 0 \\ - D3 & 1 & 0 & 0 \\ - D4 & 0 & 0 & 1 \\ - D5 & 0 & 0 & 1 \\ - D6 & 0 & 1 & 0 \\ - D7 & 0 & 1 & 0 \\ - D8 & 1 & 0 & 0 \\ - D9 & 1 & 0 & 0 \\ - D10 & 0 & 0 & 1 \\ - D13 & 0 & 0 & 0 \\ - D14 & 0 & 0 & 0 - \end{Bmatrix}$ - - $\begin{Bmatrix} - & E1 & E2 & E3 & E4 \\ - S1 & 0.3 & 0.7 & 0 & 0 \\ - S2 & 0 & 0.2 & 0.8 & 0 \\ - S3 & 0 & 0 & 0 & 0 \\ - S4 & 0.9 & 0 & 0 & 0.1 - \end{Bmatrix}$ - - Diese Darstellung erwies sich als hilfreich zur Berechnung von Ausgangswerten f"ur eine Kreuzung. Siehe hierzu das Kapitel [Berechnung] + Wird dieses Verfahren f"ur alle Aus und Eing"ange einer Kreuzung durchgef"uhrt k"onnen f"ur alle ein Verkehrswert ausgerechnet werden. } - \subsection{Lineares Gleichungssystem am Graph}{ - Ein Gleichungssystem der Form (oben beschrieben) kann als graph dargestellt werden. Die berechnung des System kann ebenfalls am Graphen passieren. - - Ausgehend von einer direkten Verbindungen von Sensorknoten zu virtuellem Kreuzungsein- bzw. ausgang Knoten, kann um die Ausgänge zu berechnen der Graph entlangiterriert werden. Die Ausgänge berechnen sich dabei gegen die Flussrichtung. - Die Eingänge berechnen sich mit der Flussrichtung. - - Forward/Backward Iteration. - } - \subsubsection{Verkehrsfluss zwischen Kreuzungen}{ - - zwischen den Kreuzungen ist das Modell ungenau. Hier k"onnen wir die Verkehrsbelastung bestimmen. Und wir k"onnen Voraussagen, dass in der n"achsten Minute viele/wenige Autos an Kreuzung x von Kreuzung y ankommen werden - } + \subsubsection{Verkehrsfluss zwischen Kreuzungen} + Zwischen Kreuzungen ist das entwickelte Modell ungenau, da Seitenstraßen und Kreuzunge nicht modelliert sind. Es kann allerdings aufgrund der Berechnungen aus \autoref{sec:berechnung:lgs:xr} ein Wert f"ur den verkehr bestimmt werden, welche von einer Kreuzung ausgehend in eine bestimmte Richtung fließt. + Dieser Wert entspricht dem f"ur den Ausgang der Kreuzung berechneten Wert, da dieser Wert aussagt wie viele Autos die kreuzung in diese Richtung verlassen haben.\\ \\ + Dadurch dass die vorliegenden Sensordaten f"ur eine Minute gemessen wurden, kann leider nicht berechnet werden wieviel des verkehrs welcher eine kreuzung verl"asst an einer anderen wieder einfließt und welcher Teil in Seitenstraßen abgeflossen ist. } \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex index 70849065..6c8bd8b8 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex @@ -1,7 +1,7 @@ \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}{ - 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 und parallel zu einem Kondensator geschaltet. Durch Anlegen eines konstanten Gleichstroms erzeugen die Kabelschleifen ein Magnetfeld auf der Stra"se, welches sich ver"andert, wenn Autos darauf stehen oder dar"uber fahren. Diese Änderung ist an dem Induktionsstrom der Spule messbar. Unterschreitet die Spannung eine Schwelle wird der Sensor als belegt erkannt. Ist die Ver"anderung der Spannung von langer Dauer, ist der Sensor von einem darauf stehenden Auto belegt. Die Elektronik der Induktionsschleife wertet die gemessene "Anderung aus und liefert bereits aufbereitet Werte, welche Auskünfte über den Verkehr geben. 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.\\ \\ + 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 und parallel zu einem Kondensator geschaltet. Durch Anlegen eines konstanten Gleichstroms erzeugen die Kabelschleifen ein Magnetfeld auf der Stra"se, welches sich ver"andert, wenn Autos darauf stehen oder dar"uber fahren. Diese Änderung ist an dem Induktionsstrom der Spule messbar. Unterschreitet die Spannung eine Schwelle wird der Sensor als belegt erkannt. Ist die Ver"anderung der Spannung von langer Dauer, ist der Sensor von einem darauf stehenden Auto belegt. Die Elektronik der Induktionsschleife wertet die gemessene "Anderung aus und liefert bereits aufbereitet Werte, welche Ausk"unfte "uber den Verkehr geben. 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}} @@ -18,18 +18,18 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \end{enumerate} [Erkl"arung] Über die Fehlerh"aufigkeit liegen keine Daten der Stadt Darmstadt vor. - Die Gültigkeit der Induktionsschleifenwerte wird in dem Kapitel \autoref{sec:validierung} genauer behandelt.\\ \\ + 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.} \item{Mischspursensor: Ein Auto auf dieser Spur kann die Kreuzung in mehr als eine Richtung verlassen.} \end{enumerate} - 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. Dabei ist nicht berücksichtigt, dass ein Verkehrsteilnehmer mithilfe einer sog. 'U-Turn' die Kreuzung in die selbe Richtung verlassen kann, aus der er kommt. + 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. Dabei ist nicht ber"ucksichtigt, dass ein Verkehrsteilnehmer mithilfe einer sog. 'U-Turn' die Kreuzung in die selbe Richtung verlassen kann, aus der er kommt. } -\subsection{adaptive Steuerung von Ampelanlagen}{ +\subsection{Adaptive Steuerung von Ampelanlagen}{ Die auf den Stra"sen verbauten Induktionsschleifen dienen der verkehrsabh"angigen Steuerung von Ampelanlagen. 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.\\ \\ todo Ampelsteuerung - Durch eine solche Ampelsteuerung verkürzt die Haltezeiten von Autos und sorgt für einen flüssigeren Verkehr, im Vergleich zu einer statischen Ampelschaltung. Dies begründet sich darin, dass die Ampelschaltung eine Spur nur freischaltet, wenn ein Fahrzeug auf dem Sensor erkannt wurde. Es besteht außerdem die Möglichkeit die Ampelphase so lange zu verlängern, bis eine Lücke in der Fahrzeugkolonne erkannt wird.\\ \\ + Durch eine solche Ampelsteuerung verk"urzt 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 ein Fahrzeug auf dem Sensor erkannt wurde. Es besteht außerdem die M"oglichkeit die Ampelphase so lange zu verl"angern, bis eine L"ucke in der Fahrzeugkolonne erkannt wird.\\ \\ Werden die Induktionsschleifen an den Haltelinien einer Kreuzung verbaut, k"onnen sie au"serdem verwendet werden um Rotlichtverst"o"se automatisch erkannt werden. } \subsection{Macro- und microskopische Modellierung von Verkehr}{ @@ -38,23 +38,23 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be } \subsection{Induktionsschleifenwerte}{ - Für die Untersuchungen dieser Arbeit stellte die Stadt Darmstadt\footnote{\url{http://www.darmstadt.de/}} die Werte der in der Stadt verbauten Induktionsschleifen. Die Daten werden in der 'live' gemessen, und für die adaptive Ampelsteuerung eingesetzt. Für diese Arbeit standen allerdings nur Daten zur Verfügung, welche über einen Zeitraum von einer Minute gemessen wurden. - Die Induktionsschleifen liefern die Werte 'count' und 'load' welche Auskunft über die Anzahl der Autos gibt, welche den Sensor passiert haben und wie lange dieser Sensor belegt war. \\ - Die Induktionsschleifen sind dabei fast ausschlie"slich an den Kreuzungseing"angen in den Stra"sen verbaut und werden über 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. Die Daten werden in der '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 passiert haben und wie lange dieser Sensor belegt war. \\ + Die Induktionsschleifen sind dabei fast ausschlie"slich an den Kreuzungseing"angen in den Stra"sen verbaut und 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 natürlich Zahl, einschlie"slich der Null.\\ \\ + 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 Verfügung 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}. + 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}. \subsubsection{CSV-Daten der Stadt Darmstadt}{ - Die von der Stadt Darmstadt zur Verfügung gestellten CSV-Dateien übermitteln die gesamten Sensorwerte der Induktionsschleifen der Stadt Darmstadt in zwei Teilen, dem Bereich 'Darmstadt Süd' und den von 'Darmstadt Nord'.\\ \\ + Die von der Stadt Darmstadt zur Verf"ugung gestellten CSV-Dateien "ubermitteln die gesamten Sensorwerte der Induktionsschleifen der Stadt Darmstadt in zwei Teilen, dem Bereich 'Darmstadt S"ud' und den von 'Darmstadt Nord'.\\ \\ Die CSV Datei ist speziell kodiert und bietet folgende Spalten an Information an: \begin{enumerate} \item{Datum und Uhrzeit der Messung} \item{Die Bezeichnung der Kreuzung} \item{Die Intervall"ange der Messung in Minuten} - \item{Die Werte 'load' und 'count' für bis zu 64 Sensoren} + \item{Die Werte 'load' und 'count' f"ur bis zu 64 Sensoren} \end{enumerate} - Die Bezeichnung der Kreuzung richtet sich dabei nach der Kreuzungsbezeichnung des Verkehrsamtes Darmstadt und ist eindeutig. Eine übersicht über ganz Darmstadt mit eingezeichneten kreuzung ist im Anhang \ref{abb:4} zu finden. Ein Kreuzungsname in Darmstadt besteht dabei aus einem 'A' und einer eindeutigen Nummer. Die L"ange des Messintervalls ist in Darmstadt als eine Minute definiert. + Die Bezeichnung der Kreuzung richtet sich dabei nach der Kreuzungsbezeichnung des Verkehrsamtes Darmstadt und ist eindeutig. Eine "ubersicht "uber ganz Darmstadt mit eingezeichneten kreuzung ist im Anhang \ref{abb:4} zu finden. Ein Kreuzungsname in Darmstadt besteht dabei aus einem 'A' und einer eindeutigen Nummer. Die L"ange des Messintervalls ist in Darmstadt als eine Minute definiert. \begin{figure} \begin{tabular}{|l|l|l|l|lllllllllllll|} Datum& Uhrzeit& Bez.& Intv.& D1Z& D1B& D2Z& D2B& D3Z& D3B& D4Z& D4B& D5Z& D5B& \dots& D64Z& D64B\\ @@ -99,19 +99,19 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \end{tabular} \caption{CSV-Datei Ausschnitt} \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. Für eine Kreuzung k"onnen dabei bis zu 64 Sensoren in der CSV bereitgestellt werden. + 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{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. Einige Übersetzungstabellen sowie die CAD-Zeichnung sind im Anhang zu finden []. } \subsubsection{MYSQL-Daten des Projektes Verkehrsvisualisierung}{ - Im Rahmen der Arbeit von \cite{thesis:mueller}, welche die Sensorwerte auf eine Karte projeziert, wurden die CSV-Dateien bereits in eine MYSQL-Datenbank überführt. - Die Sensordaten sind dort bereits mit Geoinformationen des OpenStreetMap Projektes verknüpft und geben Auskunft über Kreuzung- und Sensorpositionen.\\ \\ + Im Rahmen der Arbeit von \cite{thesis:mueller}, welche die Sensorwerte auf eine Karte projeziert, wurden die CSV-Dateien bereits in eine MYSQL-Datenbank "uberf"uhrt. + Die Sensordaten sind dort bereits mit Geoinformationen des OpenStreetMap Projektes verkn"upft und geben Auskunft "uber Kreuzung- und Sensorpositionen.\\ \\ Die Daten verwendeten Daten befinden sich dort in drei Tabelle: \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 bezüglich seiner Position in der CSV-Datei.} + \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 gespeicherte Sensorposition zu ermitteln wurde eine SQL-Abfrage\ref{lst:sql_sensorquery} entwickelt, welche Kreuzungs- und Sensornamen, sowie dessen jeweiligen Latitude und Longitude zurückgibt. Die Auswahl ist dabei auf die zehn untersuchten Kreuzungen beschr"ankt. Mehr Informationen zu dem gew"ahlten Ausschnitt sind [] zu finden. + 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. Mehr Informationen zu dem gew"ahlten Ausschnitt sind [] zu finden. \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, @@ -126,7 +126,7 @@ 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 über einen bestimmten Zeitraum. Zu Identifizierung des Sensors wird der CSV-Offset benutzt. + Eine weitere Abfrage dient dem Ermitteln der Sensorwerte "uber einen bestimmten Zeitraum. Zu Identifizierung des Sensors wird der CSV-Offset benutzt. \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, @@ -144,19 +144,19 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be AND sensors.CSVOFFSET=raw.CSVOFFSET \end{lstlisting} \end{minipage} - Zu beachten ist, dass die Zeitabfrage nach UTC-Zeit durchgeführt werden muss. + Zu beachten ist, dass die Zeitabfrage nach UTC-Zeit durchgef"uhrt werden muss. Mithilfe dieser Abfragen konnten alle ben"otigten Informationen aus der Datenbank extrahiert werden. Wie diese abgespeichert wurde wird im Kapitel \autoref{sec:modell} n"aher behandelt. } } \subsection{Geographischer Ausschnitt der Daten}{ - Um die Komplexit"at, Modellierungsaufwand und den Aufwand der Berechnungen zu reduzieren, wurde das untersuchte Gebiet auf einen kleinen Ausschnitt der Stadt (im folgenden Ministadt genannt) beschr"ankt. Dieser Ausschnitt erstreckt sich über zehn Kreuzungen, der A3, A4, A5, A12, A23, A28, A29, A46, A59 und A104. + Um die Komplexit"at, Modellierungsaufwand und den Aufwand der Berechnungen zu reduzieren, wurde das untersuchte Gebiet auf einen kleinen Ausschnitt der Stadt (im folgenden Ministadt genannt) beschr"ankt. Dieser Ausschnitt erstreckt sich "uber zehn Kreuzungen, der A3, A4, A5, A12, A23, A28, A29, A46, A59 und A104. \begin{figure} \centering \includegraphics[width=0.5\textwidth]{pic/overview_ministadt} \caption{Ministadt, Ausschnitt von Darmstadt der innerhalb dieser Arbeit betrachtet wird.} \end{figure} - Die Wahl des Ausschnitts richtete sich insbesondere nach der Anzahl der verbauten Sensorik. So finden sich auf allen zehn Kreuzungen 89 Sensoren, für welche Sensorwerte zur Verfügung stehen. Neben der Anzahl der Sensoren wurde auch darauf geachtet, dass die untersuchten Kreuzungen sog. Sonderf"allen aufweisen. Diese Sonderf"alle sind im folgenden beschrieben: + Die Wahl des Ausschnitts richtete sich insbesondere nach der Anzahl der verbauten Sensorik. So finden sich auf allen zehn Kreuzungen 89 Sensoren, f"ur welche Sensorwerte zur Verf"ugung stehen. Neben der Anzahl der Sensoren wurde auch darauf geachtet, dass die untersuchten Kreuzungen sog. Sonderf"allen aufweisen. Diese Sonderf"alle sind im folgenden beschrieben: \begin{enumerate} \item{Einbahnstra"sen: Eine Stra"se, welche nur in eine Richtung befahren werden darf.} \item{Mischspuren: Kreuzungseingangsfahrspuren, welche dem Verkehrsteilnehmer, welcher daruf steht, erlauben die Kreuzung in mehr als eine Richtung zu verlassen.} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex index 1dbd9a89..9afbc602 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex @@ -1,17 +1,17 @@ \label{sec:einleitung} -Die Anzahl der LKWs und PKWs steigt seit 1950 ständig an. +Die Anzahl der LKWs und PKWs steigt seit 1950 st"andig an. [stats] \cite{web:statista:lkw}\cite{web:statista:pkw} -Die gr"o"ser werdende Anzahl der Verkehrsteilnehmer und die damit verbundenen Massen an Autos auf den Stra"sen wird zunehmend zu einer Herausforderung für die Städte, Stra"sen, Mensch und Umwelt. +Die gr"o"ser werdende Anzahl der Verkehrsteilnehmer und die damit verbundenen Massen an Autos auf den Stra"sen wird zunehmend zu einer Herausforderung f"ur die St"adte, Stra"sen, Mensch und Umwelt. [stats] \cite{web:statista:laerm}\\ \\ -Aus diesem Grund ist die Analyse und Optimierung des Verkehrs ein wichtiger Bestandteil der Arbeit der Verkehrs"amter, damit der Verkehr weiterhin reibungslos funktioniert und den gestiegenen Anforderungen unsere Zeit gewachsen bleibt. Neben den zuständigen Verkehrsämter, haben sich einige Firmen auf dieses Thema spezialisiert und bieten Analysetools f"ur den Verkehr an. So bietet das Programm VISSIM\footnote{http://www.vissim.de} und PELOPS\footnote{PELOPS: Programm zur Entwicklung Längsdynamischer, mikrOskopischer VerkehrsProzesse in Systemrelevanter Umgebung} eine mikroskopische Modellierung des Verkehrssystems an. \\ +Aus diesem Grund ist die Analyse und Optimierung des Verkehrs ein wichtiger Bestandteil der Arbeit der Verkehrs"amter, damit der Verkehr weiterhin reibungslos funktioniert und den gestiegenen Anforderungen unsere Zeit gewachsen bleibt. Neben den zust"andigen Verkehrs"amter, haben sich einige Firmen auf die Untersuchung des Verkehrs spezialisiert und bieten Analysetools f"ur den Verkehr an. So bietet das Programm VISSIM\footnote{http://www.vissim.de} und PELOPS\footnote{PELOPS: Programm zur Entwicklung L"angsdynamischer, mikrOskopischer VerkehrsProzesse in Systemrelevanter Umgebung} eine professionelle mikroskopische Modellierung des Verkehrssystems an. \\ Dabei ist das mikroskopische Modell nur eines von einer Vielzahl an Modellen, um den Verkehr zu simulieren... \\ \\ -Neben der Anzahl von Kraftfahrzeugen auf den Straßen nimmt die Anzahl der moderne adaptiven Ampelanlagen und deren Sensorik, welche in den Stra"sen verbaut ist, zu und erlaubt es heute eine Analyse des Verkehrs auch ohne große manuelle Datenerhebungen durchzuf"uhren um den Verkehr zu untersuchen. Da die Sensorik, welche zur Steuerung der Ampelanlagen eingesetzt wird, die Aufgabe hat Autos zu erkennen und zu zählen wird in dieser Arbeit diskutiert in wieweit die Sensordaten ausreichen, um den Fluss des Verkehrs auf Kreuzungen und zwischen diesen zu modellieren.\\ \\ -Für diese Aufgabe stehen die Sensordaten von den Straßen der Stadt Darmstadt zur Verfügung, welche in einer Vielzahl ihrer Kreuzungen mit sog. Induktionsschleifen als Verkehrssensoren bestückt hat. Diese liefern Messwerte über die Anzahl der Autos, welche den Sensor passiert und solche die auf dem Sensor gestanden haben. Sie dienen dabei der adaptiven Steuerung des Verkehrs. Eine Beschreibung von Induktionsschleifen, sowie die genau Beschreibung der Daten der Stadt Darmstadt, wird im Kapitel \autoref{sec:datengrund} beschrieben.\\ \\ -Die Stadt Darmstadt stellte ihre Daten der Induktionsschleifen auf Anfrage zur Verf"ugung. Diese Sensorwerte werden in dieser Arbeit nicht zur Ampelsteuerung, allerdings f"ur die Berechnung von Verkehrsflüssen und der Vorhersage von Verkehr benutzt. Dafür wird ein Modell eines Teilausschnitts der Stadt Darmstadt erstellt und der Verkehr mithilfe der Induktionsschleifenwerte berechnet. Das entwickelte Modell ist dabei ein Graph und wird im Kapitel \autoref{sec:modell} beschrieben.\\ +Neben der Anzahl von Kraftfahrzeugen auf den Straßen nimmt die Anzahl der moderne adaptiven Ampelanlagen und deren Sensorik, welche in den Stra"sen verbaut ist, zu und erlaubt es heute eine Analyse des Verkehrs auch ohne große manuelle Datenerhebungen durchzuf"uhren um den Verkehr zu untersuchen. Da die Sensorik, welche zur Steuerung der Ampelanlagen eingesetzt wird, die Aufgabe hat Autos zu erkennen und zu z"ahlen wird in dieser Arbeit diskutiert in wieweit solche Sensordaten ausreichen, um den Fluss des Verkehrs auf Kreuzungen und zwischen diesen zu modellieren.\\ \\ +F"ur diese Aufgabe stehen die Sensordaten von den Straßen der Stadt Darmstadt zur Verf"ugung, welche in einer Vielzahl ihrer Kreuzungen mit sog. Induktionsschleifen als Verkehrssensoren best"uckt hat. Diese liefern Messwerte "uber die Anzahl der Autos, welche den Sensor passiert und solche die auf dem Sensor gestanden haben. Sie dienen dabei der adaptiven Steuerung des Verkehrs. Eine Beschreibung von Induktionsschleifen, sowie die genau Beschreibung der Daten der Stadt Darmstadt, wird im Kapitel \autoref{sec:datengrund} beschrieben.\\ \\ +Die Stadt Darmstadt stellte ihre Daten der Induktionsschleifen auf Anfrage zur Verf"ugung. Diese Sensorwerte werden in dieser Arbeit nicht zur Ampelsteuerung, allerdings f"ur die Berechnung von Verkehrsfl"ussen und der Vorhersage von Verkehr benutzt. Daf"ur wird ein Modell eines Teilausschnitts der Stadt Darmstadt erstellt und der Verkehr mithilfe der Induktionsschleifenwerte berechnet. Das entwickelte Modell ist dabei ein Graph und wird im Kapitel \autoref{sec:modell} beschrieben.\\ Diese Arbeit besch"aftigt sich neben der Auswertung dieser Daten und der Modellierung des Vekehrs mit der Fragestellung inwieweit der Verkehr anhand der Induktionsschleifenwerte rekonstruiert werden kann und mit welcher Genauigkeit. Au"serdem wird versucht f"ur eine kurze Zeitperiode in der Zukunft eine Vorhersage zu treffen, wie der Verkehr dann aussieht.\\ -Die Problematik die sich dabei auftut ist, dass nicht alle Stra"sen und Kreuzungen der Stadt Darmstadt mit Induktionsschleifen ausgestattet sind. Man m"ochte allerdings gerne Verkehrswerte f"ur diese, nicht bekannten Bereiche, berechnen oder absch"atzen, um die momentane Verkehrssituation besser einsch"atzen zu können und sich einen Überblick über die aktuelle Verkehrslage zu verschaffen.\\ -Lösungsansätze werden dafür in Kapitel \autoref{sec:berechnung} vorgestellt. Für Kreuzungen konnte dabei eine Lösung auf Basis lineare Gleichungssysteme errechnet werden. -Auch wenn alle Induktionsschleifenwerte der Stadt Darmstadt zur Verf"ugung stehen, so wurde in dieser Arbeit nur ein kleiner Ausschnitt von Darmstadt betrachtet, die sog. 'Ministadt', welcher sich über zehn Kreuzungen erstreckt. Dabei wurde der Ausschnitt so gew"ahlt, dass einige Sonderf"alle abgedeckt sind, wie z.b. eine Einbahnstra"se. Allerdings spielte bei der Auswahl des Gebiets auch die hohe Abdeckung mit Sensoren, welche auf den gewählten Kreuzungen zur Verfügung stehen.\\ +Die Problematik die sich dabei auftut ist, dass nicht alle Stra"sen und Kreuzungen der Stadt Darmstadt mit Induktionsschleifen ausgestattet sind. Man m"ochte allerdings gerne Verkehrswerte f"ur diese, nicht bekannten Bereiche, berechnen oder absch"atzen, um die momentane Verkehrssituation besser einsch"atzen zu k"onnen und sich einen Überblick "uber die aktuelle Verkehrslage zu verschaffen.\\ +L"osungsans"atze werden daf"ur in Kapitel \autoref{sec:berechnung} vorgestellt. F"ur Kreuzungen konnte dabei eine L"osung auf Basis lineare Gleichungssysteme errechnet werden. +Auch wenn alle Induktionsschleifenwerte der Stadt Darmstadt zur Verf"ugung stehen, so wurde in dieser Arbeit nur ein kleiner Ausschnitt von Darmstadt betrachtet, die sog. 'Ministadt', welcher sich "uber zehn Kreuzungen erstreckt. Dabei wurde der Ausschnitt so gew"ahlt, dass einige Sonderf"alle abgedeckt sind, wie z.b. eine Einbahnstra"se. Allerdings spielte bei der Auswahl des Gebiets auch die hohe Abdeckung mit Sensoren, welche auf den gew"ahlten Kreuzungen zur Verf"ugung stehen.\\ \begin{figure} \centering @@ -19,39 +19,52 @@ Auch wenn alle Induktionsschleifenwerte der Stadt Darmstadt zur Verf"ugung stehe \caption{Ministadt, ausschnitt von Darmstadt der innerhalb dieser Arbeit betrachtet wird.} \end{figure} -Die Einschr"ankung auf das verkleinerte Gebiet begr"undet sich aus der Menge der zu betrachtenden Daten. Das Betrachten eines kleineren Ausschnitts erm"oglichte es im Rahmen dieser Arbeit eine genauere Untersuchung durchzuf"uhren als das auf dem gesamten Stadtgebiet der Stadt Darmstadt der Fall w"are. Näheres wird im Kapitel [Daten] beschrieben.\\ +Die Einschr"ankung auf das verkleinerte Gebiet begr"undet sich aus der Menge der zu betrachtenden Daten. Das Betrachten eines kleineren Ausschnitts erm"oglichte es im Rahmen dieser Arbeit eine genauere Untersuchung durchzuf"uhren als das auf dem gesamten Stadtgebiet der Stadt Darmstadt der Fall w"are. N"aheres wird im Kapitel [Daten] beschrieben.\\ -Dabei erwies sich den Zusammenhang zwischen zwei Sensorwerten zweier Kreuzungen herzustellen als elementares Problem, welches 'Zeitproblem' getauft wurde. Es beschreibt, das es nicht trivial ist festzustellen, welcher Sensorwert zur Zeit X in Beziehung zu einem anderen Sensorwert zum Zeitpunkt Z steht. Näheres dazu im Kapitel [Berechnung].\\ +Dabei erwies sich den Zusammenhang zwischen zwei Sensorwerten zweier Kreuzungen herzustellen als elementares Problem, welches 'Zeitproblem' getauft wurde. Es beschreibt, das es nicht trivial ist festzustellen, welcher Sensorwert zur Zeit X in Beziehung zu einem anderen Sensorwert zum Zeitpunkt Z steht. N"aheres dazu im Kapitel [Berechnung].\\ -Durch lineare Gleichungssysteme konnten Verkehrswerte für und zwischen Kreuzungen ausgerechnet werden. Grundlage dieser Berechnung sind Matrizenmultiplikationen, welche in dieser Arbeit direkt am Graphen berechnet werden. -Diese Berechnungen wurden daraufhin mit einer Verkehrszählung überprüft. Da sich die Sensorwerte als besonders ungenau herausgestellt haben, wird nicht nur auf die Genauigkeit der Sensorwerte in dieser Arbeit eingegangen, auch verschiedene Lösungsvorschläge werden diskutiert, wie sich sowohl das 'Zeitproblem' lösen lässt, als auch die Genauigkeit der Sensoren erhöhen lässt. -Dabei wird auf Daten des Projekts [] zurückgegriffen, welche die Daten der Induktionsschleifen für ganz Darmstadt bereits in eine Datenbank ein gepflegt vorliegen hat. +Durch lineare Gleichungssysteme konnten Verkehrswerte f"ur und zwischen Kreuzungen ausgerechnet werden. Grundlage dieser Berechnung sind Matrizenmultiplikationen, welche in dieser Arbeit direkt am Graphen berechnet werden. +Diese Berechnungen wurden daraufhin mit einer Verkehrsz"ahlung "uberpr"uft. Da sich die Sensorwerte als besonders ungenau herausgestellt haben, wird nicht nur auf die Genauigkeit der Sensorwerte in dieser Arbeit eingegangen, auch verschiedene L"osungsvorschl"age werden diskutiert, wie sich sowohl das 'Zeitproblem' l"osen l"asst, als auch die Genauigkeit der Sensoren erh"ohen l"asst. +Dabei wird auf Daten des Projekts [] zur"uckgegriffen, welche die Daten der Induktionsschleifen f"ur ganz Darmstadt bereits in eine Datenbank ein gepflegt vorliegen hat. -In die Einleitung gehört: +In die Einleitung geh"ort: • Motivation der Arbeit: Warum ist das Thema wichtig? Kann so bleiben mit den Studien etc -• Warum ist die Aufgabe schwer zu lösen? Beschreibung der Problemstellung -• Wie wird die Aufgabe gelöst? Wie ist die Vorgehensweise? Was wird in welchem Kapitel gemacht? Kurzbeschreibung der Kapitel +• Warum ist die Aufgabe schwer zu l"osen? Beschreibung der Problemstellung +• Wie wird die Aufgabe gel"ost? Wie ist die Vorgehensweise? Was wird in welchem Kapitel gemacht? Kurzbeschreibung der Kapitel • Was sind die Ergebnisse? -• eventuell noch erzählen was Vissum macht und hier der aktuelle Stand ist. Weshalb meine Sachen für denen ihre +• eventuell noch erz"ahlen was Vissum macht und hier der aktuelle Stand ist. Weshalb meine Sachen f"ur denen ihre Sachen wichtig sind... • PTV Visum4 -: Software für Verkehrsanalysen, Verkehrsprognosen und GIS-orientierte Datenverwaltung. +: Software f"ur Verkehrsanalysen, Verkehrsprognosen und GIS-orientierte Datenverwaltung. • PTV Vissim5 -: Software für mikroskopische Verkehrssimulation +: Software f"ur mikroskopische Verkehrssimulation -\subsection{Zielsetzung}{ +zielsetzung \begin{itemize} - \item{Werte für virtuelle Sensoren} - \item{Flüssen zwischen den Kreuzungen} - \item{Werte für Kreuzungen ohne Sensoren} + \item{Werte f"ur virtuelle Sensoren} + \item{Fl"ussen zwischen den Kreuzungen} + \item{Werte f"ur Kreuzungen ohne Sensoren} \item{Blick in die Zukunft} \end{itemize} - Während der Modellierung wurden sog. 'virtuelle Sensoren' den real vorhandenen hinzugefügt, um Kreuzungen darstellen zu können. Als Zielsetzung wurde definiert Werte für diese zu berechnen. + W"ahrend der Modellierung wurden sog. 'virtuelle Sensoren' den real vorhandenen hinzugef"ugt, um Kreuzungen darstellen zu k"onnen. Als Zielsetzung wurde definiert Werte f"ur diese zu berechnen. - Die Zweistufenmodellierung erlaubt mit der Kreuzungsübersicht einen Blick auf alle modellierten Kreuzungen, stellt die Sensoren mit ihren Werten allerdings nicht dar. - Als Zielsetzung wurde definiert Flüsse zwischen den Kreuzungen zu bestimmen. + Die Zweistufenmodellierung erlaubt mit der Kreuzungs"ubersicht einen Blick auf alle modellierten Kreuzungen, stellt die Sensoren mit ihren Werten allerdings nicht dar. + Als Zielsetzung wurde definiert Fl"usse zwischen den Kreuzungen zu bestimmen. - Eine weitere Zielsetzung der Arbeit ist es Verkehrswerte für kleinere Kreuzungen ohne Sensoren zu berechnen. + Eine weitere Zielsetzung der Arbeit ist es Verkehrswerte f"ur kleinere Kreuzungen ohne Sensoren zu berechnen. Vorhersage des Verkehrs -} \ No newline at end of file + +Diese Arbeit besch"aftigt sich prim"ar mit der analyse eines Sensornetzwerkes, den Stra"sensensoren. +Sie ist daher dem Forschungsgebiet des [XXX] zuzuordnen. Allerdings besch"aftigt sie sich ebenfalls +mit Verkehrstechniken und Graphenalgorithmen. Im folgenden werden einige ausgew"ahlt Publikationen +vorgestellt. + +Michael Scholz BA +Verkehrstools, micro modellierung +Stadt darmstadt monitoring tool, unsofisticated +Christians verkehrstools + +diplomarbeit mazur.pdf +diplomarbeit steffen buhle.pdf +neubert.pdf \ 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 f5949618..75bb9337 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex @@ -1,25 +1,25 @@ \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 für 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 für 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 können. Da die Sensorwerte, welche zur Verfügung stehen allerdings über einen Zeitraum von einer Minute aufgenommen werden, eignet sich eine Micromodellierung des Verkehrs nicht. Für einen solchen Modellierungsansatz sind genauere und mehr Daten notwendig. Es stehen allerdings lediglich Messwerte von 89 Sensoren zur Verfügung.\\ \\ -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 Straßenzüge 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 Rückfluss von Autos, welche eine sog. 'U-Turn' an einer Kreuzung vollführen, nicht mit dem entwickelten Modell modelliert werden.[]\\ \\ +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.\\ \\ +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.[]\\ \\ \subsection{Modell der 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-Übersichts-Karte[] der Stadt Darmstadt, die zur Verfügung steht. Eine genaue Beschreibung der 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-Übersichts-Karte[] der Stadt Darmstadt, die zur Verf"ugung steht. Eine genaue Beschreibung der Daten ist in Kapitel \autoref{sec:datengrund} zu finden.\\ \\ F"ur das hier entwickelte Stra"senmodell wurde das Straßennetz in sieben Objekte aufgeteilt und diese modelliert: \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.} \item{Kreuzung: Eine Kreuzung ist das Zusammentreffen von zwei Stra"sen. Sie kann mit Sensoren best"uckt sein, welche den Verkehr messen.} \item{Sensor: Ein Sensor misst den Verkehr an dem Punkt des Verkehrsnetzes, an dem er verbaut ist. Er ist auf einer Fahrspur verbaut.} \item{Virtuelle Sensoren: Punkte im Stra"sennetz, f"ur welche allerdings keine Messwerte vorliegen.} - \item{Fahrspur: Eine Fahrspur bezeichnet einen Bereich der Straßenfahrbahn und zeigt auf verschiedene Ausgänge der Kreuzung. Ein Kreuzungsein bzw. -ausgang kann mehrere Fahrspuren besitzen.} + \item{Fahrspur: Eine Fahrspur bezeichnet einen Bereich der Straßenfahrbahn und zeigt auf verschiedene Ausg"ange der Kreuzung. Ein Kreuzungsein bzw. -ausgang kann mehrere Fahrspuren besitzen.} \item{Kreuzungsausgang: Ein Ausgang einer Kreuzung auf dem verkehr die Kreuzung verlassen kann.} \item{Kreuzungseingang: Ein Eingang einer Kreuzung auf dem Verkehr die Kreuzung befahren kann.} \end{enumerate} Um eine "Ubersicht "uber das zu betrachtende Gebiet der 'Ministadt' zu erhalten wurde eine "Ubersicht "uber alle Kreuzungen in dem gesamten betrachteten Gebiet erstellt. In dieser Modellierung entfallen alle Seitenstra"sen und Zwischenkreuzungen ohne Sensoren. - Die Zwischenkreuzungen entfallen, da keinerlei Messdaten f"ur diese Kreuzungen vorhanden sind, weshalb die Kreuzungsübersicht eine Verallgemeinerung des Verkehrsnetzes darstellt. Es werden dabei nur sensorbestückte Kreuzungen aufgezeigt.\\ - Mit Rechtecke werden die betrachteten Kreuzungen vermerkt, mit Kreisen die nicht mehr modellierten Nachbarkeuzungen. Pfeile weisen dabei auf, in welche Richtung der Verkehr, regelkonform fließen darf. So ist von der Kreuzung A30 nach A104 eine Einbahnstraße an den einfachen Pfeilen zu erkennen, während Straßen, welche in beide Richtungen befahren werden können mit Doppelpfeilen dargestellt werden. + Die Zwischenkreuzungen entfallen, da keinerlei Messdaten f"ur diese Kreuzungen vorhanden sind, weshalb die Kreuzungs"ubersicht eine Verallgemeinerung des Verkehrsnetzes darstellt. Es werden dabei nur sensorbest"uckte Kreuzungen aufgezeigt.\\ + Mit Rechtecke werden die betrachteten Kreuzungen vermerkt, mit Kreisen die nicht mehr modellierten Nachbarkeuzungen. Pfeile weisen dabei auf, in welche Richtung der Verkehr, regelkonform fließen darf. So ist von der Kreuzung A30 nach A104 eine Einbahnstraße an den einfachen Pfeilen zu erkennen, w"ahrend Straßen, welche in beide Richtungen befahren werden k"onnen mit Doppelpfeilen dargestellt werden. \begin{figure}[htbp!] \centering @@ -27,9 +27,9 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \caption{Kreuzungs"ubersicht 'Ministadt'in der Stadt Darmstadt} \end{figure} - Um eine Übersicht über 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.\\ \\ + 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 Kreuzungsübersicht entfallen sehr viele Details, da keine Daten für bestimmte Bereiche vorhanden sind. Dagegen können die modellierten Kreuzungen wesentlich genauer dargestellt werden und lassen sich sehr gut auf Sensorebene modellieren. Neben den realen Sensoren erhält jede Kreuzung jeweils bis zu vier Ein- und Ausgänge, modelliert als 'virtuelle Sensoren'. Die Sensoren werden dabei nach den jeweiligen Kreuzungseingängen platziert, auf dem sie in der Realität in der Straße verbaut sind. Validierungssensoren sind solche welche Rückschlüsse auf andere Sensoren der Kreuzung zulassen. Sie werden in der manuellen Modellierung aufgezeigt. In der Matrixdarstellung findet sich allerdings keinen Platz für diese, da sie eine Grundannahme der Berechnung verletzte: + In der Kreuzungs"ubersicht entfallen sehr viele Details, da keine Daten f"ur bestimmte Bereiche 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 sie eine Grundannahme der Berechnung verletzte: 'Sensoren verbinden einen virtuellen Kreuzungseingang mit einem virtuellen Kreuzungsausgang.' Wie sich Sensoren mit Validierungssensoren validieren lassen wird im Kapitel [Berechnung] genauer behandelt.\\ Alle Sensoren wurde neben der Unterteilung nach Einspursensor und Mischspursensor nochmals in Subklassen unterschieden. Einspursensoren unterteilen sich dabei in drei Subklassen:\\ Virtuelle Sensoren weisen dabei das gleiche Verhalten wie reale Sensoren auf. Sie werden auf die gleiche Weise modelliert und lassen sie ebenfalls in verschiedene Klassen aufteilen, wie weiter unten beschrieben.\\ \\ @@ -48,19 +48,19 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{enumerate} Alle beschriebenen Sensorklassen und deren Subklassen sind in dem betrachteten Ausschnitt von Darmstadt enthalten.\\ \\ - Für die Modellierung der Kreuzungen sind mehr Daten, die Positionen der Induktionsschleifen, bekannt. Die Kreuzungen werden auf Sensorebene modelliert. Sensoren werden als Achtecke mit aufgetragenen Fließrichtungen dargestellt. Straßen werden, analog zur Kreuzungsübersicht als Pfeile mit ihrer Fließrichtung eingezeichnet. - Dekoriert wird ein Kreuzungsbild dabei mit bis zu acht virtuellen Knoten, jeweils ein rechteckiger für den jeweiligen Kreuzungsausgang, ein runden jeweils für den Kreuzungseingang. Die Position des Sensors wird dahingehend vereinfacht, das er einem Kreuzungseingang zugeordnet wird und wird direkt nach dem virtuellen Eingangssensor platziert. + F"ur die Modellierung der Kreuzungen sind mehr Daten, die Positionen der Induktionsschleifen, bekannt. Die Kreuzungen werden auf Sensorebene modelliert. Sensoren werden als Achtecke mit aufgetragenen Fließrichtungen dargestellt. Straßen werden, analog zur Kreuzungs"ubersicht als Pfeile mit ihrer Fließrichtung eingezeichnet. + Dekoriert wird ein Kreuzungsbild dabei mit bis zu acht virtuellen Knoten, jeweils ein rechteckiger f"ur den jeweiligen Kreuzungsausgang, ein runden jeweils f"ur den Kreuzungseingang. Die Position des Sensors wird dahingehend vereinfacht, das er einem Kreuzungseingang zugeordnet wird und wird direkt nach dem virtuellen Eingangssensor platziert. \begin{figure}[htbp!] \label{abb:9} \centering \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} \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 für die Berechnung als hinderlich. Aus diesem Grund werden bei der computergestützten Modellierung die Eingangssensoren direkt mit den jeweiligen Ausgängen 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 abzuschätzen, da zwar Informationen "uber die einzelnen Kreuzungen zur Verf"ugung stehen, allerdings diese noch nicht auf ein Gesamtbild des Verkehrs übertragen werden kann.\\ \\ . + 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 kann.\\ \\ . Die schw"ache des Modells ist die Annahme, dass ein Auto in Luftlinie von Eingangssensor zum Ausgangssensor f"ahrt und keine Geoinformationen "uber die Kanten, die Straßen, zur Verf"ugung stehen, auch wenn diese in der manuellen Modellierung angedeutet sind. - mehr schwächen todo + mehr schw"achen todo \subsection{Modell als 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. Graphen bieten dabei zwei Modellierungseinheiten, Knoten und Kanten.\\ \\ @@ -68,7 +68,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St 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 für Graphen mitbringt. + 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. @@ -89,7 +89,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{itemize} Ein Sensor kann dabei folgende Werte halten:\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -114,10 +114,10 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St } \end{lstlisting} \end{minipage} - Dies entspricht dem Datenbankschema in dem die Daten auf einem MYSQL-Server gespeichert werden. N"ahres dazu ist im Kapitel [Daten] zu finden. Ein Sensor kann dabei einen Wert im Feld 'Value' halten, welches von einer Induktionsschleife auf der Stra"se gemessen wurde. Für virtuelle Sensoren liegen keine Sensordaten vor. Der Wert 'Value' soll berechnet werden. Das Test Value dient der Validierung der Sensoren, um einen gemessenen Wert mit einem Berechneten vergleichen. outXR und inXR bezeichnen jeweils den Namen der Kreuzung von dem der Verkehr kommt bzw. wohin er flie"st, wenn er "uber den Sensor f"ahrt. + Dies entspricht dem Datenbankschema in dem die Daten auf einem MYSQL-Server gespeichert werden. N"ahres dazu ist im Kapitel [Daten] zu finden. Ein Sensor kann dabei einen Wert im Feld 'Value' halten, welches von einer Induktionsschleife auf der Stra"se gemessen wurde. F"ur virtuelle Sensoren liegen keine Sensordaten vor. Der Wert 'Value' soll berechnet werden. Das Test Value dient der Validierung der Sensoren, um einen gemessenen Wert mit einem Berechneten vergleichen. outXR und inXR bezeichnen jeweils den Namen der Kreuzung von dem der Verkehr kommt bzw. wohin er flie"st, wenn er "uber den Sensor f"ahrt. Eine Stra"se h"alt dagegen nur die Information der Abbiegewahrscheinlichkeit.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -129,11 +129,11 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St } \end{lstlisting} \end{minipage} - Die Werte 'Target' und 'Source' geben den jeweiligen Namen der n"achsten Kreuzung an. Dies dient nicht der Berechnung, sondern ausschließlich der Darstellung, um bei einer Straße, welche in beide Richtungen befahrbar ist, beide Fl"usse unterscheiden zu k"onnen. Dazu wird jeweils entweder 'Source' oder 'Target' für jede Kante mit angegeben. + Die Werte 'Target' und 'Source' geben den jeweiligen Namen der n"achsten Kreuzung an. Dies dient nicht der Berechnung, sondern ausschließlich der Darstellung, um bei einer Straße, welche in beide Richtungen befahrbar ist, beide Fl"usse unterscheiden zu k"onnen. Dazu wird jeweils entweder 'Source' oder 'Target' f"ur jede Kante mit angegeben. } \subsubsection{Kreuzungs"ubersicht}{ - Auch hier ist eine Reduktion auf Knoten und Kanten notwendig, um die Kreuzungsübersicht als graph darstellen zu können. Folgende intuitive Festlegungen wurden f"ur diese Arbeit dabei getroffen: + Auch hier ist eine Reduktion auf Knoten und Kanten notwendig, um die Kreuzungs"ubersicht als graph darstellen zu k"onnen. Folgende intuitive Festlegungen wurden f"ur diese Arbeit dabei getroffen: \begin{itemize} \item{Stra"se sei eine Kante} \item{Kreuzung sei ein Knoten} @@ -154,7 +154,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{itemize} 'XR' entspricht dabei dem oben beschrieben Graphen der Kreuzung, ST ist eine Stra"se, wie oben beschrieben.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -186,61 +186,54 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St } \subsection{Modell als Matrix}{ - Als Grundlage f"ur die Berechnung wurde eine Matrixdarstellung f"ur Kreuzungen entwickelt. Der oben entwickelte Graph l"asst sich dabei einfach in Matrixform "uberf"uhren. Matrizen bieten z.b. durch Matrixmultiplikation die M"oglichkeit komplexe Zusammenh"ange durch einfache Rechenschritte auszurechnen. - Um eine Kreuzung zu beschreiben ist es n"otig die Verbindungen von Sensoren zu deren m"oglichen Ausg"angen bzw . Eing"angen zu modellieren. 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 anzuwenden. - Die beschreibung der Verbindungen l"asst sich mit einer Verbindungsmatrix bewerkstelligen. Dabei wird zwischen den sog. Eingangsmatrizen und den sog. Ausgangsmatrizen unterschieden. - + 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. F"ur die Matrixdarstellung werden 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 direkt anzuwenden.\\ \\ + Die Beschreibung der Verbindungen l"asst sich mit einer Verbindungsmatrix bewerkstelligen. Dabei wird zwischen der sog. Eingangsmatrix und der sog. Ausgangsmatrix unterschieden. Beide Matrixformen zusammen bilden das Kreuzungsmodell ohne Validierungssensoren ab. \subsubsection{Ausgangsmatrix}{ Die Ausgangsmatrize zeigt auf, von welchem Sensor welcher Ausgang einer Kreuzung bedient wird. - Hierf"ur werden alle Ausg"ange einer Kreuzung auf der Y-Achse der Matrix verzeichnet, alle Sensoren dieser Kreuzung auf der X-Achse. Besteht eine Verbindung zwischen Sensor und Ausgang so kann an der entsprechenden Stelle der Matrix eine Verbindung markiert werden (1). Besteht dagegen keine Verbindung wird das ebenfalls markiert (0). - - Am Beispiel der Kreuzung A23 sei das hier demonstriert.\\ - \begin{figure}[htbp!] + Hierf"ur werden alle Ausg"ange einer Kreuzung auf der Y-Achse der Matrix verzeichnet, alle Sensoren dieser Kreuzung auf der X-Achse. Besteht eine Verbindung zwischen Sensor und Ausgang so kann an der entsprechenden Stelle der Matrix eine Verbindung mit '1' markiert werden. Besteht dagegen keine Verbindung wird das ebenfalls markiert mit einer '0'.\\ \\ + Die Allgemeine Form einer Ausgangsmatrix ist + $\begin{Bmatrix} + & S_1 & S_2 & S_3 & \dots & S_n\\ + Out_1 & 0/1 & 0/1 & \dots & 0/1\\ + Out_2 & 0/1 & 0/1 & \dots & 0/1\\ + Out_3 & 0/1 & 0/1 & \dots & 0/1\\ + Out_4 & 0/1 & 0/1 & \dots & 0/1\\ + \end{Bmatrix}$ + $Out_1$ bis $Out_4$ bezeichnen dabei die Ausg"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 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}} \caption{Kreuzung A23} \end{figure} - - $\begin{Bmatrix} - & A12 & A4 & A104 \\ - D1 & 0 & 1 & 1 \\ - D2 & 0 & 1 & 0 \\ - D3 & 1 & 0 & 0 \\ - D4 & 0 & 0 & 1 \\ - D5 & 0 & 0 & 1 \\ - D6 & 0 & 1 & 0 \\ - D7 & 0 & 1 & 0 \\ - D8 & 1 & 0 & 0 \\ - D9 & 1 & 0 & 0 \\ - D10 & 0 & 0 & 1 \\ - D13 & 0 & 0 & 0 \\ - D14 & 0 & 0 & 0 + Am Beispiel der Kreuzung A23\ref{abb:a23} sei das hier demonstriert. Dabei entf"allt eine Ausgangsspalte, da die A23 eine Einbahnstraße beinhaltet, welche es verbietet die Kreuzung in eine Richtung zu verlassen. Die entsprechenden Ausgangsspalten werden dabei mit der auf den Ausgang folgenden Kreuzung benannt. + $\begin{Bmatrix} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ + A12 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A4 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A104 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ \end{Bmatrix}$ - - Diese Matrix wird als Ausgangsmatrix bezeichnet. D13 und D14 werden hier nicht verbunden, da es sich um Validierungssensoren handelt. Diese kann die Matrix nicht darstellen, ohne später in Unsauberkeiten in der Berechnung zu laufen. + Diese Matrix wird als Ausgangsmatrix bezeichnet. D13 und D14 werden hier nicht verbunden, da es sich um Validierungssensoren handelt. } \subsubsection{Eingangsmatrix}{ - Um nicht nur die Virtuellen Ausg"ange zu modellieren, sondern auch die Eing"ange ist eine zweite Matrix n"otig, die - die Eing"ange mit den Sensoren verbindet. Die Virtuellen Eing"ange werden hierf"ur auf der X-Achse aufgetragen, alle - Sensoren werden auf der Y-Achse der Matrix eingezeichnet. - - Hier im Beispiel die Eingangsmatrix von Kreuzung A23, der zentralen Kreuzung des betrachten Ausschnitts: - - $\begin{Bmatrix} - & A12 & A28 & A4 \\ - D1 & 1 & 0 & 0 \\ - D2 & 1 & 0 & 0 \\ - D3 & 0 & 1 & 0 \\ - D4 & 0 & 1 & 0 \\ - D5 & 0 & 1 & 0 \\ - D6 & 0 & 1 & 0 \\ - D7 & 0 & 1 & 0 \\ - D8 & 0 & 0 & 1 \\ - D9 & 0 & 0 & 1 \\ - D10 & 0 & 0 & 1 \\ - D13 & 0 & 0 & 0 \\ - D14 & 0 & 0 & 0 + Die Eingangsmatrix wird Analog zur Ausgangsmatrix gebildet. Sie beschreibt, welche Sensoren zu welchem Eingang der Kreuzung geh"oren. Ein Sensor geh"ort dabei zu einem Kreuzungseingang, wenn er vor der entsprechenden Haltelinie in der Straße verbaut ist. Die Virtuellen Eing"ange werden hierf"ur auf der Y-Achse aufgetragen, alle Sensoren werden auf der X-Achse der Matrix eingezeichnet.\\ \\ + Die Allgemeine Form der Matrix ist ebenfalls analog zur Ausgangsmatrix. + $\begin{Bmatrix} + & S_1 & S_2 & S_3 & \dots & S_n\\ + In_1 & 0/1 & 0/1 & \dots & 0/1\\ + In_2 & 0/1 & 0/1 & \dots & 0/1\\ + In_3 & 0/1 & 0/1 & \dots & 0/1\\ + In_4 & 0/1 & 0/1 & \dots & 0/1\\ + \end{Bmatrix}$ + $In_1$ 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. + $\begin{Bmatrix} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10 & D13 & D14\\ + A12 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + A28 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ + A4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0\\ \end{Bmatrix}$ } @@ -257,18 +250,19 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St } \subsection{Datenbankmodell}{ - Um mit einem Programm schneller und einfacher auf Die Daten zuzugreifen, bietet es sich an diese in einem Datenbank Server abzuspeichern. Hierfür wurde eine Datenbankschema erstellt, um alle Informationen, die von dem entwickelten Modell zur Visualisierung und Berechnung ben"otigte Informationen zu speichern vermag. - + Um mit einem Programm schneller und einfacher auf Die 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: \begin{enumerate} - \item{Der Graph einer Kreuzung muss in der Datenbank gespeichert werden. Er umfasst Sensoren, virtuelle Sensoren und die Verbindungen zwischen diesen.} - \item{Der Graph der Kreuzungsübersicht muss ebenfalls gespeichert werden. Das umfasst die bereits in Punkt 1 erw"ahnten Kreuzungen und deren Verbindungen untereinandern.} + \item{Der Graph einer Kreuzung. Er umfasst Sensoren, virtuelle Sensoren und die Verbindungen zwischen diesen.} + \item{Der Graph der Kreuzungs"ubersicht. Er umfasst die bereits in Punkt 1 erw"ahnten Kreuzungen und deren Verbindungen untereinander.} \item{Die Abbiegewahrscheinlichkeit welche der richtigen Verbindungen zwischen Sensor und entsprechendem virtuellen Kreuzungsausgang zugordnet ist.} \end{enumerate} + [ER diagramm] + \subsubsection{Datenbank Schema}{ - Das Datenbankschema für Sensoren sieh wie folgt aus:\\ -% optionen für listings + Das Datenbankschema f"ur Sensoren sieh wie folgt aus:\\ +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -295,11 +289,11 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{lstlisting} \end{minipage} - Dabei ist die 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 Verknüpfungen unter den Sensoren über die Sensorid identifiziert. Diese Verknüpfungen werden über die Felder 'toSensorLeftID', 'toSensorStraightID' und 'toSensorRightID' modelliert und erlauben es den Graphen aufzubauen. Verbindungen zwischen Knoten werden dabei in Verkehrsflussrichtung gespeichert. + Dabei ist die 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. Lat und Long bestimmen die Position des Sensors. Diese Informationen wurden mithilfe des Tools [] gewonnen, sofern diese noch nicht in der Datenbank vorhanden waren. In der Spalte 'sensorType' wird der Type des Sensors gespeichert. Eine zus"atzliche Tabelle erlaubt es Einzelheiten zu den einzelnen Sensoretypen zu definieren.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -316,11 +310,11 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{lstlisting} \end{minipage} - In dieser Arbeit wird nur auf die im Kapitel [Modell] definierten Sensortypen zurückgegriffen. Da die Richtung der Sensoren über ihre Verbindungen zu anderen Knoten definiert sind, wurden nur die Typen 'Sensor' und 'Virtueller Sensor' benutzt. Diese Datenbankstruktur erlaubt es allerdings durch hinzufügen einer Zeile zu sensortypes einen neuen Sensortyp zu definieren, auf den ein ein Algorithmus besonders reagiert.\\ + In dieser Arbeit wird nur auf die im Kapitel [Modell] definierten Sensortypen zur"uckgegriffen. Da die Richtung der Sensoren "uber ihre Verbindungen zu anderen Knoten definiert sind, wurden nur die Typen 'Sensor' und 'Virtueller Sensor' benutzt. Diese Datenbankstruktur erlaubt es allerdings durch hinzuf"ugen einer Zeile zu sensortypes einen neuen Sensortyp zu definieren, auf den ein ein Algorithmus besonders reagiert.\\ - Die Definition für Kreuzungen ist dagegen deutlich einfacher. Da jede Kreuzung, die Modelliert wurde h"ochsten vier Ausg"ange hat, müssen 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.\\ + 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.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -349,9 +343,9 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{minipage} Die Tabelle Values enth"alt aufbereitete Induktionsschleifenwerte. Diese werden aus der MYSQL-Datenbank des Projekts [] extrahiert, um das manuelle Parsen der CSV-Dateien zu umgehen. - Sensoren werden hierfür mit ihrer eindeutigen ID identifiziert. Durch filtern der spalte 'timestamp' ist es m"oglich beliebige Zeitpunkte aus der Datenmenge zu extrahieren.\\ + Sensoren werden hierf"ur mit ihrer eindeutigen ID identifiziert. Durch filtern der spalte 'timestamp' ist es m"oglich beliebige Zeitpunkte aus der Datenmenge zu extrahieren.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -373,10 +367,10 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{lstlisting} \end{minipage} - Die Tabelle FlowStatistics h"alt Abbiegewahrscheinlichkeiten für Sensoren. - Die Sensoren werden dabei über Kreuzungs- und Sensorname identifiziert, da Sensornamen nicht eindeutig für alle Kreuzungen sind.\\ + Die Tabelle FlowStatistics h"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. + Die Sensoren werden dabei "uber Kreuzungs- und Sensorname identifiziert, da Sensornamen nicht eindeutig f"ur alle Kreuzungen sind.\\ -% optionen für listings +% optionen f"ur listings \lstset{frame=single,language=java,numbers=left,numberstyle=\tiny\color{gray},numberbychapter=t,frame=shadowbox,rulesepcolor=\color{gray},tabsize=2} \hspace*{\dimexpr\fboxsep+\fboxrule+1em}% \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -401,4 +395,11 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \end{lstlisting} \end{minipage} - } \ No newline at end of file + } + +\subsection{Einschr"ankungen und Voraussetzungen f"ur das Modell} + Das Modell kann nicht alle Verkehrsverhalten modellieren. In diesem Abschnitt wird behandelt, welche Einschr"ankungen und Vorraussetzung f"ur das entwickelte Modell gelten m"ussen, damit der Verkehrs korrekt modelliert wird. + + [Uturn] + [Sensor n"ahe zur Kreuzung] + [verkehrsverhalten - falsch abbiegen etc] \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/relatedwork.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/relatedwork.tex index 83c2b8c4..e69de29b 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/relatedwork.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/relatedwork.tex @@ -1,14 +0,0 @@ -\label{sec:relatedwork} -Diese Arbeit besch"aftigt sich prim"ar mit der analyse eines Sensornetzwerkes, den Stra"sensensoren. -Sie ist daher dem Forschungsgebiet des [XXX] zuzuordnen. Allerdings besch"aftigt sie sich ebenfalls -mit Verkehrstechniken und Graphenalgorithmen. Im folgenden werden einige ausgew"ahlt Publikationen -vorgestellt. - -Michael Scholz BA -Verkehrstools, micro modellierung -Stadt darmstadt monitoring tool, unsofisticated -Christians verkehrstools - -diplomarbeit mazur.pdf -diplomarbeit steffen buhle.pdf -neubert.pdf \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex index c5eee579..d9623ff4 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex @@ -36,4 +36,12 @@ Hypothese: Berechnete Werte sind gen"ugend Genau. Ja/Nein -> wissenschaftliche m \subsection{Validierung der Verkehrsaufkommensvorhersage}{ hoher wert am ausgang, hoher wert an der n"achsten kreuzung } -+4 \ No newline at end of file + +\subsection{Sensor} + +\subsection{Überprüfung des Modells} + Das in Kapitel \autoref{sec:modell} entwickelte Modell muss auf seine Gültigkeit überprüft werden. Hierzu wird überprüft, ob die für das Modell getroffenen Annahmen mit einer realen Verkehrssituation angebracht sind. + + [falschabbieger] + [spurwechsler] + [uturns] \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex index 179389d0..9d54a36e 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex @@ -1,6 +1,6 @@ \label{sec:visualisierung} -In diesem Kapitel wird beschrieben, wie der im Kapitel \autoref{sec:modell} und im Kapitel \autoref{sec:berechnung} mit Werten befüllter Graph visualiert wird. Neben dem Graphen wird eine Kreuzungsübersicht mithilfe der Geoinformationen des OSM-Projektes\footnote{OSM todo} mit den untersuchten Sensoren am Computer visualisiert.\\ \\ -Visualisierung eignet sich deshalb besonders gut, da die berechneten Zusammenhänge komplex und wenig zugänglich sind. Eine Visualisierung ermöglicht eine andere Sicht auf den Sachverhalt und lässt sich leichter überprüfen. +In diesem Kapitel wird beschrieben, wie der im Kapitel \autoref{sec:modell} und im Kapitel \autoref{sec:berechnung} mit Werten befüllter Graph visualisiert wird. Neben dem Graphen wird eine Kreuzungsübersicht mithilfe der Geoinformationen des OSM-Projektes\footnote{OSM todo} mit den untersuchten Sensoren am Computer visualisiert.\\ \\ +Visualisierung eignet sich deshalb besonders gut, da die berechneten Zusammenhänge komplex und wenig zugänglich sind. Eine Visualisierung ermöglicht eine andere Sicht auf den Sachverhalt und lässt sich leichter auf Korrektheit überprüfen. \subsection{Visualisierung des Graphen mit Geoinformationen}{ Um den Zusammenhang zwischen Realit"at und dem graphenbassierten Modell herzustellen wurden die Kreuzungsinformationen auf eine Landkarte projeziert. Hierzu dient das [] Framework, welches auf die OpenStreetMap, kurz OSM, zugreift und dem Programmierer die m"oglichkeit gibt eigene Kartenanwendungen zu schreiben. @@ -17,4 +17,6 @@ Visualisierung eignet sich deshalb besonders gut, da die berechneten Zusammenhä \subsection{Visualisierung des JGraphT-Graphen}{ Die Visualisierung des JGraphT Graphen ist eine Visualisierung der Berechnungsstrucktur, da die Berechnung auf dem Graphen vollzogen wird. Mehr Informationen hierzu sind im Kapitel \autoref{sec:berechnung} zu finden. In Verbindung mit den Latidue und Longitude Koordinaten können die Knoten des Graphen auf dem Bildschirm angeordnet werden um eine Identifizierung von Objekten zu erleichtern. Der Nutzer erhält weiterhin die Fähigkeit die einzelnen Knoten manuell nachzujustieren. Dies ist insbesondere für solche Knoten ohne gültige Koordinaten hilfreich.\\ \\ Ziel dieser Visualisierung ist es die berechneten Werte darzustellen. Die Anordnung nach Koordinaten ermöglicht es den generierten Graphen einfach mit der Realität zu vergleichen. Es werden im Gegensatz zu der Visualisierung mit Luftbildern nicht nur die Kreuzungsübersicht visualisiert, sondern auch die einzelnen Kreuzungen, da für beide ein Graph vorhanden ist \autoref{sec:berechnung}. Die Erzeugung der Graphen ist dabei auf die Visualisierungsfähigkeit der Java Graphen-Bibliothek JGraph. Die JGraphT-Bibliothek bietet eine Schnittstelle zu dieser Bibliothek und erlaubt es Graphen mit wenigen Befehlen zu visualisieren. + [befehl] + [bild übersicht bild kreuzung] } \ No newline at end of file

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