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[] - - -Underfull \hbox (badness 10000) in paragraph at lines 72--72 -\T1/5fp/m/n/9.5 Quel-le: - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 72--72 -\T1/5fp/m/n/9.5 wi-ki-pe- - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 88--99 +Underfull \hbox (badness 10000) in paragraph at lines 87--98 [] -Underfull \hbox (badness 10000) in paragraph at lines 88--99 +Underfull \hbox (badness 10000) in paragraph at lines 87--98 [] -Underfull \hbox (badness 10000) in paragraph at lines 88--99 - - [] - -[16] [17 ] -Underfull \hbox (badness 10000) in paragraph at lines 105--108 +Underfull \hbox (badness 10000) in paragraph at lines 87--98 [] -Underfull \hbox (badness 10000) in paragraph at lines 109--112 +Underfull \hbox (badness 10000) in paragraph at lines 104--107 + + [] + +[17] +Underfull \hbox (badness 10000) in paragraph at lines 108--111 [] -Underfull \hbox (badness 10000) in paragraph at lines 109--112 +Underfull \hbox (badness 10000) in paragraph at lines 108--111 [] File: ext/KreuzungA23.pdf Graphic file (type pdf) -Underfull \hbox (badness 10000) in paragraph at lines 113--141 +Underfull \hbox (badness 10000) in paragraph at lines 112--140 [] -Underfull \hbox (badness 10000) in paragraph at lines 113--141 +Underfull \hbox (badness 10000) in paragraph at lines 112--140 [] [18] -Underfull \hbox (badness 10000) in paragraph at lines 142--165 +Underfull \hbox (badness 10000) in paragraph at lines 141--164 [] -Underfull \hbox (badness 10000) in paragraph at lines 142--165 +Underfull \hbox (badness 10000) in paragraph at lines 141--164 [] -Underfull \hbox (badness 10000) in paragraph at lines 166--168 +Underfull \hbox (badness 10000) in paragraph at lines 165--167 [] [19] -Underfull \hbox (badness 10000) in paragraph at lines 186--191 +Underfull \hbox (badness 10000) in paragraph at lines 185--190 [] -Underfull \hbox (badness 10000) in paragraph at lines 186--191 +Underfull \hbox (badness 10000) in paragraph at lines 185--190 [] -Underfull \hbox (badness 10000) in paragraph at lines 186--191 - 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+ File: ext/KreuzungA4.pdf Graphic file (type pdf) - [27] [28 [28] [29 ]) -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/validierung.tex" +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/validierung.tex" -LaTeX Warning: Reference `sec:berechnung:validate' on page 29 undefined on inpu +LaTeX Warning: Reference `sec:berechnung:validate' on page 30 undefined on inpu t line 5. @@ -1887,35 +1784,30 @@ Underfull \hbox (badness 10000) in paragraph at lines 4--8 [] -LaTeX Warning: Reference `thesis:michael' on page 29 undefined on input line 9. +LaTeX Warning: Reference `thesis:michael' on page 30 undefined on input line 9. -LaTeX Warning: Reference `sec:grundlagen' on page 29 undefined on input line 10 +LaTeX Warning: Reference `sec:grundlagen' on page 30 undefined on input line 10 . -Underfull \hbox (badness 10000) in paragraph at lines 9--12 +Underfull \hbox (badness 10000) in paragraph at lines 9--13 [] -Underfull \hbox (badness 10000) in paragraph at lines 9--12 +Underfull \hbox (badness 10000) in paragraph at lines 9--13 [] -Underfull \hbox (badness 10000) in paragraph at lines 9--12 +Underfull \hbox (badness 10000) in paragraph at lines 9--13 [] - 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+\contentsline {lstlisting}{\numberline {4}Befehl zur Konvertierung und Darstellung eines JGraphT Graphen als JGraph}{32}{lstlisting.4} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out index 0d49a7e3..f7497204 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out @@ -1,55 +1,55 @@ \BOOKMARK [1][-]{section.1}{\334bersicht}{}% 1 -\BOOKMARK [1][-]{section.2}{Einleitung}{}% 2 -\BOOKMARK [1][-]{section.3}{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}{Makro- und mikroskopische Modellierung von Verkehr}{section.3}% 6 -\BOOKMARK [1][-]{section.4}{Datenbasis}{}% 7 -\BOOKMARK [2][-]{subsection.4.1}{Induktionsschleifenwerte}{section.4}% 8 -\BOOKMARK [3][-]{subsubsection.4.1.1}{CSV-Dateien der Induktionsschleifenwerte}{subsection.4.1}% 9 -\BOOKMARK [3][-]{subsubsection.4.1.2}{MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}{subsection.4.1}% 10 -\BOOKMARK [2][-]{subsection.4.2}{Geographischer Ausschnitt der Daten}{section.4}% 11 -\BOOKMARK [2][-]{subsection.4.3}{CAD-Zeichnungen der Kreuzungen}{section.4}% 12 -\BOOKMARK [2][-]{subsection.4.4}{Abbiegewahrscheinlichkeiten}{section.4}% 13 -\BOOKMARK [1][-]{section.5}{Verkehrsmodell}{}% 14 -\BOOKMARK [2][-]{subsection.5.1}{Allgemeines Kreuzungsmodell}{section.5}% 15 -\BOOKMARK [2][-]{subsection.5.2}{Modell der Ministadt}{section.5}% 16 -\BOOKMARK [2][-]{subsection.5.3}{Modell als Graph}{section.5}% 17 -\BOOKMARK [3][-]{subsubsection.5.3.1}{Grundlagen}{subsection.5.3}% 18 -\BOOKMARK [3][-]{subsubsection.5.3.2}{Kreuzungsgraph}{subsection.5.3}% 19 -\BOOKMARK [3][-]{subsubsection.5.3.3}{Kreuzungs\374bersicht}{subsection.5.3}% 20 -\BOOKMARK [2][-]{subsection.5.4}{Modell als Matrix}{section.5}% 21 -\BOOKMARK [3][-]{subsubsection.5.4.1}{Ausgangsmatrix}{subsection.5.4}% 22 -\BOOKMARK [3][-]{subsubsection.5.4.2}{Eingangsmatrix}{subsection.5.4}% 23 -\BOOKMARK [2][-]{subsection.5.5}{Datenbankmodell}{section.5}% 24 -\BOOKMARK [2][-]{subsection.5.6}{Einschr\344nkungen und Schw\344chen des Modell}{section.5}% 25 -\BOOKMARK [2][-]{subsection.5.7}{Zuk\374nftige Herausforderungen des Modells}{section.5}% 26 -\BOOKMARK [3][-]{subsubsection.5.7.1}{Herausforderung: Verfolgung von Fahrzeugen \374ber eine Kreuzung hinaus}{subsection.5.7}% 27 -\BOOKMARK [3][-]{subsubsection.5.7.2}{Herausforderung: Genaues Bestimmen der Abbiegewahrscheinlichkeit}{subsection.5.7}% 28 -\BOOKMARK [1][-]{section.6}{L\366sungsans\344tze}{}% 29 -\BOOKMARK [2][-]{subsection.6.1}{Aufbereiten der Abbiegewahrscheinlichkeiten}{section.6}% 30 -\BOOKMARK [2][-]{subsection.6.2}{L\366sungsansatz: Hidden Markow Modell}{section.6}% 31 -\BOOKMARK [3][-]{subsubsection.6.2.1}{Grundlagen}{subsection.6.2}% 32 -\BOOKMARK [3][-]{subsubsection.6.2.2}{HMM f\374r eine Kreuzung}{subsection.6.2}% 33 -\BOOKMARK [2][-]{subsection.6.3}{L\366sungsansatz: Wegfindungsalgorithmen}{section.6}% 34 -\BOOKMARK [2][-]{subsection.6.4}{L\366sungsansatz: Lineares Gleichungssystem}{section.6}% 35 -\BOOKMARK [3][-]{subsubsection.6.4.1}{Grundlagen}{subsection.6.4}% 36 -\BOOKMARK [3][-]{subsubsection.6.4.2}{Lineares Gleichungssystem einer Kreuzung}{subsection.6.4}% 37 -\BOOKMARK [2][-]{subsection.6.5}{Kreuzungsberechnung am Graphen}{section.6}% 38 -\BOOKMARK [3][-]{subsubsection.6.5.1}{Verkehrsfluss zwischen Kreuzungen}{subsection.6.5}% 39 -\BOOKMARK [3][-]{subsubsection.6.5.2}{Sonderfall: Validierungssensor}{subsection.6.5}% 40 -\BOOKMARK [1][-]{section.7}{Validierung}{}% 41 -\BOOKMARK [2][-]{subsection.7.1}{Validierung durch Testdatenmenge}{section.7}% 42 -\BOOKMARK [2][-]{subsection.7.2}{Verkehrsz\344hlung}{section.7}% 43 -\BOOKMARK [2][-]{subsection.7.3}{Validierung der Verkehrsaufkommensvorhersage}{section.7}% 44 -\BOOKMARK [2][-]{subsection.7.4}{Sensor}{section.7}% 45 -\BOOKMARK [2][-]{subsection.7.5}{\334berpr\374fung des Modells}{section.7}% 46 -\BOOKMARK [1][-]{section.8}{Visualisierung}{}% 47 -\BOOKMARK [2][-]{subsection.8.1}{Visualisierung des Graphen mit JMapViewer}{section.8}% 48 -\BOOKMARK [2][-]{subsection.8.2}{Visualisierung des JGraphT-Graphen}{section.8}% 49 -\BOOKMARK [1][-]{section.9}{Ausblick}{}% 50 -\BOOKMARK [1][-]{section.9}{Bibliographie}{}% 51 -\BOOKMARK [1][-]{section.9}{Abbildungsverzeichnis}{}% 52 -\BOOKMARK [1][-]{section.9}{Quellcodeverzeichnis}{}% 53 -\BOOKMARK [1][-]{section.13}{Anhang}{}% 54 -\BOOKMARK [1][-]{figure.45}{Glossar}{}% 55 +\BOOKMARK [1][-]{section.1}{Inhaltsverzeichnis}{}% 2 +\BOOKMARK [1][-]{section.3}{Einleitung}{}% 3 +\BOOKMARK [1][-]{section.4}{Grundlagen}{}% 4 +\BOOKMARK [2][-]{subsection.4.1}{Induktionsschleifen}{section.4}% 5 +\BOOKMARK [2][-]{subsection.4.2}{Adaptive Steuerung von Ampelanlagen}{section.4}% 6 +\BOOKMARK [2][-]{subsection.4.3}{Makro- und mikroskopische Modellierung von Verkehr}{section.4}% 7 +\BOOKMARK [1][-]{section.5}{Datenbasis}{}% 8 +\BOOKMARK [2][-]{subsection.5.1}{Induktionsschleifenwerte}{section.5}% 9 +\BOOKMARK [3][-]{subsubsection.5.1.1}{CSV-Dateien der Induktionsschleifenwerte}{subsection.5.1}% 10 +\BOOKMARK [3][-]{subsubsection.5.1.2}{MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}{subsection.5.1}% 11 +\BOOKMARK [2][-]{subsection.5.2}{Geographischer Ausschnitt der Daten}{section.5}% 12 +\BOOKMARK [2][-]{subsection.5.3}{CAD-Zeichnungen der Kreuzungen}{section.5}% 13 +\BOOKMARK [2][-]{subsection.5.4}{Abbiegewahrscheinlichkeiten}{section.5}% 14 +\BOOKMARK [1][-]{section.6}{Graph-basiertes Verkehrsmodell}{}% 15 +\BOOKMARK [2][-]{subsection.6.1}{Grundlagen}{section.6}% 16 +\BOOKMARK [2][-]{subsection.6.2}{Allgemeines Verkehrsmodell}{section.6}% 17 +\BOOKMARK [2][-]{subsection.6.3}{Modell der Ministadt}{section.6}% 18 +\BOOKMARK [2][-]{subsection.6.4}{Modell als Graph}{section.6}% 19 +\BOOKMARK [3][-]{subsubsection.6.4.1}{Kreuzungsgraph}{subsection.6.4}% 20 +\BOOKMARK [3][-]{subsubsection.6.4.2}{Kreuzungs\374bersicht}{subsection.6.4}% 21 +\BOOKMARK [2][-]{subsection.6.5}{Modell als Matrix}{section.6}% 22 +\BOOKMARK [3][-]{subsubsection.6.5.1}{Ausgangsmatrix}{subsection.6.5}% 23 +\BOOKMARK [3][-]{subsubsection.6.5.2}{Eingangsmatrix}{subsection.6.5}% 24 +\BOOKMARK [2][-]{subsection.6.6}{Datenbankmodell}{section.6}% 25 +\BOOKMARK [2][-]{subsection.6.7}{Implementierung}{section.6}% 26 +\BOOKMARK [2][-]{subsection.6.8}{Zuk\374nftige Herausforderungen des Modells}{section.6}% 27 +\BOOKMARK [3][-]{subsubsection.6.8.1}{Herausforderung: Verfolgung von Fahrzeugen \374ber eine Kreuzung hinaus}{subsection.6.8}% 28 +\BOOKMARK [3][-]{subsubsection.6.8.2}{Herausforderung: Genaues Bestimmen der Abbiegewahrscheinlichkeit}{subsection.6.8}% 29 +\BOOKMARK [1][-]{section.7}{L\366sungsans\344tze}{}% 30 +\BOOKMARK [2][-]{subsection.7.1}{Aufbereiten der Abbiegewahrscheinlichkeiten}{section.7}% 31 +\BOOKMARK [2][-]{subsection.7.2}{L\366sungsansatz: Hidden Markow Modell}{section.7}% 32 +\BOOKMARK [3][-]{subsubsection.7.2.1}{Grundlagen}{subsection.7.2}% 33 +\BOOKMARK [3][-]{subsubsection.7.2.2}{HMM f\374r eine Kreuzung}{subsection.7.2}% 34 +\BOOKMARK [2][-]{subsection.7.3}{L\366sungsansatz: Wegfindungsalgorithmen}{section.7}% 35 +\BOOKMARK [2][-]{subsection.7.4}{L\366sungsansatz: Lineares Gleichungssystem}{section.7}% 36 +\BOOKMARK [3][-]{subsubsection.7.4.1}{Grundlagen}{subsection.7.4}% 37 +\BOOKMARK [3][-]{subsubsection.7.4.2}{Lineares Gleichungssystem einer Kreuzung}{subsection.7.4}% 38 +\BOOKMARK [2][-]{subsection.7.5}{Kreuzungsberechnung am Graphen}{section.7}% 39 +\BOOKMARK [3][-]{subsubsection.7.5.1}{Verkehrsfluss zwischen Kreuzungen}{subsection.7.5}% 40 +\BOOKMARK [3][-]{subsubsection.7.5.2}{Sonderfall: Validierungssensor}{subsection.7.5}% 41 +\BOOKMARK [1][-]{section.8}{Validierung}{}% 42 +\BOOKMARK 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\addcontentsline{toc}{section}{\protect\numberline{\thesection}Inhaltsverzeichnis} \tableofcontents \newpage + + %text \input{tex/einleitung} \input{tex/grundlagen} \input{tex/daten} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc index 6fd7320a..fa732b49 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc @@ -1,56 +1,56 @@ \select@language {ngerman} \contentsline {section}{\numberline {1}"Ubersicht}{1}{section.1} -\contentsline {section}{\numberline {2}Einleitung}{4}{section.2} -\contentsline {section}{\numberline {3}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}Makro- und mikroskopische Modellierung von Verkehr}{7}{subsection.3.3} -\contentsline {section}{\numberline {4}Datenbasis}{9}{section.4} -\contentsline {subsection}{\numberline {4.1}Induktionsschleifenwerte}{9}{subsection.4.1} -\contentsline {subsubsection}{\numberline {4.1.1}CSV-Dateien der Induktionsschleifenwerte}{9}{subsubsection.4.1.1} -\contentsline {subsubsection}{\numberline {4.1.2}MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}{9}{subsubsection.4.1.2} -\contentsline {subsection}{\numberline {4.2}Geographischer Ausschnitt der Daten}{11}{subsection.4.2} -\contentsline {subsection}{\numberline {4.3}CAD-Zeichnungen der Kreuzungen}{12}{subsection.4.3} -\contentsline {subsection}{\numberline {4.4}Abbiegewahrscheinlichkeiten}{12}{subsection.4.4} -\contentsline {section}{\numberline {5}Verkehrsmodell}{13}{section.5} -\contentsline {subsection}{\numberline {5.1}Allgemeines Kreuzungsmodell}{13}{subsection.5.1} -\contentsline {subsection}{\numberline {5.2}Modell der Ministadt}{13}{subsection.5.2} -\contentsline {subsection}{\numberline {5.3}Modell als Graph}{16}{subsection.5.3} -\contentsline {subsubsection}{\numberline {5.3.1}Grundlagen}{16}{subsubsection.5.3.1} -\contentsline {subsubsection}{\numberline {5.3.2}Kreuzungsgraph}{16}{subsubsection.5.3.2} -\contentsline {subsubsection}{\numberline {5.3.3}Kreuzungs"ubersicht}{17}{subsubsection.5.3.3} -\contentsline {subsection}{\numberline {5.4}Modell als Matrix}{18}{subsection.5.4} -\contentsline {subsubsection}{\numberline {5.4.1}Ausgangsmatrix}{18}{subsubsection.5.4.1} -\contentsline {subsubsection}{\numberline {5.4.2}Eingangsmatrix}{19}{subsubsection.5.4.2} -\contentsline {subsection}{\numberline {5.5}Datenbankmodell}{19}{subsection.5.5} -\contentsline {subsection}{\numberline {5.6}Einschr"ankungen und Schw"achen des Modell}{21}{subsection.5.6} -\contentsline {subsection}{\numberline {5.7}Zuk"unftige Herausforderungen des Modells}{21}{subsection.5.7} -\contentsline {subsubsection}{\numberline {5.7.1}Herausforderung: Verfolgung von Fahrzeugen "uber eine Kreuzung hinaus}{21}{subsubsection.5.7.1} -\contentsline {subsubsection}{\numberline {5.7.2}Herausforderung: Genaues Bestimmen der Abbiegewahrscheinlichkeit}{21}{subsubsection.5.7.2} -\contentsline {section}{\numberline {6}L"osungsans"atze}{22}{section.6} -\contentsline {subsection}{\numberline {6.1}Aufbereiten der Abbiegewahrscheinlichkeiten}{22}{subsection.6.1} -\contentsline {subsection}{\numberline {6.2}L"osungsansatz: Hidden Markow Modell}{22}{subsection.6.2} -\contentsline {subsubsection}{\numberline {6.2.1}Grundlagen}{23}{subsubsection.6.2.1} -\contentsline {subsubsection}{\numberline {6.2.2}HMM f"ur eine Kreuzung}{23}{subsubsection.6.2.2} -\contentsline {subsection}{\numberline {6.3}L"osungsansatz: Wegfindungsalgorithmen}{23}{subsection.6.3} -\contentsline {subsection}{\numberline {6.4}L"osungsansatz: Lineares Gleichungssystem}{23}{subsection.6.4} -\contentsline {subsubsection}{\numberline {6.4.1}Grundlagen}{24}{subsubsection.6.4.1} -\contentsline {subsubsection}{\numberline {6.4.2}Lineares Gleichungssystem einer Kreuzung}{24}{subsubsection.6.4.2} -\contentsline {subsection}{\numberline {6.5}Kreuzungsberechnung am Graphen}{26}{subsection.6.5} -\contentsline {subsubsection}{\numberline {6.5.1}Verkehrsfluss zwischen Kreuzungen}{27}{subsubsection.6.5.1} -\contentsline {subsubsection}{\numberline {6.5.2}Sonderfall: Validierungssensor}{27}{subsubsection.6.5.2} -\contentsline {section}{\numberline {7}Validierung}{29}{section.7} -\contentsline {subsection}{\numberline {7.1}Validierung durch Testdatenmenge}{29}{subsection.7.1} -\contentsline {subsection}{\numberline {7.2}Verkehrsz"ahlung}{29}{subsection.7.2} -\contentsline {subsection}{\numberline {7.3}Validierung der Verkehrsaufkommensvorhersage}{29}{subsection.7.3} -\contentsline {subsection}{\numberline {7.4}Sensor}{29}{subsection.7.4} -\contentsline {subsection}{\numberline {7.5}"Uberpr"ufung des Modells}{29}{subsection.7.5} -\contentsline {section}{\numberline {8}Visualisierung}{30}{section.8} -\contentsline {subsection}{\numberline {8.1}Visualisierung des Graphen mit JMapViewer}{30}{subsection.8.1} -\contentsline {subsection}{\numberline {8.2}Visualisierung des JGraphT-Graphen}{30}{subsection.8.2} -\contentsline {section}{\numberline {9}Ausblick}{32}{section.9} -\contentsline {section}{\numberline {10}Bibliographie}{33}{section.9} -\contentsline {section}{\numberline {11}Abbildungsverzeichnis}{34}{section.9} -\contentsline {section}{\numberline {12}Quellcodeverzeichnis}{34}{section.9} -\contentsline {section}{\numberline {13}Anhang}{35}{section.13} -\contentsline {section}{\numberline {14}Glossar}{77}{figure.45} +\contentsline {section}{\numberline {2}Inhaltsverzeichnis}{2}{section.1} +\contentsline {section}{\numberline {3}Einleitung}{4}{section.3} +\contentsline {section}{\numberline {4}Grundlagen}{6}{section.4} +\contentsline {subsection}{\numberline {4.1}Induktionsschleifen}{6}{subsection.4.1} +\contentsline {subsection}{\numberline {4.2}Adaptive Steuerung von Ampelanlagen}{7}{subsection.4.2} +\contentsline {subsection}{\numberline {4.3}Makro- und mikroskopische Modellierung von Verkehr}{7}{subsection.4.3} +\contentsline {section}{\numberline {5}Datenbasis}{9}{section.5} +\contentsline {subsection}{\numberline {5.1}Induktionsschleifenwerte}{9}{subsection.5.1} +\contentsline {subsubsection}{\numberline {5.1.1}CSV-Dateien der Induktionsschleifenwerte}{9}{subsubsection.5.1.1} +\contentsline {subsubsection}{\numberline {5.1.2}MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}{9}{subsubsection.5.1.2} +\contentsline {subsection}{\numberline {5.2}Geographischer Ausschnitt der Daten}{11}{subsection.5.2} +\contentsline {subsection}{\numberline {5.3}CAD-Zeichnungen der Kreuzungen}{12}{subsection.5.3} +\contentsline {subsection}{\numberline {5.4}Abbiegewahrscheinlichkeiten}{12}{subsection.5.4} +\contentsline {section}{\numberline {6}Graph-basiertes Verkehrsmodell}{13}{section.6} +\contentsline {subsection}{\numberline {6.1}Grundlagen}{13}{subsection.6.1} +\contentsline {subsection}{\numberline {6.2}Allgemeines Verkehrsmodell}{14}{subsection.6.2} +\contentsline {subsection}{\numberline {6.3}Modell der Ministadt}{14}{subsection.6.3} +\contentsline {subsection}{\numberline {6.4}Modell als Graph}{16}{subsection.6.4} +\contentsline {subsubsection}{\numberline {6.4.1}Kreuzungsgraph}{17}{subsubsection.6.4.1} +\contentsline {subsubsection}{\numberline {6.4.2}Kreuzungs"ubersicht}{17}{subsubsection.6.4.2} +\contentsline {subsection}{\numberline {6.5}Modell als Matrix}{18}{subsection.6.5} +\contentsline {subsubsection}{\numberline {6.5.1}Ausgangsmatrix}{18}{subsubsection.6.5.1} +\contentsline {subsubsection}{\numberline {6.5.2}Eingangsmatrix}{19}{subsubsection.6.5.2} +\contentsline {subsection}{\numberline {6.6}Datenbankmodell}{19}{subsection.6.6} +\contentsline {subsection}{\numberline {6.7}Implementierung}{21}{subsection.6.7} +\contentsline {subsection}{\numberline {6.8}Zuk"unftige Herausforderungen des Modells}{21}{subsection.6.8} +\contentsline {subsubsection}{\numberline {6.8.1}Herausforderung: Verfolgung von Fahrzeugen "uber eine Kreuzung hinaus}{21}{subsubsection.6.8.1} +\contentsline {subsubsection}{\numberline {6.8.2}Herausforderung: Genaues Bestimmen der Abbiegewahrscheinlichkeit}{21}{subsubsection.6.8.2} +\contentsline {section}{\numberline {7}L"osungsans"atze}{23}{section.7} +\contentsline {subsection}{\numberline {7.1}Aufbereiten der Abbiegewahrscheinlichkeiten}{23}{subsection.7.1} +\contentsline {subsection}{\numberline {7.2}L"osungsansatz: Hidden Markow Modell}{23}{subsection.7.2} +\contentsline {subsubsection}{\numberline {7.2.1}Grundlagen}{24}{subsubsection.7.2.1} +\contentsline {subsubsection}{\numberline {7.2.2}HMM f"ur eine Kreuzung}{24}{subsubsection.7.2.2} +\contentsline {subsection}{\numberline {7.3}L"osungsansatz: Wegfindungsalgorithmen}{24}{subsection.7.3} +\contentsline {subsection}{\numberline {7.4}L"osungsansatz: Lineares Gleichungssystem}{24}{subsection.7.4} +\contentsline {subsubsection}{\numberline {7.4.1}Grundlagen}{25}{subsubsection.7.4.1} +\contentsline {subsubsection}{\numberline {7.4.2}Lineares Gleichungssystem einer Kreuzung}{25}{subsubsection.7.4.2} +\contentsline {subsection}{\numberline {7.5}Kreuzungsberechnung am Graphen}{27}{subsection.7.5} +\contentsline {subsubsection}{\numberline {7.5.1}Verkehrsfluss zwischen Kreuzungen}{28}{subsubsection.7.5.1} +\contentsline {subsubsection}{\numberline {7.5.2}Sonderfall: Validierungssensor}{28}{subsubsection.7.5.2} +\contentsline {section}{\numberline {8}Validierung}{30}{section.8} +\contentsline {subsection}{\numberline {8.1}Validierung durch Testdatenmenge}{30}{subsection.8.1} +\contentsline {subsection}{\numberline {8.2}Verkehrsz"ahlung}{30}{subsection.8.2} +\contentsline {subsection}{\numberline {8.3}Validierung der Berechneten Verkehrswerte}{30}{subsection.8.3} +\contentsline {subsection}{\numberline {8.4}"Uberpr"ufung des Modells}{30}{subsection.8.4} +\contentsline {section}{\numberline {9}Visualisierung}{31}{section.9} +\contentsline {subsection}{\numberline {9.1}Visualisierung des Graphen mit JMapViewer}{31}{subsection.9.1} +\contentsline {subsection}{\numberline {9.2}Visualisierung des JGraphT-Graphen}{31}{subsection.9.2} +\contentsline {section}{\numberline {10}Ausblick}{33}{section.10} +\contentsline {section}{\numberline {11}Bibliographie}{34}{section.10} +\contentsline {section}{\numberline {12}Abbildungsverzeichnis}{35}{section.10} +\contentsline {section}{\numberline {13}Quellcodeverzeichnis}{35}{section.10} +\contentsline {section}{\numberline {14}Anhang}{36}{section.14} +\contentsline {section}{\numberline {15}Glossar}{78}{figure.47} diff --git a/ss2013/Bachelor Thesis/thesis_ug/ext/graphen.pdf b/ss2013/Bachelor Thesis/thesis_ug/ext/graphen.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2cfa899223916606083a7521e4ef77b7ae679fff GIT binary patch literal 11598 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\item{Umfeldbedingte Messfehler} \end{enumerate} - Zeitliche Fehler wirken sich dabei auf die Belegzeitmessung aus. Da diese nicht innerhalb dieser Arbeit betrachtet wird, hat dieser Fehlertyp keine Auswirkungen auf die verwendeten Daten. R"aumlich Messfehler beziehen sich ebenfalls auf die Belegzeitmessung und k"onnen zu Problemen mit der Bestimmung des Fahrzeugtyps f"uhren, da f"ur gleich lange Fahrzeuge verschiedene Belegzeiten gemessen werden k"onnen. Lage- und formbedingte Fehler wirken sich auf den, in dieser Arbeit benutzten, Fahrzeugz"ahlwert aus. Diese treten auf, wenn ein Fahrzeug der, mit einem Sensor best"uckten, Nachbarspur zu nahe kommt und f"alschlicherweise ein Auto f"ur diese gez"ahlt wird. Umfeldbedingte Fehler sind am schwersten festzustellen. Es handelt sich dabei um Fehler, die durch magnetische St"orquellen in der Umgebung oder schlechte Isolation der Induktionsschleife auftreten.\\ + Zeitliche Fehler wirken sich dabei auf die Belegzeitmessung aus. Da diese nicht innerhalb dieser Arbeit betrachtet wird, hat dieser Fehlertyp keine Auswirkungen auf die verwendeten Daten. R"aumlich Messfehler beziehen sich ebenfalls auf die Belegzeitmessung und k"onnen zu Problemen mit der Bestimmung des Fahrzeugtyps f"uhren, da f"ur gleich lange Fahrzeuge verschiedene Belegzeiten gemessen werden k"onnen. Lage- und formbedingte Fehler wirken sich auf den, in dieser Arbeit benutzten, Fahrzeugz"ahlwert aus. Diese treten auf, wenn ein Fahrzeug der, mit einem Sensor best"uckten, Nachbarspur zu nahe kommt und f"alschlicherweise ein Fahrzeug f"ur diese gez"ahlt wird. Umfeldbedingte Fehler sind am schwersten festzustellen. Es handelt sich dabei um Fehler, die durch magnetische St"orquellen in der Umgebung oder schlechte Isolation der Induktionsschleife auftreten.\\ + Eine Induktionsschleife kann weiterhin nicht jedes Fahrzeug detektieren. So werden Fahrräder oft nicht erkannt, da sich zu wenige Metall auf der Fahrbahn befindet, um den Sensor auszulösen. "Uber die Fehlerh"aufigkeit liegen keine Daten der Stadt Darmstadt vor. F"ur die Berechnungen dieser Arbeit wird deshalb angenommen die Sensorwerte seien korrekt. 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} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/modell - Kopie.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/modell - Kopie.tex new file mode 100644 index 00000000..d193ce41 --- /dev/null +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell - Kopie.tex @@ -0,0 +1,207 @@ +\section{Graph-basiertes Verkehrsmodell}\label{sec:modell} +In diesem Kapitel wird eine Modellierung des Verkehrsnetzes auf Basis eines Graphen vorgestellt. Es berücksichtigt im Besonderen die Verkehrssensoren, da diese Grundlage der Verkehrsflussberechnung sind. Es werden weiterhin zwei Darstellungen des Modells entwickelt. Die Darstellung als Matrix und als klassischer Graph mit Knoten und Kanten. 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.\\ +Diese Modellierung wird daraufhin für die zehn untersuchten Kreuzungen, der 'Ministadt', vorgenommen und Besonderheiten erkl"art. Die 'Ministadt' weist eine gro"se Anzahl an verbauten Sensoren in ihrem Gebiet auf und eignet sich aus diesem Grund f"ur eine Modellierung. Als Grundlage f"ur die Modellierung dienen die in Kapitel \autoref{sec:daten} beschriebenen Daten.\\ \\ +In der Industrie eingesetzte Software zur Berechnung und Modellierung von Verkehrsfl"ussen, verwenden meistens ein sog. mikroskopisches Modell des Verkehrs\footnote{vissim}, 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 Mikromodellierung des Verkehrs nicht. F"ur einen solchen Modellierungsansatz sind genauere und mehr Daten notwendig. Es stehen lediglich Messwerte von 89 Sensoren zur Verf"ugung. Eine Modellierung einzelner Autos erscheint deshalb, allein anhand der Induktionsschleifen, nicht m"oglich zu sein\\ \\ +In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welche 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. Kleinere Kreuzungen und Stra"senz"uge sind nicht mit Sensoren best"uckt und aus diesem Grund kann keine qualifiziert Aussage "uber diese gemacht werden.\\ +Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die Stra"senverkehrsordnung halten, da nur verkehrsg"ultige Verbindungen zwischen und innerhalb von Kreuzungen modelliert werden. Die beschriebene Modellierung kann dabei nicht jedes Verkehrsverhalten beschreiben. So kann beispielsweise der R"uckfluss von Autos, welche eine sog. 'U-Turn' an einer Kreuzung vollf"uhren, nicht mit dem entwickelten Modell modelliert werden. Eine genaue Beschreibung der Herausforderung des Modells ist am Ende dieses Kapitels zu finden.\\ \\ +\subsection{Grundlagen}\label{sec:modell:graph:grund} + Ein Graph ist eine Struktur, die Objekte und deren Verbindung untereinander abbilden kann. Die Objekte werden dabei Knoten, die Verbindungen Kanten genannt. Eine Kante verbindet genau zwei Knoten. Graphen lassen sich besonders gut visualisieren, indem Knoten als Punkte oder K"asten und Kanten als Linien zwischen diesen dargestellt werden.\\ \\ + Ein Graph kann als Tupel $(V, E)$ beschrieben werden. $V$ bezeichnet dabei die Menge der Knoten, + $E$ die Menge der Kanten. Die Menge der m"oglichen Kanten h"angt dabei von dem gew"ahlten Typ des Graphen ab. + Es wird zwischen folgenden Typen von Graphen unterschieden: + \begin{itemize} + \item{ungerichter Graph} + \item{gerichteter Graph} + \end{itemize} + Ein ungerichteter Graph kann genau eine Kante zwischen zwei Knoten haben. Ein gerichteter Graph dagegen kann bis zu zwei Kanten zwischen zwei Knoten haben, einen f"ur jeder Richtung. Diese Einschr"ankung gilt hingegen nicht f"ur Graphen, die Mehrfachkanten erlauben. Mehrfachkanten sind solche, welche zwei oder mehr Kanten zwischen zwei Knoten zulassen. + \begin{figure}[htbp!]\label{abb:graphen} + \centering + \fbox{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{ext/graphen}} + \caption{a) ungerichteter Graph b) gerichteter Graph c) ungerichteter Graph mit Mehrfachkanten} + \end{figure} + Bei dem, in dieser Arbeit, entworfen Graphen handelt es sich um gerichtete Graphen ohne Mehrfachkanten, da Spuren duch einen eigenen Sensorknoten modelliert und aus diesem Grund keine Mehrfachkanten ben"otigt werden. Typische Algorithmen auf einem Graphen sind die Tiefensuche, Breitensuche oder Wegfindungsalgorithmen. +\subsection{Allgemeines Verkehrsmodell} + [todo] michel zitieren + Um ein Verkehrsmodell zu entwickeln muss zuerst festgelegt werden, welche Art des Verkehrs modelliert werden soll. Da die Induktionsschleifen, welche Grundlage der Berechnung sind, nicht jedes Straßenfahrzeug detektieren kann, werden nur solche modelliert, welche die Sensoren erkennen können[verweisen?]. Das Modell wurde zusammen mit M. Scholz \cite{thesis:michael} entwickelt.\\ \\ + F"ur das hier entwickelte Stra"senmodell wurde das Stra"sennetz in sieben Objekte unterteilt: + \begin{enumerate} + \item{Stra"se: Eine Stra"se, auf der Fahrzeuge fahren d"urfen. Sie ist nicht mit Sensoren best"uckt und hat eine Flie"srichtung.} + \item{Kreuzung: Eine Kreuzung ist das Zusammentreffen von zwei Stra"sen. Sie kann mit Sensoren best"uckt sein, die 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 und mit anderen Sensoren durch Stra"sen verbunden.} + \item{Virtuelle Sensoren: Punkte im Stra"sennetz, f"ur welche keine Messwerte vorliegen. Sie verhalten sich wie Sensoren.} + \item{Fahrspur: Eine Fahrspur bezeichnet einen Bereich der Stra"senfahrbahn der auf bestimmt Ausg"ange der Kreuzung zeigt. Ein Kreuzungsein bzw. -ausgang kann mehrere Fahrspuren aufweisen.} + \item{Kreuzungsausgang: Ein Ausgang einer Kreuzung auf dem Verkehr die Kreuzung verlassen kann.} + \item{Kreuzungseingang: Ein Eingang einer Kreuzung auf dem Verkehr in die Kreuzung einfahren kann.} + \end{enumerate} +\subsection{Modell der Ministadt}\label{sec:modell:ministadt} + Die 'Ministadt' enth"alt zehn mit Sensoren best"uckte Kreuzungen. Diese Kreuzungen werden mit A3 \ref{anhang:a3}, A4 \ref{anhang:a4}, A5 \ref{anhang:a5}, A12 \ref{anhang:a12}, A23 \ref{anhang:a23}, A28 \ref{anhang:a28}, A29 \ref{anhang:a29}, A46 \ref{anhang:a46}, A59 \ref{anhang:a59}und A104 \ref{anhang:a104} bezeichnet. Die Bezeichnungen stammten dabei aus der CAD-"Ubersichtskarte \ref{abb:caddarmstadt} der Stadt Darmstadt,. Eine genaue Beschreibung des gew"ahlten geographischen Ausschnitts ist in Kapitel \autoref{sec:datengrund} zu finden.\\ \\ + + 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 Kreuzungs"ubersicht eine Verallgemeinerung des Verkehrsnetzes darstellt. Es werden dabei nur sensorbest"uckte Kreuzungen aufgezeigt.\\ + Mit Rechtecken werden die betrachteten Kreuzungen vermerkt, mit Kreisen die nicht mehr modellierten Nachbarkeuzungen. Pfeile weisen dabei die Flie"srichtung der Stra"sen aus, in welche der Verkehr regelkonform flie"sen darf. So ist von der Kreuzung A29 nach A104 eine Einbahnstra"se an den einfachen Pfeilen zu erkennen, w"ahrend Stra"sen, welche in beide Richtungen befahren werden k"onnen mit Doppelpfeilen dargestellt werden. + \begin{figure}[htbp!] + \centering + \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/Kreuzungsuebersicht}} + \caption{Kreuzungs"ubersicht 'Ministadt'in der Stadt Darmstadt} + \end{figure} + Um eine "Ubersicht "uber die zu betrachtenden Kreuzungen zu erhalten wurden h"andisch Zeichnungen von den zehn Kreuzungen angefertigt. Die gew"ahlte intuitive Modellierung entspricht in etwa der, welche sp"ater im Computer entsteht. Die Grundlage f"ur diese Modellierung sind die CAD-Zeichnungen der Kreuzungen der Stadt Darmstadt. Sie werden im Kapitel \autoref{sec:datengrund} genauer beschrieben.\\ \\ + In der Kreuzungs"ubersicht entfallen sehr viele Details, da keine Daten f"ur Seitenstra"sen zwischen den Kreuzungen vorhanden sind. Dagegen k"onnen die modellierten Kreuzungen wesentlich genauer dargestellt werden und lassen sich sehr gut auf Sensorebene modellieren. Neben den realen Sensoren erh"alt jede Kreuzung jeweils bis zu vier Ein- und Ausg"ange, modelliert als 'virtuelle Sensoren'. Die Sensoren werden dabei nach den jeweiligen Kreuzungseing"angen platziert, auf denen sie in der Realit"at in der Stra"se verbaut sind. Validierungssensoren sind solche, welche R"uckschl"usse auf andere Sensoren der Kreuzung zulassen. Sie werden in der h"andischen Modellierung aufgezeigt, in der Matrixdarstellung findet sich allerdings keinen Platz f"ur diese, da f"ur die Berechnung von der Grundannahme ausgegangen wird, dass ein Sensor direkt mit einem Kreuzungsein- und Ausgang, ohne Zwischenknoten, verbunden ist. Wie anhand des entwickelten Modells Verkehrsstr"ome berechnet werden k"onnen und wie sich Sensorwerte mit Validierungssensoren validieren lassen wird im Kapitel \autoref{sec:berechnung} genauer behandelt.\\ \\ + Alle Sensoren wurde neben der Unterteilung nach Einspursensor und Mischspursensor nochmals in Subklassen unterschieden. Einspursensoren unterteilen sich dabei in drei Subklassen:\\ + \begin{enumerate} + \item{Einspur - Geradeaus} + \item{Einspur - Links} + \item{Einspur - Rechts} + \end{enumerate} + Mischspursensoren dagegen lassen sich in vier Subklassen unterteilen: + \begin{enumerate} + \item{Mischspur - Geradeaus + Rechts} + \item{Mischspur - Geradeaus + Links} + \item{Mischspur - Geradeaus + Rechts + Links} + \item{Mischspur - Rechts + Links} + \end{enumerate} + Alle beschriebenen Sensorklassen und deren Subklassen sind in dem betrachteten Ausschnitt von Darmstadt enthalten.\\ \\ + F"ur die Modellierung der Kreuzungen sind mehr Daten bekannt - die Positionen der Induktionsschleifen. Sensoren werden als Achtecke mit aufgetragenen Flie"srichtungen dargestellt. Die Verbindungen von Sensoren und virtuellen Sensoren werden analog zur Kreuzungs"ubersicht als Pfeile mit ihrer Flie"srichtung eingezeichnet. Dekoriert wird ein Kreuzungsbild dabei mit bis zu acht virtuellen Sensorknoten, jeweils ein rechteckiger f"ur den Kreuzungsausgang, ein runden f"ur den Kreuzungseingang. Die Position des Sensors wird dahingehend vereinfacht, dass er einem Kreuzungseingang zugeordnet wird und direkt nach dem virtuellen Eingangssensor platziert wird. + \begin{figure}[htbp!] + \centering + \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} + \caption{H"andische Modellierung der Kreuzung A23} + \label{abb:a23.2} + \end{figure} + Wie in Figur \autoref{abb:a23.2} zu erkennen, sind in der Kreuzung A23 zwei Validierungssensoren verbaut. Die manuelle Modellierung verbindet diese mit den entsprechenden Eingangssensoren. Dies ist zwar korrekt, erweist sich f"ur die Berechnung allerdings 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, 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 Gesamtverkehrssituation. Sie dient, wie der Name schon sagt, der "Ubersicht. Ein wesentliches Ziel ist es Verkehrsdaten f"ur dieses Modell zu errechnen oder abzusch"atzen. Es stehen zwar Informationen "uber die einzelnen Kreuzungen zur Verf"ugung. Diese k"onnen allerdings noch nicht auf ein Gesamtbild des Verkehrs "ubertragen werden. +\subsection{Modell als Graph}\label{sec:modell:graph} + Ein naheliegender Modellierungsansatz ist es, das Stra"sennetz als Graph zu modellieren. Dies eignet sich nicht nur deshalb gut, da Graphen sehr gut erforscht und viele Algorithmen auf ihnen zur Verf"ugung stehen, sondern auch, weil die intuitiv gew"ahlte h"andische 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 lineare Gleichungen an Graphen zu l"osen erweist sich als n"utzlich. Einbahnstra"sen und Verkehr mit einer Flussrichtung m"ussen modelliert werden, daher w"ahlt man einen gerichteten Graphen, um dies abzubilden. 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 Javas moderner Template-Technik, Graphen mit beliebigen 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, die eine Visualisierungschnittstelle f"ur Graphen mitbringt. Der Kreuzungs"ubersichtsgraph soll die Graphen der einzelnen Kreuzungen als Knoten enthalten, um den Zusmmenhalt des Modells zu gew"ahrleisten.\\ \\ + Es folgt eine kurze "Ubersicht "uber Graphen und eine Beschreibung der computergest"utzten Modellierung der Kreuzungsgraphen und des Kreuzungs"ubersichtsgraphen. + \subsubsection{Kreuzungsgraph}\label{sec:modell:graph:xr} + Da der Kreuzungs"ubersichtsgraph die Kreuzungsgraphen als Knoten beinhalten soll, werden zuerst die Kreuzungsgraphen modelliert. Dabei gilt es folgende Elemente abzubilden und entweder als Knoten oder als Kante zu definieren. Validierungssensoren werden aus der Modellierung au"sen vorgelassen, um die Modellierung und Berechnung zu vereinfachen. + \begin{itemize} + \item{Stra"se: Ein nicht mit Sensoren best"uckte Stra"se, auf der Autos fahren d"urfen.} + \item{Sensor: Eine Induktionsschleife, welche Verkehrswerte misst.} + \item{Virtueller Sensor: F"ur jede Richtung der Kreuzung wird jeweils ein virtueller Ausgang und Eingang angenommen.} + \end{itemize} + Es liegt nahe, Stra"sen als Kanten und Sensoren, sowie virtuelle Sensoren, als Knoten zu modellieren. Um eine Kreuzung mit JGraphT zu modellieren wurden folgende zwei Klassen definiert: + \begin{itemize} + \item{SE: Sensoren, virtuelle und reale.} + \item{ST: Stra"se} + \end{itemize} + [Klassendiagramm todo] + Die Klasse SE kann dabei Sensorname, Position in Latitude und Longitude, sowie die Kreuzung, welche den Sensor beinhaltet, speichern. Das Feld 'sensorType' erlaubt zus"atzlich die Unterscheidung von virtuellen und realen Sensoren. Des weiteren stehen drei Felder zur Verkn"upfung mit anderen Sensoren zur Verf"ugung. Das Feld 'multipleOutputDirections' erlaubt es zu bestimmen, ob es sich um einen Mehr- oder Einspursensor handelt. Sollte es sich um einen virtuellen Ein- oder Ausgang einer Kreuzung handeln, so werden in den Feldern 'outXR' und 'inXR' die Namen der benachbarten Kreuzungen gespeichert. Zus"atzlich zu den Verkn"upfungs- und Typinformationen k"onnen noch ein Sensorwert und ein Testwert gespeichert werden. Der Wert, falls gesetzt, wird dabei zur Berechnung eingesetzt, w"ahrend der Testwert zur "Uberpr"ufung eines berechneten Ergebnisses dient. Wert und Testwert sind dabei von der Klasse 'VL'.\\ \\ + Die Klasse 'VL' kann die beiden Werte der Induktionsschleifen 'load' und 'count' halten, sowie eine Sensor ID, die eine eindeutige Zuordnung der Werte zu einem Sensor erm"oglicht. Ein Zeitstempel bestimmt dabei den Zeitpunkt der Messung. Zur "Uberpr"ufung eines Wertes mit einem Testwert wird ein gemessener Wert als Testwert gespeichert. Eine Berechnung soll nun einen Wert berechnen, der durch Vergleich mit dem gemessenem Testwert Aufschluss "uber die Genauigkeit der Berechnung gibt.\\ \\ + Die Klasse 'ST' modelliert eine Stra"se. Sie kann die Namen der Knoten, welche sie verbindet speichern, um den Graphen nicht st"andig nach den Namen der Nachbarn abzusuchen zu m"ussen. Diese beiden Werte dienen lediglich der Visualisierung. Desweiteren kann eine Gleitkommazahl gespeichert werden, welche die Abbiegewahrscheinlichkeit von einem Sensor, entlang dieser Kante, repr"asentiert. Dieser Wert dient der Aufteilung eines Mischspursensorwertes. Die Verwendung wird in Kapitel \autoref{sec:berechnung} beschrieben.\\ \\ + Um den Graph mit der JGraphT-Bibliothek zu modellieren, wurde die Klasse 'ListableDirectedGraph' benutzt \autoref{lst:sensorgraph}. Diese Klasse des Frameworks erlaubt gerichtete Graphen aufzubauen, die Struktur zur Berechnung zu verwenden und sp"ater zu visualisieren.\\ + \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} + \begin{lstlisting}[caption={[abc] Die Kreuzungsklasse XR}, label={lst:sensorgraph}, captionpos=bsec] + public ListenableDirectedGraph sensorGraph + = new ListenableDirectedGraph<>(ST.class); + \end{lstlisting} + \end{minipage} + \subsubsection{Kreuzungs"ubersicht}\label{sec:modell:graph:overview} + Auch hier ist eine Reduktion auf Knoten und Kanten notwendig, um die Kreuzungs"ubersicht als Graph darstellen zu k"onnen. Folgende Festlegung wurde hierf"ur getroffen: + \begin{itemize} + \item{Stra"se: Eine Stra"se sei eine Kante} + \item{Kreuzung: Eine Kreuzung sei ein Knoten} + \end{itemize} + [klassendiagramm] + Eine Kreuzung wird hierf"ur mit der Klasse 'XR' modelliert. Sie enth"alt den, in \autoref{lst:sensorgraph} gezeigten Sensorgraph einer Kreuzung. Weiterhin werden f"ur die Kreuzungen eine Position in Latitude und Longitude abgespeichert, sowie alle verbundenen eingehenden Kreuzungen und alle ausgehenden Kreuzungen. Das Speichern von beiden, Vorg"anger- und Nachfolgerkreuzungen, ist zum Aufbau des Graphen nicht n"otig. Daf"ur w"urden entweder Ein- oder Ausg"ange ausreichen. Um Visualisierung und Berechnung zu vereinfachen wurden allerdings beide definiert. \\ \\ + Eine Stra"se wird, wie in der Kreuzungsmodellierung mit der Klasse ST beschrieben. Das Feld f"ur die Abbiegewahrscheinlichkeit kann allerdings nicht gef"ullt werden, da keine Abbiegewahrscheinlichkeiten au"serhalb von Kreuzungen bekannt sind. Das Feld wird sp"aterhin zum Speichern von Fl"ussen zwischen den Kreuzungen benutzt. +\subsection{Modell als Matrix}\label{sec:modell:matrix} + Als Grundlage f"ur die Berechnung wurde eine Matrixdarstellung f"ur Kreuzungen entwickelt. Der oben entwickelte Graph l"asst sich dabei in eine Matrixform "uberf"uhren. Matrizen bieten z.b. durch Matrixmultiplikation die M"oglichkeit komplexe Zusammenh"ange durch einfache Rechenschritte auszudr"ucken. Mehr zu der Verwendung von Matrizen ist im Kapitel \autoref{sec:berechnung} zu finden.\\ \\ + Um en Graph einer Kreuzung zu beschreiben, ist es n"otig die Verbindungen von Sensoren zu deren m"oglichen Kreuzungsausg"angen bzw. -Eing"angen zu modellieren. F"ur Kreuzungen mit sog. Validierungssensoren ist dies nicht m"oglich, da die Validierungssensoren zwischen Sensor und Kreuzungsausgang in dem Graphen liegen. Aus diesem Grund werden f"ur die Matrixdarstellung die Validierungssensoren nicht mit abgebildet. Im Kapitel \autoref{sec:berechnung} wird nochmals n"aher darauf eingegangen, wie diese Sensoren zur L"osung eines Gleichungssystems, um Abbiegewahrscheinlichkeiten 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 den meisten Kreuzungen, ohne das Weglassen von Sensoren, 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 den Kreuzungsgraphen ohne Validierungssensoren ab. + \subsubsection{Ausgangsmatrix}\label{sec:modell:matrix:out} + Die Ausgangsmatrize zeigt auf, von welchem Sensor welcher Ausgang einer Kreuzung bedient werden kann. 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 in \autoref{tbl:ausgangsmatrixallg} beschrieben.\\ + \begin{tabular}{|l|l|l|l|l|}\label{tbl:ausgangsmatrixallg} + & $S_1$ & $S_2$ & \dots & $S_n$\\ + \hline + $Out_1$ & 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\\ + \hline + \end{tabular}\\ + $Out_1$ bis $Out_4$ bezeichnen dabei die Ausg"ange einer Kreuzung. Je nach Kreuzung k"onnen dies auch lediglich drei Ausg"ange sein. $S_1$ bis $S_n$ bezeichnen die einzelnen Sensoren, einschlie"slich der virtuellen Sensoren f"ur Kreuzungseingangsspuren ohne Sensor. Da alle modellierten Kreuzungen der Stadt Darmstadt auf jeder Eingangsspur mit Sensoren best"uckt sind, sind keine virtuellen Sensoren f"ur Eingangsspuren notwendig. Die Werte der Matrize bestimmen ob eine Verbindung zwischen Sensor und jeweiligem Kreuzungsausgang besteht. Einspursensoren besitzen nur eine Verbindung, Mischspursensoren besitzen dagegen mehr als eine Verbindung.\\ \\ + \begin{figure}[htbp!]\label{abb:a23} + \centering + \fbox{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} + \caption{Kreuzung A23} + \end{figure} + Am Beispiel der Kreuzung A23\ref{abb:a23} sei das hier demonstriert. Dabei entf"allt eine Ausgangsspalte, da die A23 eine Einbahnstra"se beinhaltet, welche es gebietet die Kreuzung nur in die eine Richtung zu verlassen. Die entsprechenden Ausgangsspalten werden dabei mit der, auf den Ausgang folgenden, Kreuzung benannt.\\ + \begin{tabular}{c|c|c|c|c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10\\ + \hline + A4 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\ + \hline + A12 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0\\ + \hline + A104 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1\\ + \end{tabular}\\ + Diese Matrix wird als Ausgangsmatrix bezeichnet. D13 und D14 werden hier nicht mit abgebildet, da es sich um Validierungssensoren handelt. + \subsubsection{Eingangsmatrix}\label{sec:modell:matrix:in} + 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 Stra"se 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 und in Abbildung \autoref{tbl:eingangsmatrixallg} beschrieben.\\ + \begin{tabular}{|l|l|l|l|l|}\label{tbl:eingangsmatrixallg} + & $S_1$ & $S_2$ & \dots & $S_n$\\ + \hline + $In_1$ & 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\\ + \hline + \end{tabular}\\ + $In_1$ bis $In_4$ bezeichnen dabei die Eing"ange einer Kreuzung. $S_1$ bis $S_n$ bezeichnen die einzelnen Sensoren, einschlie"slich 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 Einbahnstra"se begr"undet, welche "uber die Kreuzung verl"auft.\\ + \begin{tabular}{c|c|c|c|c|c|c|c|c|c|c} + & D1 & D2 & D3 & D4 & D5 & D6 & D7 & D8 & D9 & D10\\ + \hline + A4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1\\ + \hline + A12 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + \hline + A104 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ + \end{tabular}\\ + Ein- und Ausgangsmatrix zusammen beschreiben den gesamten Graphen ohne Validierungssensoren. Im Kapitel \autoref{sec:berechnung} wird n"aher auf eine m"ogliche Verwendung der Validierungssensoren eingegangen. +\subsection{Datenbankmodell}\label{sec:modell:datenbankschema} + Um mit einem Programm schneller und einfacher auf die, im Kapitel \autoref{sec:datengrund} extrahierten Daten zugreifen zu k"onnen, bietet es sich an, diese in einem Datenbank Server abzuspeichern. Hierf"ur wurde ein Datenbankschema erstellt, das 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. 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, sowie deren Verbindungen untereinander.} + \item{Die Abbiegewahrscheinlichkeit welche der richtigen Verbindungen zwischen Sensor und entsprechendem virtuellen Kreuzungsausgang zugordnet ist.} + \item{Induktionsschleifwerte der Sensoren.} + \end{enumerate} + [ER diagramm todo] + F"ur Sensoren werden daf"ur folgende Daten gespeichert: + \begin{itemize} + \item{Eindeutige ID des Sensors} + \item{Name des Sensors} + \item{Position des Sensors als Latitude und Longitude Werte} + \item{Die zu dem Sensor geh"orige Kreuzung} + \item{Der Sensortyp des Sensors} + \item{Die Verbindungen des Sensor mit bis zu drei Sensoren.} + \item{Der Typ der Spur, auf dem der Sensor verbaut ist: Misch- oder Einzelspur} + \item{F"ur virtuelle Sensoren der Aus- und Eing"ange einer Kreuzung, der Name der vorhergehenden bzw. nachfolgenden Kreuzung.} + \end{itemize} + Dabei ist eine ID ein eindeutiges Merkmal des Sensors. Der Sensorname dagegen ist nur innerhalb einer Kreuzung eindeutig. So ist auf Kreuzung A4\ref{anhang:a4} ein Sensor D11 zu finden, sowie auf Kreuzung A5\ref{anhang:a5} einer mit dem selben Namen. Dementsprechend sind Verkn"upfungen unter den Sensoren "uber die Sensor ID identifiziert. Diese Verkn"upfungen werden "uber die Felder 'toSensorLeftID', 'toSensorStraightID' und 'toSensorRightID' modelliert und erlauben es den Graphen aufzubauen. Verbindungen zwischen Knoten werden dabei in Verkehrsflussrichtung gespeichert. In der Spalte 'sensorType' wird der Type des Sensors gespeichert. Eine zus"atzliche Tabelle erlaubt es Einzelheiten zu den einzelnen Sensortypen zu definieren. In dieser Arbeit wird nur auf die beiden Sensortypen 'virtueller Sensor' und 'realer Sensor' zur"uckgegriffen. Die Datenbankstruktur erlaubt es allerdings durch hinzuf"ugen einer Zeile in der Tabelle 'bt\_sensor\_types' einen neuen Sensortyp zu definieren. Auf diesen Typ kann ein Algorithmus, der auf dem Graphen rechnet, anders als auf die anderen beiden Sensortypen reagieren.\\ \\ + 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 relativ zu anderen Objekten der Modellierung, darstellen zu k"onnen. Die Kreuzungsnamen sind in der Stadt Darmstadt eindeutig, weshalb es keine ID f"ur eine Identifikation von Kreuzungen bedarf.\\ \\ + Die Tabelle 'Values' enth"alt aufbereitete Induktionsschleifenwerte. Diese werden mit den Abfragen, welche in \autoref{sec:datengrund} beschrieben sind, aus der MYSQL-Datenbank der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten extrahiert, um das manuelle Untersuchung der CSV-Dateien zu umgehen. Sensoren werden hierf"ur mit ihrer eindeutigen ID identifiziert. Ein Zeitstempel der Sensordaten erlaubt es mehrere Datens"atze von verschiedenen Zeiten zu speichern. Ein Filter auf dem Zeitstempel erlaubt es Daten eines gew"ahlten Zeitpunktes wieder zu extrahieren. Gespeichert werden daf"ur die Werte 'load' und 'count' der Induktionsschleifen, zusammen mit der eindeutigen Sensor ID und dem entsprechen Zeitstempel.\\ \\ + Die Tabelle FlowStatistics enth"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. Da diese Werte, der Tabelle aus der Abbiegewahrscheinlichkeitstabelle der Stadt Darmstadt entnommen wurden, werden Sensoren "uber Kreuzungs- und Sensorname identifiziert und nicht "uber eine eindeutige Sensor ID. Dies ist m"oglich, obwohl Sensornamen nicht eindeutig sind, da innerhalb einer Kreuzung eine eindeutige Identifikation "uber den Namen m"oglich ist. Eine Kombination aus dem eindeutigen Kreuzungsnamen und des, innerhalb der Kreuzung, eindeutigen Sensornamens, kann ein Sensor eindeutig identifizieren. F"ur die Abbiegewahrscheinlichkeitstabelle werden, neben dem Kreuzungs- und Sensornamen, bis zu drei verschiedene Abbiegewahrscheinlichkeiten angegeben. N"amlich die Wahrscheinlichkeit, dass ein Verkehrsteilnehmer, der "uber den Sensor f"ahrt, die Kreuzung rechts, links oder geradeaus verl"asst. Zus"atzlich wird der n"achste Sensorknoten, diesmal identifiziert "uber die SensorID, f"ur jede Richtung mit angegeben. Wie die Zuordnung der Abbiegewahrscheinlichkeiten f"ur Links, Rechts und Geradeaus zu einem Knoten erfolgt, wird im Kapitel \autoref{sec:berechnung} beschrieben.\\ + Neben den Abbiegewahrscheinlichkeiten kann in der Abbiegewahrscheinlichkeitstabelle ebenfalls ein Zeitstempel und eine Intervalll"ange zu jedem Datensatz gespeichert werden. Dies erlaubt es, genauere, zeitspezifische Abbiegewahrscheinlichkeiten abzuspeichern. F"ur diese Arbeit lagen allerdings ausschlie"slich die Werte der Stadt Darmstadt vor, welche "uber alle Messungen gemittelt sind. +\subsection{Implementierung} +[todo] +\subsection{Zuk"unftige Herausforderungen des Modells} \label{sec:modell:limits} + Das entwickelte Modell kann nicht alle Verkehrsverhalten modellieren. In diesem Abschnitt wird behandelt, welche Einschr"ankungen das Modell mit sich bringt und welche Reduktionen des Detailgrades vorgenommen wurden.\\ \\ + Das Modell kann sog. 'U-Turns', nicht modellieren. Als 'U-Turn' bezeichnet man das Verkehrsman"over, dass den Verkehrsteilnehmer von dem Kreuzungseingang einer Kreuzung zu dem Ausgang, welcher in die Richtung zeigt, aus der er gekommen ist, zur"uck bringt. Dieses Verkehrsverhalten ist selten zu beobachten und wurde aus diesem nicht modelliert. Desweiteren w"urde eine Modellierung dieses Man"overs eine 'U-Turn-Wahrscheinlichkeit' erfordern, welche nicht vorliegt.\\ \\ + Eine weitere, sehr elementare Schw"ache des Modells ist die Abstraktion der Sensorposition. Wie in den manuell angefertigten Kreuzungszeichnungen wird die Position eines Sensors innerhalb des Graphenmodells einem Eingang zugeordnet. Die Latitude und Longitude Werte des Sensors werden nur zur Visualisierung benutzt und nicht zur Berechnung. Ein Spurwechseln nach dem "Uberfahren eines Sensors kann nicht modelliert werden. Die Genauigkeit des Modells h"angt folglich direkt mit der Entfernung des Sensors von der Kreuzung ab. Ist der Sensor weit entfernt, so kann ein Verkehrsteilnehmer die Spur nochmals wechseln. Ist der Sensor direkt vor der Haltelinie verbaut, kann die Spur nicht mehr gewechselt werden, wenn das Fahrzeug darauf steht. Sind die Sensoren eines Kreuzungseingangs auf verschiedenen H"ohen in die Stra"se eingelassen, so k"onnen Verkehrsteilnehmer im schlechtesten Fall "uber zwei Sensoren fahren, wenn sie nach dem "Uberfahren eines Sensors die Spur wechseln, die einen Sensor weiter vorne im Kreuzungsbereich verbaut hat.\\ \\ + Neben diesen Einschr"ankungen wird nur g"ultiges Verkehrsverhalten modelliert. So k"onnen Verkehrsteilnehmer, welche zwar auf einer Rechtsabbiegerspur stehen, allerdings geradeaus fahren, nicht von dem Modell modelliert werden.\\ \\ + Es ist allerdings denkbar, das Modell durch U-Turn-, Spurwechsel- und Falschfahrwahrscheinlichkeiten zu erg"anzen und somit die Menge der modellierbaren Kreuzungszust"ande und -"Uberg"ange zu vergr"o"sern um ein realistischeres Bild des Verkehrs zu berechnen. Allerdings lagen keine Daten "uber das Verhalten der Verkehrsteilnehmer vor. + + + + W"ahrend der Datenanalyse und Aufbereitung wurden einige Herausforderungen erkannt, die es zu l"osen gilt, da sie andernfalls die L"osungsm"oglichkeiten einschr"anken. Zum einen ist dies das Zeitproblem, welches eine Verbindung von Sensorwerten von zwei Kreuzungen nicht zul"asst, zum anderen das Abbiegeproblem, welches beschreibt, dass die Abbiegewahrscheinlichkeit nicht mit Hilfe der Sensorwerte gemessen werden kann. + \subsubsection{Herausforderung: Verfolgung von Fahrzeugen "uber eine Kreuzung hinaus} \label{sec:datengrund:probtime} + Die Daten der Induktionsschleifen sind die Werte der Sensoren "uber die letzte Minute. Sie zeigen eine Art summierte Momentaufnahme des Verkehrs an den Messpunkten. Das macht es allerdings schwer, zwei Messungen in eine Beziehung zu setzen. Bildlich gesprochen kann man nicht trivial bestimmen, wie lange ein Auto von der einen zur anderen Kreuzung ben"otigt. Da die Daten nur f"ur bestimmte Zeitpunkte zur Verf"ugung stehen, kann nicht mehr festgestellt werden, wann ein Auto, welches an Kreuzung A "uber den Sensor gefahren ist, an Kreuzung B ankommt und dort "uber einen anderen Sensor f"ahrt. Die 'Verfolgung' eines Autos ist somit nicht m"oglich, da nicht festgestellt werden kann, wie weit es sich bis zur n"achsten Momentaufnahme fortbewegt hat.\\ \\ + Dieses Problem wurde Zeitproblem getauft und konnte nicht vollst"andig gel"ost werden. Die Arbeit \cite{thesis:michael} versucht dieses Problem durch das Gleichsetzen des Kreuzungsausgangswertes mit dem Eingangswert der darauffolgenden Kreuzung zu l"osen. Dies ist allerdings nicht im Minutentakt durchzuf"uhren. Durch den Zeitversatz der Messungen m"ussen die Werte gemittelt werden. F"ur eine Berechnung des momentanen Verkehrsaufkommens zu einem Zeitpunkt eignet sich das Verfahren nicht. + \subsubsection{Herausforderung: Genaues Bestimmen der Abbiegewahrscheinlichkeit} \label{sec:datengrund:abbprob} + Das 'Abbiegeproblem' ist auf zu wenige Sensorwerte zur"uckzuf"uhren. In den Kreuzungen von Darmstadt sind die Induktionsschleifen am Kreuzungseingang verbaut, jedoch nicht am Kreuzungsausgang (bis auf wenige Ausnahmen). Es kann f"ur Mischspursensoren folglich nicht 'live' bestimmt werden, wie viele Autos in die eine und wie viele in die andere Richtung gefahren sind. Um den Fluss trotzdem bestimmen zu k"onnen, wird in dieser Arbeit mit Abbiegewahrscheinlichkeiten gearbeitet, die angeben, wie viel Prozent des Verkehrs, der "uber einen Sensor f"ahrt, die Kreuzung in welche Richtung verl"asst. Gel"ost wurde dieses Problem durch gemittelte Abbiegewahrscheinlichkeiten an den Sensoren, die von der Stadt Darmstadt ermittelt wurden. Eine L"osung des Abbiegeproblems ist mit einem fl"achendeckenden Einsatz von Vallidierungssensoren m"oglich. Mehr Informationen zu Vallierungssensoren und deren Verwendungsm"oglichkeiten sind im Kapitel \autoref{sec:berechnung} aufgezeigt. +\newpage \ 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 c226a680..5735d49e 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex @@ -8,15 +8,16 @@ In diesem Kapitel wird die Validierung der berechneten Verkehrswerte beschrieben \subsection{Verkehrsz"ahlung} Da kein anderes Testverfahren gefunden wurde, welches eine Validierung der Daten ermöglichen würde, wurde im Rahmen dieser Arbeit eine Verkehrsz"ahlung durchgef"uhrt. Diese Verkehrsz"ahlung wurde mit Hilfe von \textit{Scholz} \autoref{thesis:michael} durchgeführt. Gez"ahlt wurde dabei mit Strichliste an den Kreuzungen [], [] und []. Dabei wurden in der einen Messreihe die Autos an den Ausg"angen gez"ahlt, um die berechneten Werte der virtuellen Kreuzungsausg"ange in dem Graphenmodell validieren zu k"onnen. Desweiteren wurden die Fahrzeuge gez"ahlt, die "uber die Sensoren [] und [] gefahren sind. Jeder Sensor bzw. Ausgang wurde dafür über einen Zeitraum von 15 Minuten beobachtet und der Verkehr gezählt.\\ \\ Es wurden dabei starke Unterschiede zwischen den gezählten und den, von den Sensoren ermittelten, Werten festgestellt. Dies ist zum einen auf ungenaue und fehleranfällige Sensorik(vgl. \autoref{sec:grundlagen}) zurückzuführen, zum anderen muss für adaptiv gesteuerte Ampelanlagen sichergestellt werden, dass alle Fahrzeuge erkannt werden, um diese über die Kreuzung zu lassen. Diese Vorgabe wird dadurch erfüllt, dass die Sensorik leichter als nötig auslöst, um wirklich jedes Fahrzeug zu erkennen. Dies wiederum erhöht die Fehleranfälligkeit des Sensors. [todo auswertung]\\ \\ - In einer weiteren Untersuchung wurde der Sensor [] im Minutentakt gezählt, um eine genaueres Bild der Abweichung zu erhalten. Die gemessenen Werte lagen dabei bis zu 700\% von dem tatsächlichen Wert entfernt. Bei dieser Zählung wurden neben der Anzahl der Verkehrsteilnehmer der Fahrzeugtyp untersucht, um die Fehleranfälligkeit des Sensors für die verschiedenen Fahrzeugtypen genauer zu bestimmen.[todo auswertung]\\ \\ - \subsection{Validierung der Verkehrsaufkommensvorhersage} - hoher wert am ausgang, hoher wert an der n"achsten kreuzung - - \subsection{Sensor} - + In einer weiteren Untersuchung wurde der Sensor [] im Minutentakt gezählt, um eine genaueres Bild der Abweichung zu erhalten. Die gemessenen Werte lagen dabei bis zu 700\% von dem gezählten Wert entfernt. Bei dieser Zählung wurden neben der Anzahl der Verkehrsteilnehmer der Fahrzeugtyp untersucht, um die Fehleranfälligkeit des Sensors für die verschiedenen Fahrzeugtypen genauer zu bestimmen.[todo auswertung]\\ \\ + Die Erkenntnisse über die Ungenauigkeiten der Sensoren decken sich mit den Befunden der Arbeit [] von [][cite]. In dem dort Untersuchten Gebiet der Stadt Hannover wurde eine sehr starke Varianz der Messgenauigkeit der dort verbauten Induktionsschleifen festgestellt. + \subsection{Validierung der Berechneten Verkehrswerte} + Eine Berechnung der Verkehrswerte mittels LGS mit jeweils den Sensorwerten und den gezählten Werten ergabt eine Abweichung von bis zu x\%.[geht nicht - zeit] + [todo -> rechnung, abweichung bestimmen] + + Da die Berechnung der Kreuzungsein- und Ausgangswerte direkt von der Genauigkeit der Sensorwerte abhängt, ist die Genauigkeit der berechneten Werte entsprechend. Eine Verbesserung der Qualität der Sensordaten würde eine direkte Verbesserung der Berechneten Werte zur folge haben. \subsection{"Uberpr"ufung des Modells} + [todo ausblick] Das in Kapitel \autoref{sec:modell} entwickelte Modell muss auf seine G"ultigkeit "uberpr"uft werden. Hierzu wird "uberpr"uft, ob die f"ur das Modell getroffenen Annahmen mit einer realen Verkehrssituation angebracht sind. - [falschabbieger] [spurwechsler] [uturns]

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