From 850e42ba1edb8e759172b98de7851e8cc34403d7 Mon Sep 17 00:00:00 2001 From: rylon Date: Sat, 17 Aug 2013 19:30:46 +0200 Subject: [PATCH] thesis --- .../Bachelor Thesis/thesis_ug/TUDthesis.aux | 262 ++++---- .../Bachelor Thesis/thesis_ug/TUDthesis.bbl | 9 +- .../Bachelor Thesis/thesis_ug/TUDthesis.log | 621 +++++++++++------- .../Bachelor Thesis/thesis_ug/TUDthesis.lol | 6 +- .../Bachelor Thesis/thesis_ug/TUDthesis.out | 29 +- .../Bachelor Thesis/thesis_ug/TUDthesis.pdf | Bin 17137601 -> 17157226 bytes .../thesis_ug/TUDthesis.synctex.gz | Bin 442555 -> 477215 bytes .../Bachelor Thesis/thesis_ug/TUDthesis.toc | 47 +- .../thesis_ug/tex/ausblick.tex | 2 +- .../thesis_ug/tex/berechnung.tex | 46 +- .../thesis_ug/tex/datengrund.tex | 29 +- .../thesis_ug/tex/einleitung.tex | 14 +- .../Bachelor Thesis/thesis_ug/tex/modell.tex | 16 +- .../thesis_ug/tex/uebersicht.tex | 4 +- .../thesis_ug/tex/validierung.tex | 2 +- .../thesis_ug/tex/visualisierung.tex | 10 +- 16 files changed, 632 insertions(+), 465 deletions(-) diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux index 9f1010cc..5ad4426a 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux @@ -21,7 +21,13 @@ \newlabel{sec:uebersicht}{{1}{1}{"Ubersicht\relax }{section.1}{}} \citation{web:statista:lkw} \citation{web:statista:pkw} +\citation{web:statista:gueter} \citation{web:statista:laerm} +\citation{paper:adaptiv} +\citation{paper:kwonmurphy} +\citation{thesis:neubert} +\citation{thesis:mueller} +\citation{thesis:lehnhoff} \@writefile{toc}{\contentsline {section}{\numberline {2}Einleitung}{4}{section.2}} \newlabel{sec:einleitung}{{2}{4}{Einleitung\relax }{section.2}{}} \citation{thesis:elfers} @@ -34,7 +40,7 @@ \citation{thesis:neubert} \citation{book:rilsa} \citation{book:verkehrdata} -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Ministadt, ausschnitt von Darmstadt der innerhalb dieser Arbeit betrachtet wird.}}{5}{figure.1}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces 'Ministadt', ausschnitt von Darmstadt der innerhalb dieser Arbeit betrachtet wird.}}{5}{figure.1}} \citation{thesis:mazur} \citation{thesis:mazur} \citation{thesis:lehnhoff} @@ -42,11 +48,13 @@ \newlabel{abb:2}{{3.1}{6}{Induktionsschleifen\relax }{subfigure.2.1}{}} \newlabel{abb:3}{{3.1}{6}{Induktionsschleifen\relax }{subfigure.2.2}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Induktionsschleife mit Kabel nach Abfr\active@dq \dq@prtct{a}sen der Fahrbahn. 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+\newlabel{sec:ausblick}{{8}{31}{Ausblick\relax }{section.8}{}} \bibstyle{plainnat} \bibdata{bib/literature} \bibcite{book:rilsa}{{Arbeitsgruppe: Verkehrsmanagement}(2010)} @@ -183,60 +204,61 @@ \bibcite{lect:simumod}{{Michael Reimann}(2007)} \bibcite{thesis:michael}{{Michael Scholz}(2013)} \bibcite{web:statista:laerm}{Statista(2010)} +\bibcite{web:statista:gueter}{Statista(2012)} \bibcite{web:statista:lkw}{Statista(2013{a})} \bibcite{web:statista:pkw}{Statista(2013{b})} \bibcite{book:verkehrdata}{{Statitisches Bundesamt}(2013)} -\@writefile{toc}{\contentsline {section}{\numberline {9}Glossar}{32}{section.8}} -\@writefile{toc}{\contentsline {section}{\numberline {10}Abbildungsverzeichnis}{33}{section.8}} -\@writefile{toc}{\contentsline {section}{\numberline {11}Quellcodeverzeichnis}{33}{section.8}} -\@writefile{toc}{\contentsline {section}{\numberline {12}Anhang}{34}{section.12}} -\newlabel{sec:anhang}{{12}{34}{Anhang\relax }{section.12}{}} -\@writefile{lof}{\contentsline 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Thesis/thesis_ug/TUDthesis.bbl @@ -1,4 +1,4 @@ -\begin{thebibliography}{19} +\begin{thebibliography}{20} \providecommand{\natexlab}[1]{#1} \providecommand{\url}[1]{\texttt{#1}} \expandafter\ifx\csname urlstyle\endcsname\relax @@ -95,6 +95,13 @@ Statista. \newblock URL \url{http://de.statista.com/statistik/daten/studie/180759/umfrage/laermbelaestigung-in-deutschland-nach-geraeuschquellen/}. +\bibitem[Statista(2012)]{web:statista:gueter} +Statista. +\newblock Statista statistiken bzgl. des güteraufkommen je verkehrsträger in + deutschland in den jahren 2011 und 2012 (in millionen tonnen), June 2012. +\newblock URL + \url{http://de.statista.com/statistik/daten/studie/12240/umfrage/gueteraufkommen-in-deutschland-je-verkehrstraeger/}. + \bibitem[Statista(2013{\natexlab{a}})]{web:statista:lkw} Statista. \newblock Statista statistiken bzgl. der anzahl der gemeldeten lkw in diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log index 04ec81c4..b29a3b2a 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) 17 AUG 2013 02:04 +This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.8.13) 17 AUG 2013 19:29 entering extended mode **TUDthesis.tex -("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.tex" +("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.tex" LaTeX2e <2009/09/24> Babel and hyphenation patterns for english, afrikaans, ancientgreek, ar abic, armenian, assamese, basque, bengali, bokmal, bulgarian, catalan, coptic, @@ -956,11 +956,7 @@ File: lstlang1.sty 2013/06/27 1.5pre1 listings language file LaTeX Warning: Unused global option(s): [article,colorback,accentcolor=tud9d]. -("C:\daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux" - -LaTeX Warning: Label 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+\contentsline {lstlisting}{\numberline {3}abc}{18}{lstlisting.3} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out index 560d64cd..7609a51f 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out @@ -35,17 +35,18 @@ \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 [3][-]{subsubsection.5.4.2}{Sonderfall: Vallidierungssensor}{subsection.5.4}% 37 -\BOOKMARK [1][-]{section.6}{Visualisierung}{}% 38 -\BOOKMARK [2][-]{subsection.6.1}{Visualisierung des Graphen mit Geoinformationen}{section.6}% 39 -\BOOKMARK [2][-]{subsection.6.2}{Visualisierung des JGraphT-Graphen}{section.6}% 40 -\BOOKMARK [1][-]{section.7}{Validierung}{}% 41 -\BOOKMARK [2][-]{subsection.7.1}{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}{Ausblick}{}% 47 -\BOOKMARK [1][-]{section.8}{Glossar}{}% 48 -\BOOKMARK [1][-]{section.8}{Abbildungsverzeichnis}{}% 49 -\BOOKMARK [1][-]{section.8}{Quellcodeverzeichnis}{}% 50 -\BOOKMARK [1][-]{section.12}{Anhang}{}% 51 +\BOOKMARK [3][-]{subsubsection.5.4.3}{Abbiegewahrscheinlichkeiten}{subsection.5.4}% 38 +\BOOKMARK [1][-]{section.6}{Visualisierung}{}% 39 +\BOOKMARK [2][-]{subsection.6.1}{Visualisierung des Graphen mit Geoinformationen}{section.6}% 40 +\BOOKMARK [2][-]{subsection.6.2}{Visualisierung des JGraphT-Graphen}{section.6}% 41 +\BOOKMARK [1][-]{section.7}{Validierung}{}% 42 +\BOOKMARK [2][-]{subsection.7.1}{Testdatenmenge}{section.7}% 43 +\BOOKMARK 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--- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.toc @@ -7,7 +7,7 @@ \contentsline {subsection}{\numberline {3.4}Induktionsschleifenwerte}{8}{subsection.3.4} \contentsline {subsubsection}{\numberline {3.4.1}CSV-Dateien der Induktionsschleifenwerte}{9}{subsubsection.3.4.1} \contentsline {subsubsection}{\numberline {3.4.2}MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten}{9}{subsubsection.3.4.2} -\contentsline {subsection}{\numberline {3.5}Geographischer Ausschnitt der Daten}{10}{subsection.3.5} +\contentsline {subsection}{\numberline {3.5}Geographischer Ausschnitt der Daten}{11}{subsection.3.5} \contentsline {subsection}{\numberline {3.6}CAD-Zeichnungen der Kreuzungen}{11}{subsection.3.6} \contentsline {subsection}{\numberline {3.7}Abbiegewahrscheinlichkeiten}{12}{subsection.3.7} \contentsline {subsection}{\numberline {3.8}Herausforderungen}{12}{subsection.3.8} @@ -16,14 +16,14 @@ \contentsline {section}{\numberline {4}Verkehrsmodell}{14}{section.4} \contentsline {subsection}{\numberline {4.1}Modell der Ministadt}{14}{subsection.4.1} \contentsline {subsection}{\numberline {4.2}Modell als Graph}{16}{subsection.4.2} -\contentsline {subsubsection}{\numberline {4.2.1}Grundlagen}{16}{subsubsection.4.2.1} +\contentsline {subsubsection}{\numberline {4.2.1}Grundlagen}{17}{subsubsection.4.2.1} \contentsline {subsubsection}{\numberline {4.2.2}Kreuzungsgraph}{17}{subsubsection.4.2.2} -\contentsline {subsubsection}{\numberline {4.2.3}Kreuzungs\active@dq \dq@prtct {u}bersicht}{19}{subsubsection.4.2.3} -\contentsline {subsection}{\numberline {4.3}Modell als Matrix}{19}{subsection.4.3} +\contentsline {subsubsection}{\numberline {4.2.3}Kreuzungs\active@dq \dq@prtct {u}bersicht}{18}{subsubsection.4.2.3} +\contentsline {subsection}{\numberline {4.3}Modell als Matrix}{18}{subsection.4.3} \contentsline {subsubsection}{\numberline {4.3.1}Ausgangsmatrix}{19}{subsubsection.4.3.1} \contentsline {subsubsection}{\numberline {4.3.2}Eingangsmatrix}{20}{subsubsection.4.3.2} -\contentsline {subsection}{\numberline {4.4}Datenbankmodell}{21}{subsection.4.4} -\contentsline {subsection}{\numberline {4.5}Einschr\active@dq \dq@prtct {a}nkungen und Schw\active@dq \dq@prtct {a}chen des Modell}{22}{subsection.4.5} +\contentsline {subsection}{\numberline {4.4}Datenbankmodell}{20}{subsection.4.4} +\contentsline {subsection}{\numberline {4.5}Einschr\active@dq \dq@prtct {a}nkungen und Schw\active@dq \dq@prtct {a}chen des Modell}{21}{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} @@ -31,21 +31,22 @@ \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 {5.3.2}Lineares Gleichungssystem einer Kreuzung}{25}{subsubsection.5.3.2} +\contentsline {subsection}{\numberline {5.4}Kreuzungsberechnung am Graphen}{27}{subsection.5.4} \contentsline {subsubsection}{\numberline {5.4.1}Verkehrsfluss zwischen Kreuzungen}{27}{subsubsection.5.4.1} -\contentsline {subsubsection}{\numberline {5.4.2}Sonderfall: Vallidierungssensor}{28}{subsubsection.5.4.2} -\contentsline {section}{\numberline {6}Visualisierung}{28}{section.6} -\contentsline {subsection}{\numberline {6.1}Visualisierung des Graphen mit Geoinformationen}{28}{subsection.6.1} -\contentsline {subsection}{\numberline {6.2}Visualisierung des JGraphT-Graphen}{28}{subsection.6.2} -\contentsline {section}{\numberline {7}Validierung}{29}{section.7} -\contentsline {subsection}{\numberline {7.1}Testdatenmenge}{29}{subsection.7.1} -\contentsline {subsection}{\numberline {7.2}Verkehrsz\active@dq \dq@prtct {a}hlung}{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}\active@dq \dq@prtct {U}berpr\active@dq \dq@prtct {u}fung des Modells}{29}{subsection.7.5} -\contentsline {section}{\numberline {8}Ausblick}{30}{section.8} -\contentsline {section}{\numberline {9}Glossar}{32}{section.8} -\contentsline {section}{\numberline {10}Abbildungsverzeichnis}{33}{section.8} -\contentsline {section}{\numberline {11}Quellcodeverzeichnis}{33}{section.8} -\contentsline {section}{\numberline {12}Anhang}{34}{section.12} +\contentsline {subsubsection}{\numberline {5.4.2}Sonderfall: Vallidierungssensor}{27}{subsubsection.5.4.2} +\contentsline {subsubsection}{\numberline {5.4.3}Abbiegewahrscheinlichkeiten}{27}{subsubsection.5.4.3} +\contentsline {section}{\numberline {6}Visualisierung}{29}{section.6} +\contentsline {subsection}{\numberline {6.1}Visualisierung des Graphen mit Geoinformationen}{29}{subsection.6.1} +\contentsline {subsection}{\numberline {6.2}Visualisierung des JGraphT-Graphen}{29}{subsection.6.2} +\contentsline {section}{\numberline {7}Validierung}{30}{section.7} +\contentsline {subsection}{\numberline {7.1}Testdatenmenge}{30}{subsection.7.1} +\contentsline {subsection}{\numberline {7.2}Verkehrsz\active@dq \dq@prtct {a}hlung}{30}{subsection.7.2} +\contentsline {subsection}{\numberline {7.3}Validierung der Verkehrsaufkommensvorhersage}{30}{subsection.7.3} +\contentsline {subsection}{\numberline {7.4}Sensor}{30}{subsection.7.4} +\contentsline {subsection}{\numberline {7.5}\active@dq \dq@prtct {U}berpr\active@dq \dq@prtct {u}fung des Modells}{30}{subsection.7.5} +\contentsline {section}{\numberline {8}Ausblick}{31}{section.8} +\contentsline {section}{\numberline {9}Glossar}{33}{section.8} +\contentsline {section}{\numberline {10}Abbildungsverzeichnis}{34}{section.8} +\contentsline {section}{\numberline {11}Quellcodeverzeichnis}{34}{section.8} +\contentsline {section}{\numberline {12}Anhang}{35}{section.12} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex index 1c27a05a..5600dcee 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex @@ -16,5 +16,5 @@ Dadurch w"urde eine Genauere und bessere Modellierung des Verkehrs m"oglich. [genauere sensordaten] [genauere abbiegewahrscheinlichkeiten] [validierungssensoren] -Die nächste Generation der verkehrsabhängig gesteuerten Ampelanlagen, die sog. voll-adaptiven Lichtanlagen, erlauben es Kreuzungen untereinander Sensorwerte auszutauschen um den Verkehr noch besser fließen zu lassen. Es ist zu erwarten, das mit dieser neuen Technik noch mehr Sensorik auf die Straßen der Großstädte gelangt und eine wesentlich genauere Untersuchung des Verkehrs zulässt. +Die n"achste Generation der verkehrsabh"angig gesteuerten Ampelanlagen, die sog. voll-adaptiven Lichtanlagen, erlauben es Kreuzungen untereinander Sensorwerte auszutauschen um den Verkehr noch besser fließen zu lassen. Es ist zu erwarten, das mit dieser neuen Technik noch mehr Sensorik auf die Straßen der Großst"adte gelangt und eine wesentlich genauere Untersuchung des Verkehrs zul"asst. \newpage \ 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 5493d57e..88b1ca87 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex @@ -1,6 +1,6 @@ \section{L"osungsans"atze}\label{sec:berechnung} In diesem Kapitel werden drei L"osungsans"atze f"ur die 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 Werte zu berechnen und Fragen zu lösen: +Es galt folgende Werte zu berechnen und Fragen zu l"osen: \begin{enumerate} \item{Werte f"ur virtuelle Sensoren innerhalb einer Kreuzung.}\label{problem:1} \item{Wie viele Autos verlassen die Kreuzung in Richtung Norden/S"uden/Westen/Osten.}\label{problem:2} @@ -11,7 +11,7 @@ Es galt folgende Werte zu berechnen und Fragen zu lösen: \item{Verkehrswerte f"ur einen Zeitpunkt in der Zuknunft berechnen.}\label{problem:7} \end{enumerate} Es wurden im Rahmen dieser Arbeit mehrere Berechnungsans"atze daraufhin "uberpr"uft, ob sie eines der gegebenen Problem l"osen kann. Die beschriebenen Ans"atze sind 'Hidden Markov Modell', 'Wegfindungsalorithmen' wie A* und 'lineares Gleichungssystem' und werden in jeweils in einem eigenen Unterkapitel diskutiert.\\ \\ -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, da alle modellierten Kreuzungen auf den Einfahrtsspuren mit Sensoren bestückt sind. Kann die Herausforderung, Werte für virtuelle Sensoren zu berechnen, gelöst werden, so w"urden damit ebenfalls die Herausforderung einen Verkehrswert f"ur den jeweiligen Kreuzungsausgang zu berechnen gel"ost werden \ref{problem:2}. +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, da alle modellierten Kreuzungen auf den Einfahrtsspuren mit Sensoren best"uckt sind. Kann die Herausforderung, Werte f"ur virtuelle Sensoren zu berechnen, gel"ost werden, so w"urden damit ebenfalls die Herausforderung einen Verkehrswert f"ur den jeweiligen Kreuzungsausgang zu berechnen gel"ost werden \ref{problem:2}. \subsection{L"osungsansatz: Hidden Markow Modell}\label{sec:berechnung:hmm} [todo] Das Hidden Markow Modell(HMM) ist ein Modell zur Beschreibung von Systemen mit versteckten Zust"anden. Es ist nach dem russischen Mathematiker Andrei Andrejewitsch Markow benannt. Es schien ein geignetes Modell zu sein, da es vermag sowohl bekannte als auch unbekannte Einheiten zu modellieren, in Verbindung einer "Ubergangswahrscheinlichkeit. [ref] Im Folgendem werden die Grundlagen von Hidden Marokw Modellen umrissen. @@ -26,11 +26,11 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst au"serdem entspricht das Verfahren durch den "zufall" eher besserem Raten. \subsection{L"osungsansatz: Wegfindungsalgorithmen}\label{sec:berechnung:astar} - Um den Weg eines Fahrzeugs oder einer Fahrzeugkolonne zu simulieren bieten sich Wegfindungsalgorithmen an, da sie den k"urzesten Weg zum Ziel finden und das dem Verhalten des Menschen, einen Ort anzufahren, "ahnelt. Die Idee die Anzahl der Autos anhand der Sensorwerte zu bestimmen und diese durch das Straßennetz zu ihrem Ziel fahren zu lassen erschien als eine gute L"osung. Aus dem Studium bekannte Algorithmen wie der A* k"onnen ein solches Wegfindungsproblem l"osen. Insbesondere die M"oglichkeit einen Graphen direkt zur Berechnung zu verwenden, ließen diesen Ansatz erfolgsversprechend aussehen. Die benötigte Absch"atzung der Distanz zwischen Start und Ziel Knoten w"are dabei die Luftlinie zwischen diesen. Da keine Werte "uber einzelne Autos, sondern nur Messwerte "uber eine Minute zur Verf"ugung standen musste nicht nur ein einzelnes Auto, sondern eine Autokolonne simuliert werden.\\ \\ + Um den Weg eines Fahrzeugs oder einer Fahrzeugkolonne zu simulieren bieten sich Wegfindungsalgorithmen an, da sie den k"urzesten Weg zum Ziel finden und das dem Verhalten des Menschen, einen Ort anzufahren, "ahnelt. Die Idee die Anzahl der Autos anhand der Sensorwerte zu bestimmen und diese durch das Straßennetz zu ihrem Ziel fahren zu lassen erschien als eine gute L"osung. Aus dem Studium bekannte Algorithmen wie der A* k"onnen ein solches Wegfindungsproblem l"osen. Insbesondere die M"oglichkeit einen Graphen direkt zur Berechnung zu verwenden, ließen diesen Ansatz erfolgsversprechend aussehen. Die ben"otigte Absch"atzung der Distanz zwischen Start und Ziel Knoten w"are dabei die Luftlinie zwischen diesen. 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. Voraussetzung 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 Voraussetzung f"ur eine korrekte Berechnung. In Kapitel \autoref{sec:modell werden die Einschr"ankungen des Modells n"aher erl"autert.\\ \\ - Durch Addition derjenigen Sensorwerte, welche auf den jeweiligen Ausgang zeigen, kann ein Wert f"ur diesen ausgerechnet werden. F"ur Mischspursensoren werden daf"ur Abbiegewahrscheinlichkeiten ben"otigt, um den Sensorwert entsprechend dem Abbiegeverhalten der Verkehrsteilnehmer auf die Ausg"ange zu verteilen. Die Abbiegewahrscheinlichkeit gibt dabei an, wieviel Prozent des Verkehrs, welcher "uber den Sensor fließt dem jeweiligen Ausgangsknoten zugeordnet werden kann. Der Sensorwert wird entsprechend mit der jeweiligen Abbiegewahrscheinlichkeit multipliziert und auf den Ausgang addiert. Einspursensoren k"onnen dagegen direkt auf den Ausgang addiert werden, auf den sie zeigen, ohne das Abbiegewahrscheinlichkeiten von N"oten sind. Um das Berechnungsmodell einheitlich zu halten wurde bei der Matrizenrechnung eine Abbiegewahrscheinlichkeit von 1.0 f"ur Einspursensoren angegeben, da 100\% des Verkehrs, welcher über den Einspursensor fließt, an dem entsprechenden Ausgang ankommen muss.\\ \\ + Das in Kapitel \autoref{sec:modell} beschriebene Modell erlaubt es mithilfe von linearen Gleichungssystemen einen Wert f"ur jeden Kreuzungsein- und Ausgang zu berechnen. Voraussetzung 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 Voraussetzung f"ur eine korrekte Berechnung. In Kapitel \autoref{sec:modell} werden die Einschr"ankungen des Modells n"aher erl"autert.\\ \\ + Durch Addition derjenigen Sensorwerte, welche auf den jeweiligen Ausgang zeigen, kann ein Wert f"ur diesen ausgerechnet werden. F"ur Mischspursensoren werden daf"ur Abbiegewahrscheinlichkeiten ben"otigt, um den Sensorwert entsprechend dem Abbiegeverhalten der Verkehrsteilnehmer auf die Ausg"ange zu verteilen. Die Abbiegewahrscheinlichkeit gibt dabei an, wieviel Prozent des Verkehrs, welcher "uber den Sensor fließt dem jeweiligen Ausgangsknoten zugeordnet werden kann. Der Sensorwert wird entsprechend mit der jeweiligen Abbiegewahrscheinlichkeit multipliziert und auf den Ausgang addiert. Einspursensoren k"onnen dagegen direkt auf den Ausgang addiert werden, auf den sie zeigen, ohne das Abbiegewahrscheinlichkeiten von N"oten sind. Um das Berechnungsmodell einheitlich zu halten wurde bei der Matrizenrechnung eine Abbiegewahrscheinlichkeit von 1.0 f"ur Einspursensoren angegeben, da 100\% des Verkehrs, welcher "uber den Einspursensor fließt, an dem entsprechenden Ausgang ankommen muss.\\ \\ 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, kurz LGS[gls:lgs], ist ein System linearer Gleichungen. Ein solches System hat n Unbekannte und m Gleichungen. Eine allgemeine Darstellungsform ist in Abbildung \ref{lgs:allgemein} beschrieben.\\ @@ -76,11 +76,11 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst a_{m1} & a_{m2} & \cdots & a_{mn} & b_m \end{array}\right) \end{equation} - Ein lineares Gleichungssystem ist genau dann eindeutig l"osbar wenn der Rang der Koeffizientenmatrix gleich dem Rang der erweiterten Koeffizientenmatrix; $R(A) = R(A|b)$. Gilt zusätzlich die Bedingung, dass der Rang der erweiterten Koeffizientenmatrix der Anzahl der Unbekannten des Vektors $x$ entspricht, so ist das LGS eindeutig lösbar. \\ \\ + Ein lineares Gleichungssystem ist genau dann eindeutig l"osbar wenn der Rang der Koeffizientenmatrix gleich dem Rang der erweiterten Koeffizientenmatrix; $R(A) = R(A|b)$. Gilt zus"atzlich die Bedingung, dass der Rang der erweiterten Koeffizientenmatrix der Anzahl der Unbekannten des Vektors $x$ entspricht, so ist das LGS eindeutig l"osbar. \\ \\ F"ur ein solches Gleichungssystem existieren verschiedene L"osungsverfahren. Ein Beispiel ist der Gaus-Algorithmus. [gaus ref]. Neben dem Gaus-Algorithmus existieren viele weitere L"osungsalgorithmen, einschließlich numerische Verfahren. Die Qualit"at der L"osung h"angt dabei von dem gew"ahlten L"osungsverfahren und dem vorliegenden Gleichungssystem ab. \subsubsection{Lineares Gleichungssystem einer Kreuzung}\label{sec:berechnung:lgs:xr} - Die Beziehungen zwischen Induktionsschleifensensoren und Kreuzungsein- und Ausg"angen kann durch eine lineares Gleichungssystem ausgedr"uckt werden. Der Wert f"ur den Ausgang errechnet sich aus der Summe aller, diesem Kreuzungseingang zugeordneten, Sensoren. Ein Kreuzungsausgang errechnet sich aus den Werten derjenigen Sensoren, wessen Spur dem Verkehr erlauben diesen Kreuzungsausgang zu bedienen. Dabei muss zwischen Einspursensoren und Mischspursensoren unterschieden werden. Einspursensoren k"onnen direkt auf den Ausgang addiert werden, w"ahrend f"ur Mischspursensoren eine Abbiegewahrscheinlichkeit ben"otigt wird, die angibt, wie viel des gemessenen Verkehrs 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. Um einen Wert für den Kreuzungseingang zu berechnen, werden keine Abbiegewahrscheinlichkeiten ben"otigt und die Sensorwerte k"onnen direkt, unerheblich ob nun Misch- oder Einzelspursensor, auf den Eingang addiert werden. Dies begründet sich in der Tatsache, das alle Sensoren an den Kreuzungseingängen verbaut sind und der gemessene Wert eindeutig einem Eingang zugeordnet werden kann.\\ \\ + 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 des gemessenen Verkehrs 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. Um einen Wert f"ur den Kreuzungseingang zu berechnen, werden keine Abbiegewahrscheinlichkeiten ben"otigt und die Sensorwerte k"onnen direkt, unerheblich ob nun Misch- oder Einzelspursensor, auf den Eingang addiert werden. Dies begr"undet sich in der Tatsache, das alle Sensoren an den Kreuzungseing"angen verbaut sind und der gemessene Wert eindeutig einem Eingang zugeordnet werden kann.\\ \\ Allgemein kann der Verkehrswert des Kreuzungsein- und -Ausgang durch die in Abbildung \autoref{equ:xrallgemein} beschriebene Gleichung ausgedr"uckt werden. \begin{equation}\label{equ:xrallgemein} Kreuzungausgang_x = \sum ES_{xi} + \sum MS_{xj}*ABW_{xj} @@ -101,7 +101,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst & 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\\ - + \dots\\ In_m & 0/1 & 0/1 & \dots & 0/1\\ \end{Bmatrix} * @@ -125,7 +125,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst & 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\\ - + \dots\\ Out_m & 0/1 & 0/1 & \dots & 0/1\\ \end{Bmatrix} * @@ -144,7 +144,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst Out_m\\ \end{Bmatrix} \end{equation} - Zur Erl"auterung wird nochmals die A23\ref{abb:a23} betrachtet. Die in Kapitel \autoref{sec:modell} entwickelte Matrixdarstellung erweist sich als hilfreich und kann durch dekorieren mit Abbiegewahrscheinlichkeiten zur Berechnung einer L"osung genutzt werden. Hierf"ur werden Verbindungen zwischen Einspursensoren und dem Aus- bzw. Eingang nach wie vor mit einer '1' markiert, da alle Verkehr der "uber diesen Sensor fließt genau einem Ausgang zugeordnet werden kann, kann 100\% des Wertes auf den entsprechenden Ausgang "ubertragen werden. F"ur Mischspursensoren dagegen werden die Verbindungen durch eine Fließkommazahl ersetzt, welche die jeweilige Abbiegewahrscheinlichkeit repr"asentiert. Durch Multiplikation der Matrix mit den gemessenen Sensorwerten eines bestimmten Zeitpunktes, kann ein Wert f"ur die Ein- und Ausg"ange zu diesem Zeitpunkt berechnet werden, sofern aller, in die Kreuzung einstr"omender, Verkehr von Sensoren erfasst wird und für alle Mischspursensoren Abbiegewahrscheinlichkeiten vorliegen. Abbildung \ref{abb:a23calc} beschreibt diese Berechnung für die Ein- und Ausgänge der Kreuzung A23 zum Zeitpunkt []. + Zur Erl"auterung wird nochmals die A23\ref{abb:a23} betrachtet. Die in Kapitel \autoref{sec:modell} entwickelte Matrixdarstellung erweist sich als hilfreich und kann durch dekorieren mit Abbiegewahrscheinlichkeiten zur Berechnung einer L"osung genutzt werden. Hierf"ur werden Verbindungen zwischen Einspursensoren und dem Aus- bzw. Eingang nach wie vor mit einer '1' markiert, da alle Verkehr der "uber diesen Sensor fließt genau einem Ausgang zugeordnet werden kann, kann 100\% des Wertes auf den entsprechenden Ausgang "ubertragen werden. F"ur Mischspursensoren dagegen werden die Verbindungen durch eine Fließkommazahl ersetzt, welche die jeweilige Abbiegewahrscheinlichkeit repr"asentiert. Durch Multiplikation der Matrix mit den gemessenen Sensorwerten eines bestimmten Zeitpunktes, kann ein Wert f"ur die Ein- und Ausg"ange zu diesem Zeitpunkt berechnet werden, sofern aller, in die Kreuzung einstr"omender, Verkehr von Sensoren erfasst wird und f"ur alle Mischspursensoren Abbiegewahrscheinlichkeiten vorliegen. Abbildung \ref{abb:a23calc} beschreibt diese Berechnung f"ur die Ein- und Ausg"ange der Kreuzung A23 zum Zeitpunkt []. Eingangsmatrix:[todo] \begin{equation}\label{abb:a23calc} \begin{Bmatrix} @@ -205,7 +205,7 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst 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 und jede lineare Gleichung für sich gelöst werden kann. Dies ist darauf zur"uckzuf"uhren, dass alle Sensorwerte f"ur diese Kreuzung bekannt und alle eingehenden Spuren mit Sensoren best"uckt sind. Desweiteren stehen f"ur alle Mischspursensoren Abbiegewahrscheinlichkeiten der Stadt Darmstadt zur Verf"ugung.\\ \\ + F"ur die Kreuzung A23 ist es nicht n"otig ein Gleichungssystem zu l"osen, da alle ben"otigten Werte bekannt sind und jede lineare Gleichung f"ur sich gel"ost werden kann. Dies ist darauf zur"uckzuf"uhren, dass alle Sensorwerte f"ur diese Kreuzung bekannt und alle eingehenden Spuren mit Sensoren best"uckt sind. Desweiteren stehen f"ur alle Mischspursensoren Abbiegewahrscheinlichkeiten der Stadt Darmstadt zur Verf"ugung.\\ \\ Im folgenden wird diskutiert in wiefern das Gleichungssystem mit unbekannten Eingangsspuren bzw. unbekannten Abbiegewahrscheinlichkeiten gel"ost werden kann.\\ Durch hinzuf"ugen es virtuellen Sensors f"ur einen weiteren Kreuzungseingang wird das Gleichungssystem zu einem eben solchen, da nun Unbekannte in der Gleichung auftauchen. Dies f"uhrt unmittelbar zur Unl"osbarkeit des Systems, da Rang[]. Am Beispiel der A23 sei das demonstriert. Hierf"ur wird der Sensor D10 zu einer virtuellen Sensor, welcher keine Werte liefert (siehe Abbildung \ref{abb:a23d10virt}). [todo] @@ -238,30 +238,28 @@ Das Ziel f"ur \ref{problem:1} virtuelle Sensoren Werte zu berechnen war das erst A104 & A104\\ \end{Bmatrix} \end{equation} - Dieses System ist nicht l"osbar, da zu viele Unbekannte in der Gleichung auftauchen. Dies liegt insbesondere an fehlenden Ausgangswerten der Kreuzung. Diese k"onnen allerdings nicht bestimmt werden. Siehe hierfür \ref{sec:modell}.[todo?] Durch Zus"atzliche Gleichungen k"onnen die Werte weiter eingeschr"ankt werden. Dies f"uhrt allerdings nicht zur L"osbarkeit des Systems. So müssen alle aufaddierten Abbiegewahrscheinlichkeiten eines Sensors kleiner gleich eins sein. Eine weitere Möglichkeit das Gleichungssystem zu erweitern ist die Zuhilfenahme der Vallierungssensoren. Da auf dem untersuchten Gebiet lediglich drei Valliderungssensoren verbaut sind trägt eine Einbeziehung dieser Sensoren in das LGS ebenfalls nicht zu einer Lösung bei. Eine genauere Diskussion über die Validierungssensoren und deren Verwendungsmöglichkeiten bei einem flächendeckendem Einsatz auf Kreuzungen wird in einem eigenen Unterkapitel weiter unten behandelt. \\ \\ - Eine weitere Anwendung ist die Berechnung der Abbiegewahrscheinlichkeiten. Unter der Annahme, dass alle Werte der Sensoren bekannt, allerdings f"ur einen Mischspursensor die Abbiegewahrscheinlichkeiten nicht bekannt sind. Allerdings ist auch dieses System nicht l"osbar, da abermals zu viele Unbekannte in dem System auftauchen. Auch hier sind die fehlenden Ausgangsverkehrswerte eine Kreuzung der Grund, weshalb es zu keiner Lösung kommen kann. Auch diese Anwendung wird in dem Unterkapitel zu Valliderungssensoren behandelt.[todo?] + Dieses System ist nicht l"osbar, da zu viele Unbekannte in der Gleichung auftauchen. Dies liegt insbesondere an fehlenden Ausgangswerten der Kreuzung. Diese k"onnen allerdings nicht bestimmt werden. Siehe hierf"ur \ref{sec:modell}.[todo?] Durch Zus"atzliche Gleichungen k"onnen die Werte weiter eingeschr"ankt werden. Dies f"uhrt allerdings nicht zur L"osbarkeit des Systems. So m"ussen alle aufaddierten Abbiegewahrscheinlichkeiten eines Sensors kleiner gleich eins sein. Eine weitere M"oglichkeit das Gleichungssystem zu erweitern ist die Zuhilfenahme der Vallierungssensoren. Da auf dem untersuchten Gebiet lediglich drei Valliderungssensoren verbaut sind tr"agt eine Einbeziehung dieser Sensoren in das LGS ebenfalls nicht zu einer L"osung bei. Eine genauere Diskussion "uber die Validierungssensoren und deren Verwendungsm"oglichkeiten bei einem fl"achendeckendem Einsatz auf Kreuzungen wird in einem eigenen Unterkapitel weiter unten behandelt. \\ \\ + Eine weitere Anwendung ist die Berechnung der Abbiegewahrscheinlichkeiten. Unter der Annahme, dass alle Werte der Sensoren bekannt, allerdings f"ur einen Mischspursensor die Abbiegewahrscheinlichkeiten nicht bekannt sind. Allerdings ist auch dieses System nicht l"osbar, da abermals zu viele Unbekannte in dem System auftauchen. Auch hier sind die fehlenden Ausgangsverkehrswerte eine Kreuzung der Grund, weshalb es zu keiner L"osung kommen kann. Auch diese Anwendung wird in dem Unterkapitel zu Valliderungssensoren behandelt.[todo?] \subsection{Kreuzungsberechnung am Graphen}\label{sec:berechnung:graph} Da alle modellierten Kreuzungen der 'Ministadt' alle eingehenden Spuren mit Sensoren versehen haben, k"onnen die Gleichungen f"ur die jeweiligen Ausg"ange unabh"angig voneinander gel"ost werden. Dies erlaubt es die Ausg"ange bzw. Eing"ange mithilfe des Graphen zu berechnen. Das entwickelte Verfahren macht 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 todo] F"ur Ausgangsknoten einer Kreuzung kann das selbe Verfahren benutzt werden. Allerdings werden alle eingehenden Kanten, entgegen der Verkehrsflussrichtung, vom Ausgangsknoten ausgehend, verfolgt und die Sensorwerte aufaddiert. F"ur Mischspursensoren wird dabei der Wert mit der an der Kante annotierten Abbiegewahrscheinlichkeit multipliziert. [bild mit berechnung] - Wird dieses Verfahren f"ur alle Aus- und Eing"ange einer Kreuzung durchgef"uhrt k"onnen f"ur alle ein Verkehrswert ausgerechnet werden unter der Vorraussetzung, dass alle Eingangsspuren der Kreuzung mit Sensoren bestückt sind.\\ \\ - Die zeitlose Übertragen der Werte am Kreuzungseingang auf den Ausgang begründet sich mit der Tatsache, dass alle vorliegenden Sensorwerte den Verkehr über einen Zeitraum von einer Minute messen und nach ende des Intervalls einen Anzahl an Verkehrsteilnehmern ausweist, die über den Sensor gefahren sind. Die gemessenen Verkehrsteilnehmer haben die Kreuzung folglich bereits passiert. Lediglich die letzten Autos könnten sich noch auf der Kreuzung befinden. Dies wird allerdings vernachlässigt. + Wird dieses Verfahren f"ur alle Aus- und Eing"ange einer Kreuzung durchgef"uhrt k"onnen f"ur alle ein Verkehrswert ausgerechnet werden unter der Vorraussetzung, dass alle Eingangsspuren der Kreuzung mit Sensoren best"uckt sind.\\ \\ + Die zeitlose Übertragen der Werte am Kreuzungseingang auf den Ausgang begr"undet sich mit der Tatsache, dass alle vorliegenden Sensorwerte den Verkehr "uber einen Zeitraum von einer Minute messen und nach ende des Intervalls einen Anzahl an Verkehrsteilnehmern ausweist, die "uber den Sensor gefahren sind. Die gemessenen Verkehrsteilnehmer haben die Kreuzung folglich bereits passiert. Lediglich die letzten Autos k"onnten sich noch auf der Kreuzung befinden. Dies wird allerdings vernachl"assigt. \subsubsection{Verkehrsfluss zwischen Kreuzungen}\label{sec:berechnung:betweenxr} Zwischen Kreuzungen ist das entwickelte Modell ungenau, da Seitenstraßen und Kreuzungen ohne Sensoren nicht modelliert werden. 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 wie viel des Verkehrs, welcher eine Kreuzung verl"asst, an einer anderen wieder einfließt und welcher Teil in Seitenstraßen abgeflossen ist, da die Messungen zweier Kreuzungen nicht in eine Beziehung gesetzt werden können. + Dadurch dass die vorliegenden Sensordaten f"ur eine Minute gemessen wurden, kann leider nicht berechnet werden wie viel des Verkehrs, welcher eine Kreuzung verl"asst, an einer anderen wieder einfließt und welcher Teil in Seitenstraßen abgeflossen ist, da die Messungen zweier Kreuzungen nicht in eine Beziehung gesetzt werden k"onnen. \subsubsection{Sonderfall: Vallidierungssensor}\label{sec:berechnung:vallidate} - [todo] - Mit beiden Matrizen wird eine Kreuzung ohne Validierungssensoren vollst"andig beschrieben. Sind dagegen valliderungssensoren Vorhanden, so beschriebt die Matrix nicht mehr den kompletten Graphen wie das beispiel der [] zeigt: - - [Eingansmatrix] - [Ausgangsmatrix] - - Die Verbindung von Sensor [] nach Sensor [] wird hier nicht modelliert. + (todo) + Mit beiden Matrizen wird eine Kreuzung ohne Validierungssensoren vollst"andig beschrieben. Sind dagegen valliderungssensoren Vorhanden, so beschriebt die Matrix nicht mehr den kompletten Graphen wie das beispiel der Kreuzung () zeigt: + (Eingansmatrix) + (Ausgangsmatrix) + Die Verbindung von Sensor () nach Sensor () wird hier nicht modelliert. F"ur die Berechnung wird sich zeigen, dass das unerheblich ist, sofern man - Sensor[] in der Ausgangsmatrix f"ur die Zeile [][] eintr"agt. Die Berechnung der Geradeausspur ist dann wie folgend: [] - [] = A. + Sensor() in der Ausgangsmatrix f"ur die Zeile ()() eintr"agt. Die Berechnung der Geradeausspur ist dann wie folgend: () - () = A. \subsubsection{Abbiegewahrscheinlichkeiten} [todo] diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex index 4f53944e..9a98212a 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/datengrund.tex @@ -14,7 +14,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \subfigure[Schematischer Aubau einer Induktionsschleife Quelle: \cite{thesis:mazur}.]{\includegraphics[width=0.5\textwidth-2\fboxsep-2\fboxrule]{pic/induktionsschleife-schema}} \label{abb:3} \end{figure} - Wie bei jedem Sensor sind die Messungen unter Vorbehalt des Fehlers zu betrachten. In der Arbeit von \cite{thesis:lehnhoff} wurden die Induktionsschleifen des Stadtgebiets von Hannover untersucht und festgestellt, das es sehr starke Unterschiede der Messgenauigkeit unter den Sensoren gibt, so wird in dieser Arbeit festgestellt, dass bei nur einem Drittel der Sensoren eine Messgenauigkeit von 90\% erreicht wird w"ahrend ein gleichgroßer andere Teil eine Genauigkeit von unter 40\% aufweist. Laut dem Merkblatt zu Detektoren f"ur den Straßenverkehr \cite{merk:street} wird für Messfehler von Induktionsschleifen zwischen vier Fehlertypen unterschieden: + Wie bei jedem Sensor sind die Messungen unter Vorbehalt des Fehlers zu betrachten. In der Arbeit von \cite{thesis:lehnhoff} wurden die Induktionsschleifen des Stadtgebiets von Hannover untersucht und festgestellt, das es sehr starke Unterschiede der Messgenauigkeit unter den Sensoren gibt, so wird in dieser Arbeit festgestellt, dass bei nur einem Drittel der Sensoren eine Messgenauigkeit von 90\% erreicht wird w"ahrend ein gleichgroßer andere Teil eine Genauigkeit von unter 40\% aufweist. Laut dem Merkblatt zu Detektoren f"ur den Straßenverkehr \cite{merk:street} wird f"ur Messfehler von Induktionsschleifen zwischen vier Fehlertypen unterschieden: \begin{enumerate} \item{Zeitlich bedinge Messfehler} \item{R"aumliche Messfehler} @@ -22,7 +22,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \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"alschlicher weise ein Auto f"ur diese gez"ahlt wird. Umfeldbedingte Fehler sind am schwersten festzustellen. Es handelt sich dabei um Fehler, die durch magnetische St"orquellen in der Umgebung oder schlechte Isolation der Induktionsschleife auftreten.\\ - "Uber die Fehlerh"aufigkeit liegen keine Daten der Stadt Darmstadt vor. Für 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. \\ \\ + "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} \item{Einspursensor: Ein Auto auf dieser Spur kann die Kreuzung nur in genau eine Richtung verlassen.} @@ -31,7 +31,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be Diese Unterscheidung ist wichtig, da Mischspursensoren neben den Induktionsschleifenwerte noch sog. Abbiegewahrscheinlichkeiten ben"otigen, um Kreuzungszusammenh"ange zu berechnen. Die Verwendung der Abbiegewahrscheinlichkeiten ist im Kapitel \autoref{sec:berechnung} beschrieben. \subsection{Adaptive Steuerung von Ampelanlagen}\label{sec:datengrund:adapt} Mit der Zunahme des motorisierten Verkehrs erhielten Anfang des 20. Jahrhunderts sog. Verkehrspolizisten die Aufgabe den Verkehr an Kreuzungen zu regeln. 1924 wurde am Potzdamer Platz in Berlin die erste Ampel errichtet, um die gestiegenen Personalkosten der Verkehrspolizisten zu reduzieren. In den folgenden Jahren wurde die Ampeltechnik weiter verbessert, an der manuellen Steuerung durch Verkehrspolizisten wurde allerdings festgehalten.\\ - Die erste verkehrsabh"angige Steuerung wurde 1928 von Charles Adler jr. entwickelt und in Baltimore,Maryland das erste mal eingesetzt\cite{paper:adaptiv}[direct cite]. Bevor allerdings diese Technik Einzug in den allt"aglichen Kreuzungsverkehr fand vergingen noch etwa 40 Jahre. Heute sind die Kreuzungen vieler großer Städte mit dieser Steuerungstechnik ausgestattet. Die meisten der eingesetzten verkehrsbah"angigen Ampelsteuerungen setzen sog. Ablauflogiken ein, die es erlauben zu pr"ufen, ob eine zeitliche oder logische Bedingung der Kreuzung verletzt ist. Im Rahmen dieser Bedingungen kann die Umlaufzeit, Versatzzeit, Phasenfolge und/oder die Freigabezeit dynamisch dem Verkehr angepasst werden. Um den Bedarf an Freigabezeit zu berechnen kommen die oben beschriebenen Induktionsschleifen zum Einsatz um den Verkehr zu messen. Wird ein Auto auf einem Sensor erkannt, so kann die Ampelphase verl"angert oder die entsprechende Verkehrsrichtung freigeschaltet werden. Diese verkehrsabh"angige Steuerung von Lichtanlagen wird 'adaptive Steuerung' genannt.\\ \\ + Die erste verkehrsabh"angige Steuerung wurde 1928 von Charles Adler jr. entwickelt und in Baltimore,Maryland das erste mal eingesetzt\cite{paper:adaptiv}[direct cite]. Bevor allerdings diese Technik Einzug in den allt"aglichen Kreuzungsverkehr fand vergingen noch etwa 40 Jahre. Heute sind die Kreuzungen vieler großer St"adte mit dieser Steuerungstechnik ausgestattet. Die meisten der eingesetzten verkehrsbah"angigen Ampelsteuerungen setzen sog. Ablauflogiken ein, die es erlauben zu pr"ufen, ob eine zeitliche oder logische Bedingung der Kreuzung verletzt ist. Im Rahmen dieser Bedingungen kann die Umlaufzeit, Versatzzeit, Phasenfolge und/oder die Freigabezeit dynamisch dem Verkehr angepasst werden. Um den Bedarf an Freigabezeit zu berechnen kommen die oben beschriebenen Induktionsschleifen zum Einsatz um den Verkehr zu messen. Wird ein Auto auf einem Sensor erkannt, so kann die Ampelphase verl"angert oder die entsprechende Verkehrsrichtung freigeschaltet werden. Diese verkehrsabh"angige Steuerung von Lichtanlagen wird 'adaptive Steuerung' genannt.\\ \\ Durch eine solche Ampelsteuerung verk"urzt sich die Haltezeiten von Autos und sorgt f"ur einen fl"ussigeren Verkehr, im Vergleich zu einer sog. Festzeitsteuerung\cite{paper:adaptiv}, welche die Ampel nach fest definierten Ampelphasen schaltet. Dies begr"undet sich darin, dass die adaptive Ampelschaltung eine Spur nur freischaltet, wenn diese von einem Fahrzeug, detektiert mithilfe des Sensor in der Straße, ben"otigt wird. Es besteht außerdem die M"oglichkeit die Ampelphase so lange zu verl"angern, bis eine L"ucke in der Fahrzeugkolonne erkannt wird um ein Zug von Autos "uber die Kreuzung zu lassen. Werden die Induktionsschleifen an den Haltelinien einer Kreuzung verbaut, k"onnen sie au"serdem verwendet werden um Rotlichtverst"o"se automatisch zu erkennen.\\ \\ Die Steuerung der Ampelanlagen ist ein Teil der Verkehrsmanagement \autoref{abb:verkehrsmanagement} und ist f"ur viele andere Bereiche der Verkehrstechnik von großem Interesse, da die Ampeln Sensordaten liefern, die vielf"altig verwendet werden k"onnen. Ein Beispiel der Verwendung ist diese Arbeit, die aus den erfassten Induktionsschleifenwerten Verkehrsfl"usse berechnet. \begin{figure} \label{abb:verkehrsmanagement} @@ -47,7 +47,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be \item{Gestaltungsmodelle: dient der Voraussage von Ver"anderungen des Verkehrsverhaltens bei (infrastruckturellen) Maßnahmen.} \item{Optimierungsmodelle: dient der Optimierung von Verkehr.} \end{enumerate} - Da im Rahmen dieser Arbeit Werte für Kreuzungsausgänge vorhergesagt bzw. angenähert werden, handelt es sich bei den hier diskutierten Modellen um ein Prognosemodell. + Da im Rahmen dieser Arbeit Werte f"ur Kreuzungsausg"ange vorhergesagt bzw. angen"ahert werden, handelt es sich bei den hier diskutierten Modellen um ein Prognosemodell. Desweiteren wird zwischen den Genauigkeitsstufen des Modells unterschieden. Dies trifft insbesondere auf Flussmodelle zu, da diese auf verschiedenen Ebenen modelliert werden k"onnen. Es wird zwischen vier Genauigkeitsstufen unterschieden \cite{lect:simumod}: \begin{itemize} \item{makroskopisch: Modellierung auf Basis von Fahrzeugkollektiven} @@ -74,6 +74,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be Die Bezeichnung der Kreuzungen richtet sich dabei nach der Kreuzungsbezeichnung des Verkehrsamtes[todo] Darmstadt und ist eindeutig. Eine "Ubersicht "uber ganz Darmstadt mit eingezeichneten Kreuzungen ist im Anhang \ref{abb:caddarmstadt} zu finden. Ein Kreuzungsname in Darmstadt besteht dabei aus einem 'A' und einer eindeutigen Nummer. Die L"ange des Messintervalls ist in Darmstadt auf eine Minute definiert. Ein Ausschnitt einer solchen CSV-Datei ist in \ref{tbl:csv} zu sehen. \begin{figure}\label{tbl:csv} \begin{tabular}{|l|l|l|l|lllllllllll|} + \hline Datum& Uhrzeit& Bez.& Intv.& D1Z& D1B& D2Z& D2B& D3Z& D3B& D4Z& D4B& \dots& D64Z& D64B\\ \hline 08.08.13 & 00:19:00 & A 8 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \dots & 0 & 0\\ @@ -88,7 +89,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be 08.08.13 & 00:19:00 & A 31 & 1 & & & & & & & & & \dots & 0 & 0\\ 08.08.13 & 00:19:00 & A 33 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & \dots & 0 & 0\\ 08.08.13 & 00:19:00 & A 34 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & \dots & 0 & 0\\ - \vdots + \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots\\ \hline \end{tabular} \caption{CSV-Datei Ausschnitt von 8.8.2013} @@ -96,15 +97,15 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be 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-Datei bereitgestellt werden. Um die Zuordnung von CSV-Spalte zu dem ta"achlichen Sensornamen herzustellen, werden sog. "Ubersetzungstabellen ben"otigt. Diese ordnen einer CSV-Sensorspalte (1-64) einen kreuzungsspezifischen Sensornamen zu, welcher der Sensorbezeichnung der CAD-Zeichnungen[gls:cad] der Kreuzungen entspricht. In der Praxis wird eine solche "Ubersetzungstabelle durch einen Offset auf der CSV-Datei im Computer nachgebildet. F"ur die in diese Arbeit modellierten Kreuzungen sind "Ubersetzungstabellen sowie die CAD-Zeichnung im Anhang zu finden \ref{anhang:a3} ff. . \subsubsection{MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten} \label{sec:datengrund:inductvalues:mysql} Im Rahmen der Arbeit von \cite{thesis:mueller}, wurde eine JEE6\footnote{todo adress jee6}[gls:jee6] Anwendung entwickelt, welche die aufbereiteten Verkehrsdaten der Stadt Darmstadt bereit stellt. Hierf"ur wurden die CSV-Dateien geparsed und in eine MYSQL-Datenbank "uberf"uhrt. Die dort gesammelten Sensordaten wurden bereits mit Geoinformation des OpenStreetMap Projektes verkn"upft und erlauben eine Positionierung von Kreuzungs- und Sensorknoten mithilfe der bereitgestellten Latitude und Longitude Werte.\\ \\ - [todo ER Diagramm] + (todo ER Diagramm) Aus dieser Datenbank wurden alle Sensorwerte und Positionsangaben, welche im Rahmen dieser Arbeit ben"otigten wurden, entnommen. Die gesuchten Daten sind dabei auf drei Tabellen verteilt: \begin{enumerate} \item{jee\_crmodel\_CrossroadDim: In dieser Tabelle werden Kreuzungsname und -Position abgespeichert.} - \item{jee\_crmodel\_SensorDim: In dieser Tabelle werden Sensorname und -Position gespeicher, sowie die Kreuzung, auf der der Sensor verbaut ist, über eine eindeutige ID mit der Tabelle jee\_crmodel\_CrossroadDim verknüpft. Ein CSV-Offset identifiziert den Sensor bez"uglich seiner Position in der CSV-Datei.} + \item{jee\_crmodel\_SensorDim: In dieser Tabelle werden Sensorname und -Position gespeicher, sowie die Kreuzung, auf der der Sensor verbaut ist, "uber eine eindeutige ID mit der Tabelle jee\_crmodel\_CrossroadDim verkn"upft. Ein CSV-Offset identifiziert den Sensor bez"uglich seiner Position in der CSV-Datei.} \item{jee\_trafficlight\_rawevents: In dieser Tabelle werden die eingelesenen CSV-Dateien der Stadt gespeichert. Dies umfasst neben den Werten 'load' und 'count' und Messdatum, die zugeh"orige Kreuzung. Ein Sensor kann anhand des gespeicherten CSV-Offsets mit jee\_crmodel\_SensorDim identifiziert und lokalisiert werden.} \end{enumerate} Um die Daten f"ur eigene Zwecke verwenden zu k"onnen, wurden die ben"otigten Teile extrahiert und in einem eigenen Datenbankschema abgespeichert. Mehr Informationen zu dem entwickelten Datenbankmodell sind im Kapitel \autoref{sec:modell:datenbankschema} zu finden. Desweiteren wurden verschiedene SQL-Abfragen entwickelt, um die ben"otigten Informationen zu extrahieren.\\ \\ - Um die gespeicherte Sensorposition zu ermitteln wurde eine SQL-Abfrage \ref{lst:sql_sensorquery} entwickelt, welche Kreuzungs- und Sensornamen, sowie dessen jeweiligen Latitude und Longitude zur"uckgibt. Die Auswahl ist dabei auf die zehn untersuchten Kreuzungen beschr"ankt. Das Feld 'VALIDTO' in der Kreuzungstabelle bestimmt dabei, ob die Kreuzung noch in Betrieb ist. Sensornamen können ebefalls mit dieser Abfrage gefiltert werden. In der Abgebildeten SQL-Abfrage \ref{lst:sql_sensorquery} werden Sensoren welche mit 'D' beginnen herausgefiltert, da fast ausschließlich alle Sensoren, welche zur Kreuzungmodellierung und -Berechnung verwendet wurden ein führendes 'D' aufweisen. + Um die gespeicherte Sensorposition zu ermitteln wurde eine SQL-Abfrage \ref{lst:sql_sensorquery} entwickelt, welche Kreuzungs- und Sensornamen, sowie dessen jeweiligen Latitude und Longitude zur"uckgibt. Die Auswahl ist dabei auf die zehn untersuchten Kreuzungen beschr"ankt. Das Feld 'VALIDTO' in der Kreuzungstabelle bestimmt dabei, ob die Kreuzung noch in Betrieb ist. Sensornamen k"onnen ebefalls mit dieser Abfrage gefiltert werden. In der Abgebildeten SQL-Abfrage \ref{lst:sql_sensorquery} werden Sensoren welche mit 'D' beginnen herausgefiltert, da fast ausschließlich alle Sensoren, welche zur Kreuzungmodellierung und -Berechnung verwendet wurden ein f"uhrendes 'D' aufweisen.\\ \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} \begin{lstlisting}[caption={[SQL-Abfrage der Sensorens] SQL-Abfrage der Sensoren}, label={lst:sql_sensorquery}, captionpos=bsec] SELECT CD.REALNAME AS CR_NAME, @@ -120,7 +121,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be AND SD.CROSSROAD_ID = CD.ID AS sensors \end{lstlisting} - \end{minipage} + \end{minipage}\\ Eine weitere Abfrage \ref{lst:sql_dataquery} dient dem Ermitteln der Sensorwerte "uber einen bestimmten Zeitraum. Zu Identifizierung des Sensors wird der CSV-Offset benutzt. Die extrahierten Daten entsprechen dem Inhalt einer CSV-Datei der Stadt Darmstadt. Die Abfrage aus \autoref{lst:sql_sensorquery} wird dabei mit einer Abfrage auf der Tabelle 'jee\_trafficlight\_rawevents kombiniert. Auf diese Weise erh"alt man Sowohl die Sensor und Kreuzungsinformationen, als auch die Z"ahlwerte der Induktionsschleifen. Ein Filter auf der Spalte 'DATETIME' der Ampelrohdaten erlaubt eine Auswahl des Zeitpunktes. Dabei ist zu beachten, dass die Zeitangaben in UTC-Zeitformat angegeben werden m"ussen. \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} \begin{lstlisting}[caption={[SQL-Abfrage der Sensorwerte] SQL-Abfrage der Sensorwerte}, label={lst:sql_dataquery}, captionpos=bsec] @@ -161,7 +162,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be Sie geben Aufschluss, an welcher Stelle ein Sensor in der Stra"sendecke verbaut ist und weist dessen kreuzungsinternen Namen aus, welcher zu Identifizierung des Sensors ben"otigt wird. Die CAD-Zeichnungen dienen der manuellen Modellierung des Stra"senmodells, sowie der Identifizierung der Sensoren sowie der Zuordnung ihrer Sensor-Klasse und -Typs. So sind in den CAD-Zeichnungen die Fahrspuren und deren erlaubte Flie"srichtung markiert. Aufgrund dessen konnte eine Zuordnung von Sensoren nach ihrer Klasse, Einspursensor oder Mischspursensor, vorgenommen werden. Des weiteren wurden mithilfe der CAD-Zeichnungen die Verbindungen von Sensor zu virtuellem Kreuzungsausgangsknoten manuell in der Datenbank vermerkt, um den, im Kapitel\autoref{sec:modell} entwickelten, Graphen aufzuspannen. Die CAD-Zeichnungen der Kreuzungen der 'Ministadt' sind dem Anhang beigef"ugt \ref{anhang:a3}. \subsection{Abbiegewahrscheinlichkeiten}\label{sec:datengrund:abbw} - Von der Stadt Darmstadt wurden neben den Sensorwerten, gemittelte Abbiegewahrscheinlichkeiten f"ur einige der Induktionsschleifen zur Verf"ugung gestellt, welche f"ur die Berechnung von Verkehrsfl"ussen bei Mischspursensoren ben"otigt werden. Die Abbiegewahrscheinlichkeiten eines Sensors beschreiben dabei wie viel Prozent des Verkehrs, welcher "uber den Sensor flie"st, zu den jeweiligen Ausgang der Kreuzung flie"sen darf. N"aheres ist im Kapitel \autoref{sec:berechnung} zu finden. Diese Daten wurden mithilfe von Video"uberwachung der zu untersuchenden Kreuzungen, f"ur die Planungsabteilung des Verkehrsamtes[todo name] der Stadt ermittelt. Alle Werte sind dabei "uber alle Messungen eines Tages gemittelt und liegen in PDF-Format für die beiden Teile der Stadt, Nord und S"ud, vor \ref{abb:abbwnorth}\ref{abb:abbwsouth}.\\ \\ + Von der Stadt Darmstadt wurden neben den Sensorwerten, gemittelte Abbiegewahrscheinlichkeiten f"ur einige der Induktionsschleifen zur Verf"ugung gestellt, welche f"ur die Berechnung von Verkehrsfl"ussen bei Mischspursensoren ben"otigt werden. Die Abbiegewahrscheinlichkeiten eines Sensors beschreiben dabei wie viel Prozent des Verkehrs, welcher "uber den Sensor flie"st, zu den jeweiligen Ausgang der Kreuzung flie"sen darf. N"aheres ist im Kapitel \autoref{sec:berechnung} zu finden. Diese Daten wurden mithilfe von Video"uberwachung der zu untersuchenden Kreuzungen, f"ur die Planungsabteilung des Verkehrsamtes[todo name] der Stadt ermittelt. Alle Werte sind dabei "uber alle Messungen eines Tages gemittelt und liegen in PDF-Format f"ur die beiden Teile der Stadt, Nord und S"ud, vor \ref{abb:abbwnorth}\ref{abb:abbwsouth}.\\ \\ \cite{thesis:michael} hat im Rahmen seiner Bachelorarbeit diese Daten in eine MYSQL-Datenbank "ubertragen. Desweiteren berechnet er genauere Abbiegewahrscheinlichkeiten f"ur die einzelnen Knoten, indem mithilfe einer Mittelung die Ausgangswerte einer Kreuzung in Beziehung zu einem Wert am benachbarten Kreuzungseingang gesetzt werden. Diese Daten lagen allerdings noch nicht vor und konnten aus diesem Grund im Rahmen dieser Arbeit nicht untersucht werden.\\ \\ Die aufbereiteten Abbiegewahrscheinlichkeiten der Stadt liegen in der Form (Kreuzung, Sensor, Geradeaus, Links, Rechts) (siehe Tabelle \ref{tbl:abbw}) vor. Die Werte f"ur Links, Rechts und Geradeaus sind dabei in einer komplexen Form angegeben und m"ussen zur Verwendung auf eine Gleitkommazahl reduziert werden. Desweiteren gilt es die Richtung vom Sensor unabh"angig zu machen, da die Angaben Links, Rechts und Geradeaus sich auf die Fahrtrichtung des Verkehrs "uber den Sensor beziehen.\\ \\ Zu Reduzierung der Werte auf Gleitkommazahlen wurden die Daten manuell bearbeitet. Die CAD-Zeichnungen dienen dabei als Hilfe, um die kreuzungsspezifischen Angaben interpretieren zu k"onnen. Ein Aufbereiteter Ausschnitt der Abbiegewahrscienlichkeiten ist in Tabelle \ref{tbl:abbw} zu finden. @@ -179,12 +180,12 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be A126 & D21 & (+A126.D21*0,4)*1+0 & (+A126.D21*0,6)*1+0 & NULL\\ A12 & D11 & NULL & NULL & (+A12.D11*0,4)*1+0\\ \hline - \end{tabular} + \end{tabular}\\ \\ \begin{tabular}{|l|l|l|l|l|} \hline Intersection & Sensor & DirectionStraight & DirectionLeft & DirectionRight\\ \hline - A104 & D3 & NULL & NULL & (+A104.D3*0,15)*1+0\\ + A104 & D3 & NULL & NULL & 0,15\\ A111 & D11 & 0,7 & 0,2 & 0,1\\ A111 & D21 & 0,15 & 0,65 & 0,2\\ A111 & D31 & 0,6 & 0,1 & 0,3\\ @@ -200,7 +201,7 @@ In diesem Kapitel werden die Grundlagen der Verkehrstechnik und -Modellierung be W"ahrend der Datenanalyse und Aufbereitung wurden einige Herausforderungen erkannt, die es zu l"osen gilt, da sie andernfalls die L"osungsm"oglichkeiten einschr"anken. Zum einen ist das das Zeitproblem, welches eine Verbindung von Sensorwerten von zwei Kreuzungen nicht zul"asst, zum anderen das Abbiegeproblem, welches beschreibt, das die Abbiegewahrscheinlichkeit nicht mithilfe der Sensorwerte gemessen werden kann. \subsubsection{Das Zeitproblem}\label{sec:datengrund:probtime} Die Daten der Induktionsschleifen sind die Werte der Sensoren "uber die letzte Minute. Sie zeigen eine Art summierte Momentaufnahme des Verkehrs an den Messpunkten. Das macht es allerdings schwer zwei Messungen in eine Beziehung zu stellen. Bildlich gesprochen kann man nicht trivial bestimmen, wie lange ein Auto von der einen zur anderen Kreuzung ben"otigt. Da die Daten nur f"ur bestimmte Zeitpunkte zur Verf"ugung stehen, kann nicht mehr festgetsllt werden wann ein Auto, welches an Kreuzung A "uber den Sensor gefahren ist, an Kreuzung B ankommt und dort "uber einen anderen Sensor f"ahrt. Eine 'Verfolgung' eines Autos ist somit nicht m"oglich, da nicht festgestellt werden kann, wie weit es bis zur n"achsten Momentaufnahme fortbewegt hat.\\ \\ - Dieses Problem wurde Zeitproblem getauft und konnte nicht vollständig gelöst werden. Die Arbeit \cite{thesis:michael} versucht dieses Problem durch das Gleichsetzen des Kreuzungsausgangswertes mit dem Eingangswert der darauffolgenden Kreuzung zu lösen. Dies ist allerdings nicht im Minutentakt durchzuführen, sondern durch den Zeitversatz der Messungen müssen die Werte gemittelt werden. Für eine Berechnung des momentanen Verkehrsaufkommens zu einem Zeitpunkt eignet sich das Verfahren allerdings nicht. + 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, sondern 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 allerdings nicht. \subsubsection{Das Abbiegeproblem}\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, allerdings 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 gerechnet, welche angeben, wie viel Prozent des Verkehrs, welcher "uber einen Sensor f"ahrt, die Kreuzung in welche Richtung verl"asst. Gelöst wurde dieses Problem durch gemittelte Abbiegewahrscheinlichkeiten an den Sensoren, welche von der Stadt Darmstadt ermittelt wurden. Eine Lösung des Abbiegeproblems ist mit einem flächendeckenden Einsatz von Vallidierungssensoren möglich. Mehr Informationen zu Vallierungssensoren und deren Verwendungsmöglichkeiten sind im Kapitel \autoref{sec:berechnung} aufgezeigt. + Das 'Abbiegeproblem' ist auf zu wenige Sensorwerte zur"uckzuf"uhren. In den Kreuzungen von Darmstadt sind die Induktionsschleifen am Kreuzungseingang verbaut, allerdings 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 gerechnet, welche angeben, wie viel Prozent des Verkehrs, welcher "uber einen Sensor f"ahrt, die Kreuzung in welche Richtung verl"asst. Gel"ost wurde dieses Problem durch gemittelte Abbiegewahrscheinlichkeiten an den Sensoren, welche 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/einleitung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex index 15212db3..64354f74 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/einleitung.tex @@ -1,18 +1,18 @@ \section{Einleitung}\label{sec:einleitung} -Die Anzahl der LKWs und PKWs auf den Straßen Deutschlands steigt st"andig an. Insbesondere die moderne hochindustrialisierte Produktion von Autos ließen deren Preise fallen und erlaubten es Jedermann ein eigenes Auto zu besitzen. So waren im Jahre 1955 lediglich 1.748 tausend PKWs und 603 tausend LKWs gemeldet. Heute, 2013 sind 43.431 tausend PKWs und 2.579 tausend LKWs auf den Straßen Deutschlands unterwegs\cite{web:statista:lkw}\cite{web:statista:pkw}. Dabei ist neben dem Personenverkehr besonders der Güterverkehr eine große Belastung für die Straßen. Das Statistische Bundesamt\footnote{Die Website des Statistischen Bundesamtes ist unter http://www.destatis.de/ zu erreichen.} weist in einer Erhebung der Anteile der Verkehrsträger im Güterverkehr aus Deutschland in die EU\cite{web:statista:gueter} den Straßenverkehr mit 57\% aus während Bahn- und Schifffahrtsverkehr lediglich einen Anteil von unter 10\% an dem Gütertransport haben. Die gr"o"ser gewordene Anzahl der Verkehrsteilnehmer auf den Stra"sen wird zunehmend zu einer Belastung f"ur die St"adte, Stra"sen, Mensch und Umwelt. In einer Umfrage von 2010 des Umweltbundesamt \footnote{Die Website des Umwelt Bundesamtes ist unter http://www.umweltbundesamt.de/ zu erreichen.} unter der Bevölkerung, gaben 57\% der Befragten an von Straßenverkehrslärm belästigt zu werden\cite{web:statista:laerm}. Aus dies Grund ist die Verbesserung des innerstädtischen Verkehrs, ob nun durch Umgehungsstraßen, Feinstaubfilter oder andere Maßnahmen, immer auch eine Verbesserung der Lebensqualität der dort lebenden und arbeitenden Menschen.\\ \\ -Eine dieser Maßnahmen ist der Einsatz verkehrsaufkommensgesteuerter Ampelanlagen. Besonders in größeren Städten, welche unter hohem Verkehrsaufkommen leiden setzen diese Technik seit einigen Jahren vermehrt ein. Sie ermöglichen es der Ampel mithilfe von, in der Fahrbahndecke verbauten Sensoren, ihre Ampelphasen, unter gewissen Rahmenbedingung, selbst zu steuern. Die Sensorik erkennt dabei, ob ein Auto an der Haltelinie steht und fordert eine Freigabe der Fahrtrichtung. Durch Einsatz einer solchen verkehrsaufkommensgesteuerter Ampel kann nachweislich \cite{paper:adaptiv} eine Verbesserung des Verkehrsflusses erreicht und die Haltezeiten an der Ampel verkürzt werden. Zunehmend werde auch sog. 'voll-adaptive' Ampelsteuerungen eingesetzt, welche neben den Sensorwerten der jeweiligen Kreuzung auch die Sensorwerte benachbarter Kreuzungen in die Berechnung der Ampelphasen einfließen lassen. Dieser Ansatz verspricht einen noch flüssigeren Verkehr und eine nochmalige Verbesserung des Verkehrsflusses.\\ \\ -Neben einer verbesserten Ampelsteuerung um den Verkehr schneller fließen zu lassen, haben sich einige Firmen auf die Untersuchung des Verkehrs spezialisiert und bieten Analysewerkzeuge f"ur den Verkehr an. So bietet das Programm VISSIM\footnote{Die Website der Software VISSIM lautet \url{http://www.vissim.de/}} und PELOPS\footnote{PELOPS: Programm zur Entwicklung L"angsdynamischer, mikrOskopischer VerkehrsProzesse in Systemrelevanter Umgebung} eine professionelle Modellierung von Verkehr an. Dabei kommt eine sog. mikroskopische Verkehrsmodellierung zum Einsatz. Mikroskopische Verkehrsmodelle modellieren dabei jeden einzelnen Verkehrsteilnehmer um Beziehungen unter diesen aufzeigen und berechnen zu können. So bestimmt sich die Geschwindigkeit eines Autos in einem solchen Modell in der Regel aus der des Vordermanns.\\ \\ -In dieser Arbeit wird untersucht inwieweit die Sensorik einer verkehrsaufkommensgesteuerten Ampelanlage ausreicht, um zu bestimmen, in welche Richtung und wie viel des Verkehr aus und in die Kreuzungen fließt. Dies ist besonders interessant, da die Sensorik bereits auf der Straße verbaut ist und keine manuellen Datenerhebungen notwendig sind. Die Herausforderung ist dabei, dass nicht alle Stra"sen und Kreuzungen mit Induktionsschleifen ausgestattet sind, da nicht alle Kreuzungen Ampelanlagen aufweisen, welche die Sensorik erfordert. Man m"ochte allerdings Verkehrswerte f"ur diese, nicht bekannten Bereiche, berechnen oder absch"atzen können, um die momentane Verkehrssituation besser einsch"atzen und sich einen Überblick "uber die aktuelle Verkehrslage zu verschaffen zu k"onnen. Dabei erweist sich die geringe Sensormenge und der große Abstand zwischen diesen, als die größten Herausforderungen. Für die Untersuchung wurde ein Ausschnitt des Straßennetzes der Stadt Darmstadt\footnote{Die Website der Stadt Darmstadt ist unter \url{http://www.darmstadt.de/} zu erreichen.} gewählt und ein Modell für Kreuzungen und un ein zweites Modell für zwischen den Kreuzungen erstellt. Hierfür wird, im Gegensatz zu industriellen Verkehrssimulationswerkzeugen ein macroskopischer Ansatz gewählt um der geringen Sensordichte gerecht zu werden.\\ \\ +Die Anzahl der LKWs und PKWs auf den Straßen Deutschlands steigt st"andig an. Insbesondere die moderne hochindustrialisierte Produktion von Autos ließen deren Preise fallen und erlaubten es Jedermann ein eigenes Auto zu besitzen. So waren im Jahre 1955 lediglich 1.748 tausend PKWs und 603 tausend LKWs gemeldet. Heute, 2013 sind 43.431 tausend PKWs und 2.579 tausend LKWs auf den Straßen Deutschlands unterwegs\cite{web:statista:lkw}\cite{web:statista:pkw}. Dabei ist neben dem Personenverkehr besonders der G"uterverkehr eine große Belastung f"ur die Straßen. Das Statistische Bundesamt\footnote{Die Website des Statistischen Bundesamtes ist unter http://www.destatis.de/ zu erreichen.} weist in einer Erhebung der Anteile der Verkehrstr"ager im G"uterverkehr aus Deutschland in die EU\cite{web:statista:gueter} den Straßenverkehr mit 57\% aus w"ahrend Bahn- und Schifffahrtsverkehr lediglich einen Anteil von unter 10\% an dem G"utertransport haben. Die gr"o"ser gewordene Anzahl der Verkehrsteilnehmer auf den Stra"sen wird zunehmend zu einer Belastung f"ur die St"adte, Stra"sen, Mensch und Umwelt. In einer Umfrage von 2010 des Umweltbundesamt \footnote{Die Website des Umwelt Bundesamtes ist unter http://www.umweltbundesamt.de/ zu erreichen.} unter der Bev"olkerung, gaben 57\% der Befragten an von Straßenverkehrsl"arm bel"astigt zu werden\cite{web:statista:laerm}. Aus dies Grund ist die Verbesserung des innerst"adtischen Verkehrs, ob nun durch Umgehungsstraßen, Feinstaubfilter oder andere Maßnahmen, immer auch eine Verbesserung der Lebensqualit"at der dort lebenden und arbeitenden Menschen.\\ \\ +Eine dieser Maßnahmen ist der Einsatz verkehrsaufkommensgesteuerter Ampelanlagen. Besonders in gr"oßeren St"adten, welche unter hohem Verkehrsaufkommen leiden setzen diese Technik seit einigen Jahren vermehrt ein. Sie erm"oglichen es der Ampel mithilfe von, in der Fahrbahndecke verbauten Sensoren, ihre Ampelphasen, unter gewissen Rahmenbedingung, selbst zu steuern. Die Sensorik erkennt dabei, ob ein Auto an der Haltelinie steht und fordert eine Freigabe der Fahrtrichtung. Durch Einsatz einer solchen verkehrsaufkommensgesteuerter Ampel kann nachweislich \cite{paper:adaptiv} eine Verbesserung des Verkehrsflusses erreicht und die Haltezeiten an der Ampel verk"urzt werden. Zunehmend werde auch sog. 'voll-adaptive' Ampelsteuerungen eingesetzt, welche neben den Sensorwerten der jeweiligen Kreuzung auch die Sensorwerte benachbarter Kreuzungen in die Berechnung der Ampelphasen einfließen lassen. Dieser Ansatz verspricht einen noch fl"ussigeren Verkehr und eine nochmalige Verbesserung des Verkehrsflusses.\\ \\ +Neben einer verbesserten Ampelsteuerung um den Verkehr schneller fließen zu lassen, haben sich einige Firmen auf die Untersuchung des Verkehrs spezialisiert und bieten Analysewerkzeuge f"ur den Verkehr an. So bietet das Programm VISSIM\footnote{Die Website der Software VISSIM lautet \url{http://www.vissim.de/}} und PELOPS\footnote{PELOPS: Programm zur Entwicklung L"angsdynamischer, mikrOskopischer VerkehrsProzesse in Systemrelevanter Umgebung} eine professionelle Modellierung von Verkehr an. Dabei kommt eine sog. mikroskopische Verkehrsmodellierung zum Einsatz. Mikroskopische Verkehrsmodelle modellieren dabei jeden einzelnen Verkehrsteilnehmer um Beziehungen unter diesen aufzeigen und berechnen zu k"onnen. So bestimmt sich die Geschwindigkeit eines Autos in einem solchen Modell in der Regel aus der des Vordermanns.\\ \\ +In dieser Arbeit wird untersucht inwieweit die Sensorik einer verkehrsaufkommensgesteuerten Ampelanlage ausreicht, um zu bestimmen, in welche Richtung und wie viel des Verkehr aus und in die Kreuzungen fließt. Dies ist besonders interessant, da die Sensorik bereits auf der Straße verbaut ist und keine manuellen Datenerhebungen notwendig sind. Die Herausforderung ist dabei, dass nicht alle Stra"sen und Kreuzungen mit Induktionsschleifen ausgestattet sind, da nicht alle Kreuzungen Ampelanlagen aufweisen, welche die Sensorik erfordert. Man m"ochte allerdings Verkehrswerte f"ur diese, nicht bekannten Bereiche, berechnen oder absch"atzen k"onnen, um die momentane Verkehrssituation besser einsch"atzen und sich einen Überblick "uber die aktuelle Verkehrslage zu verschaffen zu k"onnen. Dabei erweist sich die geringe Sensormenge und der große Abstand zwischen diesen, als die gr"oßten Herausforderungen. F"ur die Untersuchung wurde ein Ausschnitt des Straßennetzes der Stadt Darmstadt\footnote{Die Website der Stadt Darmstadt ist unter \url{http://www.darmstadt.de/} zu erreichen.} gew"ahlt und ein Modell f"ur Kreuzungen und un ein zweites Modell f"ur zwischen den Kreuzungen erstellt. Hierf"ur wird, im Gegensatz zu industriellen Verkehrssimulationswerkzeugen ein macroskopischer Ansatz gew"ahlt um der geringen Sensordichte gerecht zu werden.\\ \\ F"ur diese Aufgabe stehen die Sensordaten von den Ampelanlagen der Stadt Darmstadt zur Verf"ugung, welche in einer Vielzahl ihrer Kreuzungen mit sog. Induktionsschleifen, Verkehrssensoren, best"uckt hat. Diese liefern im Minutentakt Messwerte "uber die Anzahl der Autos, welche den Sensor passiert und solche die auf dem Sensor gestanden haben. Es wurde ein Ausschnitt von zehn Kreuzungen betrachtet, welche eine hohe Sensordichte aufweisen. 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.\\ \\ -Grundlage dieser Arbeit sind insbesondere die Arbeit \cite{paper:kwonmurphy}, welche eine Modellierung von Freeway-Verkehrs vornimmt und mithilfe eines Hidden Markov Modell die Geschwindigkeit von Verkehrsteilnehmer vorhersagt, die Arbeit \cite{thesis:neubert}, welche mithilfe von zellular Automaten den Verkehr auf Autobahnen simuliert, sowie die Daten der Arbeit \cite{thesis:mueller}, welche die Verkehrsdaten der Stadt Darmstadt bereits aufbereitet hat. Die Arbeit \cite{thesis:lehnhoff} erwies sich als Hilfreich zu Validierung, so konnten die dort befundenen Sensorungenauigkeiten bestätigt werden.\\ \\ -Eine Beschreibung der Grundlagen, sowie die genau Beschreibung der Daten der Stadt Darmstadt, wird im Kapitel \autoref{sec:datengrund} vorgenommen. Das entwickelte Graphen-basierte Zweistufenmodell für Kreuzungen und zwischen Kreuzungen wird in Kapitel \autoref{sec:modell} vorgestellt. Es modelliert neben den Induktionsschleifen sog. 'virtuelle Sensoren' für welche keine Sensorwerte vorliegen. +Grundlage dieser Arbeit sind insbesondere die Arbeit \cite{paper:kwonmurphy}, welche eine Modellierung von Freeway-Verkehrs vornimmt und mithilfe eines Hidden Markov Modell die Geschwindigkeit von Verkehrsteilnehmer vorhersagt, die Arbeit \cite{thesis:neubert}, welche mithilfe von zellular Automaten den Verkehr auf Autobahnen simuliert, sowie die Daten der Arbeit \cite{thesis:mueller}, welche die Verkehrsdaten der Stadt Darmstadt bereits aufbereitet hat. Die Arbeit \cite{thesis:lehnhoff} erwies sich als Hilfreich zu Validierung, so konnten die dort befundenen Sensorungenauigkeiten best"atigt werden.\\ \\ +Eine Beschreibung der Grundlagen, sowie die genau Beschreibung der Daten der Stadt Darmstadt, wird im Kapitel \autoref{sec:datengrund} vorgenommen. Das entwickelte Graphen-basierte Zweistufenmodell f"ur Kreuzungen und zwischen Kreuzungen wird in Kapitel \autoref{sec:modell} vorgestellt. Es modelliert neben den Induktionsschleifen sog. 'virtuelle Sensoren' f"ur welche keine Sensorwerte vorliegen. [todo collage] \begin{figure} \centering \includegraphics[width=0.5\textwidth]{pic/overview} \caption{'Ministadt', ausschnitt von Darmstadt der innerhalb dieser Arbeit betrachtet wird.} \end{figure} -Es wird daraufhin in Kapitel \autoref{sec:berechnung} beschrieben wie anhand dieses Modells ein Verkehrsfluss aus den Kreuzungen heraus berechnet werden kann. Dafür werden verschiedene Ans"atze diskutiert und eine Lösung mithilfe linearer Gleichungssysteme vorgestellt, um Werte für 'virtuelle Sensoren' zu berechnen. Durch weitere lineare Gleichungen konnten auch für Flüsse zwischen Kreuzungen Werte berechnet werden. Grundlage dieser Berechnung sind Matrizenmultiplikationen, welche in dieser Arbeit direkt am entwickelten Graphen berechnet werden. Des weiteren wird untersucht inwieweit der Verkehr anhand der gegebenen Daten vorhergesagt werde kann. Im Kapitel \autoref{sec:visualisierung} werden zwei Visualisierungen des Modells anhand des gewählten Ausschnitts des Straßennetz der Stadt Darmstadt erläutert, woraufhin im Kapitel \autoref{sec:validierung} die Ergebnisse und das Modell auf ihre Gültigkeit hin überprüft werden. Hierfür wurde eine Verkehrszählung vorgenommen, um die berechneten Daten überprüfen zu können. Abschließend werden die Ergebnisse dieser Arbeit in Kapitel \autoref{sec:ausblick} zusammengefasst und ein Ausblick gegen, wie sich die errechneten Werte weiter verbessern lassen. +Es wird daraufhin in Kapitel \autoref{sec:berechnung} beschrieben wie anhand dieses Modells ein Verkehrsfluss aus den Kreuzungen heraus berechnet werden kann. Daf"ur werden verschiedene Ans"atze diskutiert und eine L"osung mithilfe linearer Gleichungssysteme vorgestellt, um Werte f"ur 'virtuelle Sensoren' zu berechnen. Durch weitere lineare Gleichungen konnten auch f"ur Fl"usse zwischen Kreuzungen Werte berechnet werden. Grundlage dieser Berechnung sind Matrizenmultiplikationen, welche in dieser Arbeit direkt am entwickelten Graphen berechnet werden. Des weiteren wird untersucht inwieweit der Verkehr anhand der gegebenen Daten vorhergesagt werde kann. Im Kapitel \autoref{sec:visualisierung} werden zwei Visualisierungen des Modells anhand des gew"ahlten Ausschnitts des Straßennetz der Stadt Darmstadt erl"autert, woraufhin im Kapitel \autoref{sec:validierung} die Ergebnisse und das Modell auf ihre G"ultigkeit hin "uberpr"uft werden. Hierf"ur wurde eine Verkehrsz"ahlung vorgenommen, um die berechneten Daten "uberpr"ufen zu k"onnen. Abschließend werden die Ergebnisse dieser Arbeit in Kapitel \autoref{sec:ausblick} zusammengefasst und ein Ausblick gegen, wie sich die errechneten Werte weiter verbessern lassen. \cite{thesis:elfers} \cite{paper:kwonmurphy} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex index 8ce795be..84af4d52 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex @@ -43,12 +43,12 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \label{abb:a23.2} \centering \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/KreuzungA23}} - \caption{Händische Modellierung der Kreuzung A23} + \caption{H"andische Modellierung der Kreuzung A23} \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, erwies 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, so ist im Vergleich die Kreuzungs"ubersicht relativ ungenau, da Seitenstra"sen nicht modelliert werden und alle Kreuzungen als gleich weit voneinander entfernt betrachtet werden. Die gew"ahlte Modellierung hat folglich zwei Genauigkeitsstufen. Die "Ubersicht "uber die Kreuzungen gew"ahrt einen Blick auf die Gesammtverkehrssituation. Sie dient wie der Name schon sagt, der "Ubersicht. Ein wesentliches Ziel ist es Verkehrsdaten f"ur dieses Modell zu errechnen oder abzusch"atzen, da zwar Informationen "uber die einzelnen Kreuzungen zur Verf"ugung stehen, allerdings diese noch nicht auf ein Gesamtbild des Verkehrs "ubertragen werden k"onnen. \subsection{Modell als Graph}\label{sec:modell:graph} - Ein naheliegender Modellierungsansatz ist es, das Stra"sennetz als Graph zu modellieren. Dies eignet sich nicht nur, da Graphen sehr gut erforscht und viele Algorithmen auf ihnen zur Verf"ugung stehen, sonder auch, weil die intuitiv gew"ahlte manuelle Modellierung sich als Graph darstellen l"asst. Aus diesem Grund wurden Graphen als Basis der computergest"utzten Modellierung gew"ahlt. Insbesondere die M"oglichkeit Graphen in Matrizen zu "uberf"uhren, oder lineare Gleichungen an Graphen zu lösen erweist sich als n"utzlich. Da Einbahnstra"sen und Verkehr mit einer Flussrichtung modelliert werden m"ussen, w"ahlt man einen gerichteten Graphen. Da sich die Zweistufenmodellierung als n"utzlich erwiesen hat, wird auch diese als Graph im Computer abgebildet. Daf"ur m"ussen zwei verschiedenen Graphen aufgebaut werden. Der einer Kreuzung, mit Sensoren und virtuellen Sensoren als Knoten, sowie Stra"sen als Kanten. Der Graph der Kreuzungs"ubersicht dagegen hat Kreuzungen als Knoten und ebenfalls Stra"sen als Kanten.\\ \\ + 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 lineare Gleichungen an Graphen zu l"osen erweist sich als n"utzlich. Da Einbahnstra"sen und Verkehr mit einer Flussrichtung modelliert werden m"ussen, w"ahlt man einen gerichteten Graphen. Da sich die Zweistufenmodellierung als n"utzlich erwiesen hat, wird auch diese als Graph im Computer abgebildet. Daf"ur m"ussen zwei verschiedenen Graphen aufgebaut werden. Der einer Kreuzung, mit Sensoren und virtuellen Sensoren als Knoten, sowie Stra"sen als Kanten. Der Graph der Kreuzungs"ubersicht dagegen hat Kreuzungen als Knoten und ebenfalls Stra"sen als Kanten.\\ \\ Zur Modellierung am Computer wird auf die Java Bibliothek JGraphT zur"uckgegriffen. Sie erlaubt es, dank Javas moderner Template-Technik, 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. Der Kreuzungs"ubersichtsgraphen soll die Graphen der einzelnen Kreuzungen als Knoten enthalten um den Zusmmenhalt des Modells zu gew"ahrleisten.\\ \\ Es folgt eine kurze "Ubersicht "uber Graphen, woraufhin die computergest"utzte Modellierung des Kreuzungsgraph und Kreuzungs"ubersichtsgraphen beschrieben wird. \subsubsection{Grundlagen}\label{sec:modell:graph:grund} @@ -70,7 +70,7 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \subfigure[Ungerichter Graph mit Mehrfachkanten. Quelle: wikipedia.org] {\includegraphics[width=0.1\textwidth-2\fboxsep-2\fboxrule]{pic/200px-Graph_ungerichtet_Mehrfachkanten}} \label{abb:graph:multi} \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 benötigt werden. Typische Algorithmen auf einem Graphen sind die Tiefensuche, Breitensuche oder Wegfindungsalgorithmen. + 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. \subsubsection{Kreuzungsgraph}\label{sec:modell:graph:xr} Da der Kreuzungs"ubersichtsgraph die Kreuzungsgraphen als Knoten beinhalten soll, wird zuerst der Kreuzungsgraph modelliert. Dabei gilt es folgende Elemente abzubilden und entweder als Knoten oder Kante zu definieren. Validierungssensoren werden aus der Modellierung außenvorgelassen, um Modellierung und Berechnung zu vereinfachen. \begin{itemize} @@ -84,8 +84,8 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St \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 zusätzlich 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 Wert 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, welche eine eindeutige Zuordnung der Werte zu einem Sensor erm"oglicht. Ein Zeitstempel bestimmt dabei den Zeitpunkt der Messung der Werte. Zur "Uberpr"ufung eines Wertes mit einem Testwert wird ein gemessener Wert als Testwert gespeichert. Eine Berechnung soll nun einen Wert berechnen, der durch Vergleich mit dem gemessenem Testwert Aufschluss über die Genauigkeit der Berechnung gibt.\\ \\ + 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 Wert 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, welche eine eindeutige Zuordnung der Werte zu einem Sensor erm"oglicht. Ein Zeitstempel bestimmt dabei den Zeitpunkt der Messung der Werte. Zur "Uberpr"ufung eines Wertes mit einem Testwert wird ein gemessener Wert als Testwert gespeichert. Eine Berechnung soll nun einen Wert berechnen, der durch Vergleich mit dem gemessenem Testwert Aufschluss "uber die Genauigkeit der Berechnung gibt.\\ \\ Die Klasse ST modelliert eine Straße. Sie kann die Namen der Knoten, welche sie verbindet speichern, um den Graphen nicht st"andig nach den Namen der Nachbarn abzusuchen zu m"ussen. Diese beiden Werte dienen lediglich der Visualisierung. Desweiteren kann eine Gleitkommazahl gespeichert werden, welche die Abbiegewahrscheinlichkeit von einem Sensor, entlang dieser Kante, repr"asentiert. 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 diese sp"ater zu visualisieren.\\ \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} @@ -192,12 +192,12 @@ Die Grundannahme f"ur das Modell ist, dass sich die Verkehrsteilnehmer an die St Dabei ist eine ID ein eindeutiges Merkmahl 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} einen 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 den ein Algorithmus, welcher auf dem Graphen rechnet, anders als auf die anderen beiden Sensortypen reagieren kann.\\ \\ Die Definition f"ur Kreuzungen ist dagegen deutlich einfacher. Da jede Kreuzung, die modelliert wurde h"ochsten vier Ausg"ange hat, m"ussen jeweils 4 Ausg"ange sowie 4 Eing"ange modelliert werden. Auch hier werden Latitude und Logitude ben"otigt, um die Kreuzung auf einer Karte, oder realativ zu anderen Objekten der Modellierung, darstellen zu k"onnen. Die Kreuzungsnamen sind in der Stadt Darmstadt eindeutig, weshalb es keine ID f"ur eine Identifikation von Kreuzungen bedarf.\\ \\ Die Tabelle Values enth"alt aufbereitete Induktionsschleifenwerte. Diese werden mit den Abfragen, welche in \autoref{sec:datengrund} beschrieben sind, aus der MYSQL-Datenbank der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten extrahiert, um das manuelle Parsen der CSV-Dateien zu umgehen. Sensoren werden hierf"ur mit ihrer eindeutigen ID identifiziert. Ein Zeitstempel der Sensordaten erlaubt es mehrere Datens"atze von verschiedenen Zeiten zu speichern. Ein Filter auf dem Zeitstempel erlaubt es Daten eines gew"ahlten Zeitpunktes 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 h"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. Da diese Werte dieser Tabelle aus der Abbiegewahrscheinlichkeitstabelle der Stadt Darmstadt entnommen wurden, werden Sensoren "uber Kreuzungs- und Sensorname identifiziert und nicht "uber eine eindeutige Sensor ID. Dies ist m"oglich, obwohl Sensornamen nicht eindeutig sind, da sie innerhalb einer Kreuzung eine eindeutige Identifikation "uber den Namen möglich ist. Eine Kombination aus dem eindeutigem Kreuzungsnamen und der innerhalb der Kreuzung eindeutigen Sensornamens, kann ein Sensor eindeutig identifizieren. F"ur die Abbiegewahrscheinlichkeitentabelle werden neben dem Kreuzungs- und Sensornamen, bis zu drei verschiedenen Abbiegewahrscheinlichkeiten angegeben. Die Wahrscheinlichkeit, das ein Verkehrsteilnehmer, welcher "uber den Sensor f"ahrt rechts, links oder geradeaus die Kreuzung verl"asst. Zus"atzlich wird der n"achste Sensorknoten, diesmal identifiziert "uber die Sensorid, f"ur jede Richtung mit angegeben. Wie die Zuordnung der Abbiegewahrscheinlichkeiten für Links, Rechts und Geradeaus zu einem Knoten erfolgt, wird im Kapitel \autoref{sec:berechnung} beschrieben.\\ + Die Tabelle FlowStatistics h"alt Abbiegewahrscheinlichkeiten f"ur Sensoren. Da diese Werte dieser Tabelle aus der Abbiegewahrscheinlichkeitstabelle der Stadt Darmstadt entnommen wurden, werden Sensoren "uber Kreuzungs- und Sensorname identifiziert und nicht "uber eine eindeutige Sensor ID. Dies ist m"oglich, obwohl Sensornamen nicht eindeutig sind, da sie innerhalb einer Kreuzung eine eindeutige Identifikation "uber den Namen m"oglich ist. Eine Kombination aus dem eindeutigem Kreuzungsnamen und der innerhalb der Kreuzung eindeutigen Sensornamens, kann ein Sensor eindeutig identifizieren. F"ur die Abbiegewahrscheinlichkeitentabelle werden neben dem Kreuzungs- und Sensornamen, bis zu drei verschiedenen Abbiegewahrscheinlichkeiten angegeben. Die Wahrscheinlichkeit, das ein Verkehrsteilnehmer, welcher "uber den Sensor f"ahrt rechts, links oder geradeaus die Kreuzung verl"asst. Zus"atzlich wird der n"achste Sensorknoten, diesmal identifiziert "uber die Sensorid, f"ur jede Richtung mit angegeben. Wie die Zuordnung 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 abgespeichert werden. Dies erlaubt es genauere, zeitspezifische, Abbiegewahrscheinlichkeiten abzuspeichern. F"ur diese Arbeit lagen allerdings ausschließlich die Werte der Stadt Darmstadt vor, welche "uber alle Messungen gemittelt sind. \subsection{Einschr"ankungen und Schw"achen des Modell}\label{sec:modell:limits} Das entwickelte Modell kann nicht alle Verkehrsverhalten modellieren. In diesem Abschnitt wird behandelt, welche Einschr"ankungen das Modell mitbringt und welche Reduktionen des Detailgrades vorgenommen wurden.\\ \\ - Das Modell kann sog. 'U-Turns', nicht modellieren. Als 'U-Turn' bezeichnet man dasjenige Verkehrsman"over, welches den Verkehrsteilnehmer von dem Kreuzungseingang einer Kreuzung zu dem Ausgang, welcher in die Richtung zeigt, aus der er gekommen ist, zurück 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.\\ \\ - Ein weitere, sehr elementare Schw"ache des Modells ist die Abstraktion der Sensorposition. Wie in den manuell angefertigten Kreuzungszeichnungen wird die Position eines Sensors innerhalb des Graphenmodells einem Eingang zugeordnet. Die Latitude und Longitude Werte des Sensors werden nur zur Visualisierung benutzt und nicht zur Berechnung. Dies erlaubt allerdings einen Spurwechsel, nach dem "Uberfahren eines Sensors, nicht zu modellieren. Die Genauigkeit des Modells h"angt folglich direkt mit der Entfernung des Sensors von der Kreuzung ab. Ist der Sensor weit entfernt, so kann ein 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 Höhen in die Straße eingelassen, so können Verkehrsteilnehmer im schlechtesten Fall über zwei Sensoren fahren, wenn sie nach dem überfahren eines Sensors die Spur wechseln, welche einen Sensor weiter vorne im Kreuzungsbereich verbaut hat.\\ \\ + Das Modell kann sog. 'U-Turns', nicht modellieren. Als 'U-Turn' bezeichnet man dasjenige Verkehrsman"over, welches den Verkehrsteilnehmer von dem Kreuzungseingang einer Kreuzung zu dem Ausgang, welcher in die Richtung zeigt, aus der er 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.\\ \\ + Ein weitere, sehr elementare Schw"ache des Modells ist die Abstraktion der Sensorposition. Wie in den manuell angefertigten Kreuzungszeichnungen wird die Position eines Sensors innerhalb des Graphenmodells einem Eingang zugeordnet. Die Latitude und Longitude Werte des Sensors werden nur zur Visualisierung benutzt und nicht zur Berechnung. Dies erlaubt allerdings einen Spurwechsel, nach dem "Uberfahren eines Sensors, nicht zu modellieren. Die Genauigkeit des Modells h"angt folglich direkt mit der Entfernung des Sensors von der Kreuzung ab. Ist der Sensor weit entfernt, so kann ein 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 Straße eingelassen, so k"onnen Verkehrsteilnehmer im schlechtesten Fall "uber zwei Sensoren fahren, wenn sie nach dem "uberfahren eines Sensors die Spur wechseln, welche 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 dekorieren und somit die Menge der modellierbaren Kreuzungszust"ande und -"Uberg"ange zu vergr"oßern um ein realistischeres Bild des Verkehrs zu berechnen. Allerdings lagen keine Daten "uber das Verhalten der Verkehrsteilnehmer vor. \newpage \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/uebersicht.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/uebersicht.tex index cdee9ea4..b8a7a1d7 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/uebersicht.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/uebersicht.tex @@ -1,7 +1,7 @@ \section{"Ubersicht}\label{sec:uebersicht} -In Ballungsgebieten, vornehmlich St"adten, steigt die Anzahl der Verkehrsteilnehmer. Insbesondere die Anzahl der Autos ist in den letzten Jahren drastisch gestiegen. Diese zunehmende Belastung wirkt sich auf Stra"sen, auf den Verkehr und durch Verschmutzung und L"armbelastung auch auf den Menschen aus. Um der gestiegenen Anzahl an Fahrzeugen gerecht zu werden wurden verkehrsabh"angige Ampelanlagen entwickelt, welche ihre Ampelphasen dem Verkehrsaufkommen anpassen können. Hierf"ur wird der Verkehr der einzelnen Spuren einer Kreuzung mithilfe von Sensoren - Induktionsschleifen - erfasst. Mit der fortschreitenden Technisierung und dem gestiegenem Verkehr erhielten diese 'adaptiv' gesteuerten Ampelanlagen Einzug in die Straßen gr"oßerer St"adte, um die bereits vorhandenen Straßen besser nutzen zu k"onnen.\\ \\ +In Ballungsgebieten, vornehmlich St"adten, steigt die Anzahl der Verkehrsteilnehmer. Insbesondere die Anzahl der Autos ist in den letzten Jahren drastisch gestiegen. Diese zunehmende Belastung wirkt sich auf Stra"sen, auf den Verkehr und durch Verschmutzung und L"armbelastung auch auf den Menschen aus. Um der gestiegenen Anzahl an Fahrzeugen gerecht zu werden wurden verkehrsabh"angige Ampelanlagen entwickelt, welche ihre Ampelphasen dem Verkehrsaufkommen anpassen k"onnen. Hierf"ur wird der Verkehr der einzelnen Spuren einer Kreuzung mithilfe von Sensoren - Induktionsschleifen - erfasst. Mit der fortschreitenden Technisierung und dem gestiegenem Verkehr erhielten diese 'adaptiv' gesteuerten Ampelanlagen Einzug in die Straßen gr"oßerer St"adte, um die bereits vorhandenen Straßen besser nutzen zu k"onnen.\\ \\ In dieser Arbeit wird untersucht in wieweit man durch Verkehrsdaten, welche mithilfe von Induktionsschleifen auf den Stra"sen erfasst werden, Verkehrsfl"usse voraussagen und Stra"senbelastungen berechnen kann. Hierf"ur wurde ein zweistufiges Graphen-basiertes Modell der Stra"se entwickelt und verschiedene Ans"atze, um Verkehrsfl"usse innerhalb einer Kreuzung und zwischen Kreuzungen zu berechnen, diskutiert. Als Grundlage dieser Berechnungen dienen Induktionsschleifenwerte der Stadt Darmstadt, welche eine Vielzahl ihrer Kreuzungen mit Induktionsschleifen versehen hat.\\ \\ -Mithilfe von Linearen Gleichungssystemen konnten Verkehrsfl"usse innerhalb von Kreuzungen, sowie ein Anzahl an Verkehrsteilnehmer, welche eine Kreuzung in eine bestimmte Richtung verlassen, berechnet werden. Neben den Sensorwerten der Induktionsschleifen kamen dabei sog. Abbiegewahrscheinlichkeiten zum Einsatz, welche ebenfalls von der Stadt Darmstadt zur Verf"ugung gestellt wurden. Eine Visualisierung des entwickelten Graphen erlaubt es die berechneten Verkehrsflüsse besser zu untersuchen und zu verstehen, Die Validit"at der ermittelten Daten h"angt allerdings von den zugrundeliegenden Sensorwerten ab. In einer Verkehrsz"ahlung konnten ein Teil der modellierten Sensoren untersucht und bei einigen Sensoren eine sehr hohe Genauigkeit feststellen werden. Bei anderen Sensoren ergab die Z"ahlung allerdings Abweichungen von bis zu siebenhundert Prozent.\\ \\ +Mithilfe von Linearen Gleichungssystemen konnten Verkehrsfl"usse innerhalb von Kreuzungen, sowie ein Anzahl an Verkehrsteilnehmer, welche eine Kreuzung in eine bestimmte Richtung verlassen, berechnet werden. Neben den Sensorwerten der Induktionsschleifen kamen dabei sog. Abbiegewahrscheinlichkeiten zum Einsatz, welche ebenfalls von der Stadt Darmstadt zur Verf"ugung gestellt wurden. Eine Visualisierung des entwickelten Graphen erlaubt es die berechneten Verkehrsfl"usse besser zu untersuchen und zu verstehen, Die Validit"at der ermittelten Daten h"angt allerdings von den zugrundeliegenden Sensorwerten ab. In einer Verkehrsz"ahlung konnten ein Teil der modellierten Sensoren untersucht und bei einigen Sensoren eine sehr hohe Genauigkeit feststellen werden. Bei anderen Sensoren ergab die Z"ahlung allerdings Abweichungen von bis zu siebenhundert Prozent.\\ \\ \section*{Abstract} In urban areas, most notably Cities, have an increasing the number of road users. diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex index 0043beba..2e20746c 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex @@ -40,7 +40,7 @@ Hypothese: Berechnete Werte sind gen"ugend Genau. Ja/Nein -> wissenschaftliche m \subsection{Sensor} \subsection{"Uberpr"ufung 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. + 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] diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex index 8aa053cd..eb785cc8 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/visualisierung.tex @@ -1,6 +1,6 @@ \section{Visualisierung}\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 visualisiert wird. Neben dem Graphen wird eine Kreuzungsübersicht mithilfe der Geoinformationen der JEE6 Anwendung 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 oder Fehler überprüfen. +In diesem Kapitel wird beschrieben, wie der im Kapitel \autoref{sec:modell} und im Kapitel \autoref{sec:berechnung} mit Werten bef"ullter Graph visualisiert wird. Neben dem Graphen wird eine Kreuzungs"ubersicht mithilfe der Geoinformationen der JEE6 Anwendung mit den untersuchten Sensoren am Computer visualisiert.\\ \\ +Visualisierung eignet sich deshalb besonders gut, da die berechneten Zusammenh"ange komplex und wenig zug"anglich sind. Eine Visualisierung erm"oglicht eine andere Sicht auf den Sachverhalt und l"asst sich leichter auf Korrektheit oder Fehler "uberpr"ufen. \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. @@ -15,9 +15,9 @@ 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. + 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 k"onnen die Knoten des Graphen auf dem Bildschirm angeordnet werden um eine Identifizierung von Objekten zu erleichtern. Der Nutzer erh"alt weiterhin die F"ahigkeit die einzelnen Knoten manuell nachzujustieren. Dies ist insbesondere f"ur solche Knoten ohne g"ultige Koordinaten hilfreich.\\ \\ + Ziel dieser Visualisierung ist es die berechneten Werte darzustellen. Die Anordnung nach Koordinaten erm"oglicht es den generierten Graphen einfach mit der Realit"at zu vergleichen. Es werden im Gegensatz zu der Visualisierung mit Luftbildern nicht nur die Kreuzungs"ubersicht visualisiert, sondern auch die einzelnen Kreuzungen, da f"ur beide ein Graph vorhanden ist \autoref{sec:berechnung}. Die Erzeugung der Graphen ist dabei auf die Visualisierungsf"ahigkeit 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] + [bild "ubersicht bild kreuzung] } \newpage \ No newline at end of file