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[12 ] -Underfull \hbox (badness 10000) in paragraph at lines 114--145 +(Font) Font shape `T1/5fp/m/sl' tried instead on input line 103. + [12] +Underfull \hbox (badness 10000) in paragraph at lines 124--155 [] -Underfull \hbox (badness 10000) in paragraph at lines 109--147 +Underfull \hbox (badness 10000) in paragraph at lines 119--157 [] -Underfull \hbox (badness 10000) in paragraph at lines 109--147 +Underfull \hbox (badness 10000) in paragraph at lines 119--157 [] -Underfull \hbox (badness 10000) in paragraph at lines 109--147 +Underfull \hbox (badness 10000) in paragraph at lines 119--157 [] -[13]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/modell.tex -" +[13 ] [14]) +("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/modell.tex" -LaTeX Warning: Reference `sec:datengrund' on page 14 undefined on input line 3. +LaTeX Warning: Reference `sec:datengrund' on page 15 undefined on input line 3. @@ -1530,15 +1532,14 @@ Underfull \hbox (badness 10000) in paragraph at lines 2--8 [] -[14] LaTeX Warning: Reference `sec:daten:geo' on page 15 undefined on input line 9. - + File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) - + File: ext/KreuzungA23.pdf Graphic file (type pdf) @@ -1566,14 +1567,14 @@ Underfull \hbox (badness 10000) in paragraph at lines 9--30 [] -[15 ] +[15] [16 ] Underfull \hbox (badness 10000) in paragraph at lines 31--33 [] -[16 ] + Underfull \hbox (badness 10000) in paragraph at lines 41--43 [] @@ -1593,15 +1594,14 @@ Underfull \hbox (badness 10000) in paragraph at lines 55--58 [] - +[17] Underfull \hbox (badness 10000) in paragraph at lines 59--63 [] - + File: ext/graphen.pdf Graphic file (type pdf) -[17] Underfull \hbox (badness 10000) in paragraph at lines 81--84 [] @@ -1611,18 +1611,18 @@ Underfull \hbox (badness 10000) in paragraph at lines 81--84 [] - -Underfull \hbox (badness 10000) in paragraph at lines 92--95 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 92--95 - - [] - [18 ] - + +Underfull \hbox (badness 10000) in paragraph at lines 92--95 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 92--95 + + [] + + File: ext/KreuzungA23marked.pdf Graphic file (type pdf) @@ -1635,7 +1635,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 96--136 [] - +[19] Underfull \hbox (badness 10000) in paragraph at lines 137--171 [] @@ -1645,10 +1645,10 @@ Underfull \hbox (badness 10000) in paragraph at lines 137--171 [] -[19 ] -LaTeX Warning: Reference `sec:datengrund' on page 20 undefined on input line 17 +LaTeX Warning: Reference `sec:datengrund' on page 21 undefined on input line 17 2. @@ -1656,118 +1656,113 @@ Underfull \hbox (badness 10000) in paragraph at lines 172--174 [] -[20] -Underfull \hbox (badness 10000) in paragraph at lines 192--197 + +File: pic/er_bt.png Graphic file (type png) + [21 ] +Underfull \hbox (badness 10000) in paragraph at lines 197--202 [] -Underfull \hbox (badness 10000) in paragraph at lines 192--197 +Underfull \hbox (badness 10000) in paragraph at lines 197--202 [] -Underfull \hbox (badness 10000) in paragraph at lines 192--197 +Underfull \hbox (badness 10000) in paragraph at lines 197--202 [] - + File: pic/classdiagStreet.png Graphic file (type png) -Underfull \hbox (badness 10000) in paragraph at lines 198--206 +Underfull \hbox (badness 10000) in paragraph at lines 203--211 [] -[21] +[22] File: pic/classdiagAlgo.png Graphic file (type png) -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Overfull \hbox (14.46513pt too wide) in paragraph at lines 210--238 -[] \T1/5ch/m/n/9.5 Die Klas- - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -Underfull \hbox (badness 10000) in paragraph at lines 210--238 +Underfull \hbox (badness 10000) in paragraph at lines 215--244 [] -[22 ] -Underfull \vbox (badness 10000) has occurred while \output is active [] - - [23 ] -Underfull \hbox (badness 10000) in paragraph at lines 244--246 +[23 ] [24 ] +Underfull \hbox (badness 10000) in paragraph at lines 250--252 [] -Underfull \hbox (badness 10000) in paragraph at lines 247--253 +Underfull \hbox (badness 10000) in paragraph at lines 253--259 [] -Underfull \hbox (badness 10000) in paragraph at lines 247--253 +Underfull \hbox (badness 10000) in paragraph at lines 253--259 [] -Underfull \hbox (badness 10000) in paragraph at lines 247--253 +Underfull \hbox (badness 10000) in paragraph at lines 253--259 [] -Underfull \hbox (badness 10000) in paragraph at lines 247--253 +Underfull \hbox (badness 10000) in paragraph at lines 253--259 [] -Underfull \hbox (badness 10000) in paragraph at lines 247--253 +Underfull \hbox (badness 10000) in paragraph at lines 253--259 [] -Underfull \hbox (badness 10000) in paragraph at lines 254--256 +Underfull \hbox (badness 10000) in paragraph at lines 260--262 [] -[24] [25]) +[25] [26]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/berechnung.tex" Underfull \hbox (badness 10000) in paragraph at lines 2--4 @@ -1798,11 +1793,11 @@ Underfull \hbox (badness 10000) in paragraph at lines 43--45 [] -[26] +[27] Missing character: There is no â in font mdbchr7t! 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Missing character: There is no ¬ in font mdbchr7t! - + File: pic/500px-Hmm_temporal_bayesian_net.png Graphic file (type png) @@ -1810,7 +1805,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 52--66 [] -[27 ] Underfull \hbox (badness 10000) in paragraph at lines 72--75 @@ -1836,7 +1831,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 83--84 [] -[28] +[29] Underfull \hbox (badness 10000) in paragraph at lines 91--94 [] @@ -1851,12 +1846,12 @@ Underfull \hbox (badness 10000) in paragraph at lines 130--132 [] -[29] +[30] Underfull \hbox (badness 10000) in paragraph at lines 189--193 [] -[30] +[31] Underfull \hbox (badness 10000) in paragraph at lines 239--244 [] @@ -1876,7 +1871,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 270--277 [] -[31] +[32] Underfull \hbox (badness 10000) in paragraph at lines 278--281 [] @@ -1886,14 +1881,14 @@ Underfull \hbox (badness 10000) in paragraph at lines 282--284 [] - + File: ext/KreuzungA4.pdf Graphic file (type pdf) - [32] [33 [33] [34 ]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/validierung.tex" -LaTeX Warning: Reference `sec:berechnung:validate' on page 34 undefined on inpu +LaTeX Warning: Reference `sec:berechnung:validate' on page 35 undefined on inpu t line 5. @@ -1912,7 +1907,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 4--8 [] -LaTeX Warning: Reference `thesis:michael' on page 34 undefined on input line 9. +LaTeX Warning: Reference `thesis:michael' on page 35 undefined on input line 9. @@ -1930,7 +1925,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 9--13 [] -[34]) +[35]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/visualisierung.t ex" Underfull \hbox (badness 10000) in paragraph at lines 2--4 @@ -1948,17 +1943,17 @@ Package hyperref Warning: No autoref name for `subfigure' on input line 13. Package hyperref Warning: No autoref name for `subfigure' on input line 13. - + File: pic/osm_overview.png Graphic file (type png) File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) - + File: pic/jgraphuebersicht.png Graphic file (type png) - + File: pic/jgraphxr.png Graphic file (type png) Underfull \hbox (badness 10000) in paragraph at lines 22--47 @@ -1970,7 +1965,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 22--47 [] -[35] [36 ]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/ausblick.tex" Underfull \hbox (badness 10000) in paragraph at lines 2--7 @@ -1987,7 +1982,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 2--7 [] -[37 ]) ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.bb l" @@ -1996,7 +1991,7 @@ Underfull \hbox (badness 2158) in paragraph at lines 45--50 er-run-gen mit-tels Zel-lu-la-r-au-to-ma-ten für den [] -) [38] +) [39] Class scrartcl Warning: Usage of deprecated \float@listhead! (scrartcl) You should use the features of package `tocbasic' @@ -2008,209 +2003,209 @@ e 82. ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.lol") \tf@lol=\write8 -[39] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/anhang.tex" +[40] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/anhang.tex" pdfTeX warning: pdflatex.exe (file C:/Daten/source/college/ss2013/Bachelor Thes is/thesis_ug/ext/overviewmap.pdf): PDF inclusion: found PDF version <1.6>, but at most version <1.5> allowed - + File: ext/overviewmap.pdf Graphic file (type pdf) - + File: ext/MessgruppentabelleNord-2013-01-08.pdf Graphic file (type pdf) - + File: ext/MessgruppentabelleSued-2013-01-08.pdf Graphic file (type pdf) - [40] [41 ] [42 [41] [42 ] [43 ] [43 ] [44 ] File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) - [44 + [45 ] -[45] +[46] File: ext/KreuzungA3.pdf Graphic file (type pdf) - + File: ext/A3_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_3_L4.pdf Graphic file (type pdf) File: ext/KreuzungA4.pdf Graphic file (type pdf) - + File: ext/A4_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_4_L3.pdf Graphic file (type pdf) - + File: ext/KreuzungA5.pdf Graphic file (type pdf) - + File: ext/A5_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_5_L3.pdf Graphic file (type pdf) - + File: ext/KreuzungA12.pdf Graphic file (type pdf) - + File: ext/A12_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_12.pdf Graphic file (type pdf) -[46 +[47 -] [47 ] [48 ] [49 ] [50] [51 ] [52 ] [53 ] [54 ] [49 ] [50 ] [51] [52 ] [53 ] [54 ] [55 ] -[55 ] [56 ] [57 ] File: ext/KreuzungA23.pdf Graphic file (type pdf) - + File: ext/A23_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_23_L1.pdf Graphic file (type pdf) - + File: ext/KreuzungA28.pdf Graphic file (type pdf) - + File: ext/A28_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_28_L1.pdf Graphic file (type pdf) - + File: ext/KreuzungA29.pdf Graphic file (type pdf) - + File: ext/A29_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_29_L2.pdf Graphic file (type pdf) - + File: ext/KreuzungA46.pdf Graphic file (type pdf) - + File: ext/A46_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_46_L1.pdf Graphic file (type pdf) - [57] [58 ] [59 ] [60] [61 [58] [59 ] [60 ] [61] [62 ] -[62 ] [63 ] [64 ] [65 ] [66 ] [67 ] [68 ] [64 ] [65 ] [66 ] [67 ] [68 ] [69 ] - + File: ext/KreuzungA59.pdf Graphic file (type pdf) - + File: ext/A59_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_59.pdf Graphic file (type pdf) - + File: ext/KreuzungA104.pdf Graphic file (type pdf) - + File: ext/A104_Uebersetzungstabelle.pdf Graphic file (type pdf) - + File: ext/DA_A_104_L1.pdf Graphic file (type pdf) - [69] [70 ] [71 ] [72 ] [73 ] [74 [70] [71 ] [72 ] [73 ] [74 ] [75 -] [75 ] [76 ] [77 ] [78 ] [77 ] [78 ] [79 ] - + File: ext/verkehrszaehlung.pdf Graphic file (type pdf) - + File: ext/verkehrszaehlung_08_05.pdf Graphic file (type pdf) -) [79 +) [80 -] [80 ] [81 ] [82 ] No file TUDthesis.gls. Package atveryend Info: Empty hook `BeforeClearDocument' on input line 90. -[82] +[83] Package atveryend Info: Empty hook `AfterLastShipout' on input line 90. ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux") Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 90. Package rerunfilecheck Info: File `TUDthesis.out' has not changed. -(rerunfilecheck) Checksum: 8D973AE307B6137E8EDC8F3DEC3C3376;4182. +(rerunfilecheck) Checksum: 99D114AD98591730055E117C413C226F;4102. LaTeX Warning: There were undefined references. ) Here is how much of TeX's memory you used: - 17656 strings out of 494019 - 269059 string characters out of 3145626 - 483760 words of memory out of 3000000 - 20054 multiletter control sequences out of 15000+200000 + 17723 strings out of 494019 + 269826 string characters out of 3145626 + 483357 words of memory out of 3000000 + 20112 multiletter control sequences out of 15000+200000 179147 words of font info for 125 fonts, out of 3000000 for 9000 714 hyphenation exceptions out of 8191 65i,13n,77p,2255b,1293s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -2230,9 +2225,9 @@ oftmake/stafford/5sfr8a.pfb> -Output written on TUDthesis.pdf (85 pages, 16949550 bytes). +Output written on TUDthesis.pdf (86 pages, 16983056 bytes). PDF statistics: - 2326 PDF objects out of 2487 (max. 8388607) - 347 named destinations out of 1000 (max. 500000) - 700 words of extra memory for PDF output out of 10000 (max. 10000000) + 2341 PDF objects out of 2487 (max. 8388607) + 354 named destinations out of 1000 (max. 500000) + 702 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.lol b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.lol index 4805eaa1..cb6f2d4a 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.lol +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.lol @@ -1,5 +1,5 @@ -\contentsline {lstlisting}{\numberline {1}SQL-Abfrage der Sensorens}{11}{lstlisting.1} +\contentsline {lstlisting}{\numberline {1}SQL-Abfrage der Sensorens}{12}{lstlisting.1} \contentsline {lstlisting}{\numberline {2}SQL-Abfrage der Sensorwerte}{12}{lstlisting.2} -\contentsline {lstlisting}{\numberline {3}abc}{23}{lstlisting.3} -\contentsline {lstlisting}{\numberline {4}abc}{23}{lstlisting.4} -\contentsline {lstlisting}{\numberline {5}Befehl zur Konvertierung und Darstellung eines JGraphT Graphen als JGraph}{36}{lstlisting.5} +\contentsline {lstlisting}{\numberline {3}JGraphT-Definition des Kreuzungsgraphen}{24}{lstlisting.3} +\contentsline {lstlisting}{\numberline {4}JGraphT-Definition des Kreuzungs"ubersichtsgraphen}{24}{lstlisting.4} +\contentsline {lstlisting}{\numberline {5}Befehl zur Konvertierung und Darstellung eines JGraphT Graphen als JGraph}{37}{lstlisting.5} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out index fd57762c..6a0706af 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.out @@ -42,13 +42,12 @@ \BOOKMARK [2][-]{subsection.8.1}{Validierung durch Testdatenmenge}{section.8}% 42 \BOOKMARK [2][-]{subsection.8.2}{Verkehrsz\344hlung}{section.8}% 43 \BOOKMARK [2][-]{subsection.8.3}{Validierung der Berechneten 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\contentsline {subsection}{\numberline {5.3}CAD-Zeichnungen der Kreuzungen}{13}{subsection.5.3} \contentsline {subsection}{\numberline {5.4}Abbiegewahrscheinlichkeiten}{13}{subsection.5.4} -\contentsline {section}{\numberline {6}Graphen-basiertes Verkehrsmodell}{14}{section.6} +\contentsline {section}{\numberline {6}Graphen-basiertes Verkehrsmodell}{15}{section.6} \contentsline {subsection}{\numberline {6.1}H"andische Modellierung der Ministadt}{15}{subsection.6.1} -\contentsline {subsection}{\numberline {6.2}Allgemeines Verkehrsmodell auf Basis eines Graphen}{16}{subsection.6.2} -\contentsline {subsubsection}{\numberline {6.2.1}Grundlagen}{17}{subsubsection.6.2.1} +\contentsline {subsection}{\numberline {6.2}Allgemeines Verkehrsmodell auf Basis eines Graphen}{17}{subsection.6.2} +\contentsline {subsubsection}{\numberline {6.2.1}Grundlagen}{18}{subsubsection.6.2.1} \contentsline {subsubsection}{\numberline {6.2.2}Kreuzungsgraph}{18}{subsubsection.6.2.2} -\contentsline {subsubsection}{\numberline {6.2.3}Kreuzungs"ubersichtsgraph}{18}{subsubsection.6.2.3} -\contentsline {subsection}{\numberline {6.3}Matrixdarstellung des Kreuzungsmodells}{18}{subsection.6.3} +\contentsline {subsubsection}{\numberline {6.2.3}Kreuzungs"ubersichtsgraph}{19}{subsubsection.6.2.3} +\contentsline {subsection}{\numberline {6.3}Matrixdarstellung des Kreuzungsmodells}{19}{subsection.6.3} \contentsline {subsubsection}{\numberline {6.3.1}Ausgangsmatrix}{19}{subsubsection.6.3.1} \contentsline {subsubsection}{\numberline {6.3.2}Eingangsmatrix}{20}{subsubsection.6.3.2} -\contentsline {subsection}{\numberline {6.4}Datenbankmodell}{20}{subsection.6.4} -\contentsline {subsection}{\numberline {6.5}Implementierung}{21}{subsection.6.5} -\contentsline {subsection}{\numberline {6.6}Zuk"unftige Herausforderungen des Modells}{24}{subsection.6.6} -\contentsline {subsubsection}{\numberline {6.6.1}Herausforderung: Verfolgung von Fahrzeugen "uber eine Kreuzung hinaus}{24}{subsubsection.6.6.1} -\contentsline {subsubsection}{\numberline {6.6.2}Herausforderung: Genaues Bestimmen des Abbiegeverhaltens}{25}{subsubsection.6.6.2} -\contentsline {section}{\numberline {7}L"osungsans"atze}{26}{section.7} -\contentsline {subsection}{\numberline {7.1}Aufbereiten der Abbiegewahrscheinlichkeiten}{26}{subsection.7.1} -\contentsline {subsection}{\numberline {7.2}L"osungsansatz: Hidden Markow Modell}{27}{subsection.7.2} -\contentsline {subsubsection}{\numberline {7.2.1}Grundlagen}{27}{subsubsection.7.2.1} -\contentsline {subsubsection}{\numberline {7.2.2}HMM f"ur eine Kreuzung}{28}{subsubsection.7.2.2} -\contentsline {subsection}{\numberline {7.3}L"osungsansatz: Wegfindungsalgorithmen}{28}{subsection.7.3} -\contentsline {subsection}{\numberline {7.4}L"osungsansatz: Lineares Gleichungssystem}{28}{subsection.7.4} -\contentsline {subsubsection}{\numberline {7.4.1}Grundlagen}{29}{subsubsection.7.4.1} -\contentsline {subsubsection}{\numberline {7.4.2}Lineares Gleichungssystem einer Kreuzung}{29}{subsubsection.7.4.2} -\contentsline {subsection}{\numberline {7.5}Kreuzungsberechnung am Graphen}{31}{subsection.7.5} -\contentsline {subsubsection}{\numberline {7.5.1}Verkehrsfluss zwischen Kreuzungen}{32}{subsubsection.7.5.1} -\contentsline {subsubsection}{\numberline {7.5.2}Sonderfall: Validierungssensor}{32}{subsubsection.7.5.2} -\contentsline {section}{\numberline {8}Validierung}{34}{section.8} -\contentsline {subsection}{\numberline {8.1}Validierung durch Testdatenmenge}{34}{subsection.8.1} -\contentsline {subsection}{\numberline {8.2}Verkehrsz"ahlung}{34}{subsection.8.2} -\contentsline {subsection}{\numberline {8.3}Validierung der Berechneten Verkehrswerte}{34}{subsection.8.3} -\contentsline {subsection}{\numberline {8.4}"Uberpr"ufung des Modells}{34}{subsection.8.4} -\contentsline {section}{\numberline {9}Visualisierung}{35}{section.9} -\contentsline {subsection}{\numberline {9.1}Visualisierung des Graphen mit JMapViewer}{35}{subsection.9.1} -\contentsline {subsection}{\numberline {9.2}Visualisierung des JGraphT-Graphen}{35}{subsection.9.2} -\contentsline {section}{\numberline {10}Fazit \& Ausblick}{37}{section.10} -\contentsline {section}{\numberline {11}Bibliographie}{38}{section.10} -\contentsline {section}{\numberline {12}Abbildungsverzeichnis}{39}{section.10} -\contentsline {section}{\numberline {13}Quellcodeverzeichnis}{39}{section.10} -\contentsline {section}{\numberline {14}Anhang}{40}{section.14} -\contentsline {section}{\numberline {15}Glossar}{82}{figure.55} +\contentsline {subsection}{\numberline {6.4}Datenbankmodell}{21}{subsection.6.4} +\contentsline {subsection}{\numberline {6.5}Implementierung}{22}{subsection.6.5} +\contentsline {subsection}{\numberline {6.6}Zuk"unftige Herausforderungen des Modells}{25}{subsection.6.6} +\contentsline {subsubsection}{\numberline {6.6.1}Herausforderung: Verfolgung von Fahrzeugen "uber eine Kreuzung hinaus}{25}{subsubsection.6.6.1} +\contentsline {subsubsection}{\numberline {6.6.2}Herausforderung: Genaues Bestimmen des Abbiegeverhaltens}{26}{subsubsection.6.6.2} +\contentsline {section}{\numberline {7}L"osungsans"atze}{27}{section.7} +\contentsline {subsection}{\numberline {7.1}Aufbereiten der Abbiegewahrscheinlichkeiten}{27}{subsection.7.1} +\contentsline {subsection}{\numberline {7.2}L"osungsansatz: Hidden Markow Modell}{28}{subsection.7.2} +\contentsline {subsubsection}{\numberline {7.2.1}Grundlagen}{28}{subsubsection.7.2.1} +\contentsline {subsubsection}{\numberline {7.2.2}HMM f"ur eine Kreuzung}{29}{subsubsection.7.2.2} +\contentsline {subsection}{\numberline {7.3}L"osungsansatz: Wegfindungsalgorithmen}{29}{subsection.7.3} +\contentsline {subsection}{\numberline {7.4}L"osungsansatz: Lineares Gleichungssystem}{29}{subsection.7.4} +\contentsline {subsubsection}{\numberline {7.4.1}Grundlagen}{30}{subsubsection.7.4.1} +\contentsline {subsubsection}{\numberline {7.4.2}Lineares Gleichungssystem einer Kreuzung}{30}{subsubsection.7.4.2} +\contentsline {subsection}{\numberline {7.5}Kreuzungsberechnung am Graphen}{32}{subsection.7.5} +\contentsline {subsubsection}{\numberline {7.5.1}Verkehrsfluss zwischen Kreuzungen}{33}{subsubsection.7.5.1} +\contentsline {subsubsection}{\numberline {7.5.2}Sonderfall: Validierungssensor}{33}{subsubsection.7.5.2} +\contentsline {section}{\numberline {8}Validierung}{35}{section.8} +\contentsline {subsection}{\numberline {8.1}Validierung durch Testdatenmenge}{35}{subsection.8.1} +\contentsline {subsection}{\numberline {8.2}Verkehrsz"ahlung}{35}{subsection.8.2} +\contentsline {subsection}{\numberline {8.3}Validierung der Berechneten Verkehrswerte}{35}{subsection.8.3} +\contentsline {section}{\numberline {9}Visualisierung}{36}{section.9} +\contentsline {subsection}{\numberline {9.1}Visualisierung des Graphen mit JMapViewer}{36}{subsection.9.1} +\contentsline {subsection}{\numberline {9.2}Visualisierung des JGraphT-Graphen}{36}{subsection.9.2} +\contentsline {section}{\numberline {10}Fazit \& Ausblick}{38}{section.10} +\contentsline {section}{\numberline {11}Bibliographie}{39}{section.10} +\contentsline {section}{\numberline {12}Abbildungsverzeichnis}{40}{section.10} +\contentsline {section}{\numberline {13}Quellcodeverzeichnis}{40}{section.10} +\contentsline {section}{\numberline {14}Anhang}{41}{section.14} +\contentsline {section}{\numberline {15}Glossar}{83}{figure.57} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex index 0e953681..22478dbe 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/ausblick.tex @@ -4,4 +4,10 @@ Desweiteren ist es m"oglich durch den fl"achendeckenden Einsatz von Validierungs Au"serdem ist es denkbar das Modell mit mehr Informationen zu \textit{taggen} um die Berchnung zu verbessern. Ein Beispiel w"are das Auftragen der H"ochstgeschwindigkeit auf die Kanten des entwickelten Graphen.\\ \\ Die durch Modell und Berechnung gewonnenen Erkenntnisse k"onnen zur Optimierung von Verkehr, als Analysetool oder zur Planung von neuen Kreuzungen eingesetzt werden. Insbesondere da die Technisierung des Verkehrssystems fortschreitet, ist damit zu rechnen, dass mehr Sensoren auf die Stra"sen gelangen. So plant Deutschland in einer Gesetzesinitiative[] sog. Blackboxen f"ur PKWs vorzuschreiben. Diese k"onnen neben Geschwindigkeit, Fahr- und Bremsverhalten die GPS-Position des Fahrzeugs "ubermitteln. Diese Daten w"urden eine Echtzeit-Simulation des Verkehrs erlauben. Insbesondere der fl"achendeckende Einsatz in PKWs w"urden millionen Sensoren auf die Stra"se bringen. \\ \\ 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 flie"sen zu lassen. Es ist zu erwarten, das mit dieser neuen Technik noch mehr Induktionsschleifensensorik auf die Stra"sen der Gro"sst"adte gelangt und eine wesentlich genauere Untersuchung des Verkehrs zul"asst. + + [todo ausblick] + Das in Kapitel \autoref{sec:modell} entwickelte Modell muss auf seine G"ultigkeit "uberpr"uft werden. Hierzu wird "uberpr"uft, ob die f"ur das Modell getroffenen Annahmen mit einer realen Verkehrssituation angebracht sind. + [falschabbieger] + [spurwechsler] + [uturns] \newpage \ No newline at end of file diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/daten.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/daten.tex index 109ab188..d78e4a4b 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/daten.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/daten.tex @@ -40,7 +40,12 @@ In diesem Kapitel werden die Verkehrsdaten, die f"ur diese Arbeit zur Verf"ugung Sensorspalten, welche auf Z enden, bezeichnen den \textit{count}-Wert des jeweiligen Sensors, solche die auf B enden den \textit{load}-Wert. Jede Zeile in der CSV-Datei repr"asentiert 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 tats"achlichen Sensornamen herzustellen, werden sog. \textit{"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 \textit{"Ubersetzungstabellen} sowie die CAD-Zeichnung im Anhang zu finden [\ref{anhang:a3}]\footnote{Die CAD-Zeichnungen, sowie die "Ubersetzungstabellen aller Kreuzungen sind unter \url{http://www.da-sense.de/trafficdata/} zu finden}. \subsubsection{MYSQL-Daten der JEE6 Anwendung zur Bereitstellung von Verkehrsdaten} \label{sec:datengrund:inductvalues:mysql} Im Rahmen der Arbeit von \textsc{C. M"uller}\cite{thesis:mueller}, wurde eine JEE6\footnote{Das aktuelle JEE-Framework ist unter \url{http://www.oracle.com/technetwork/java/javaee/overview/} zu erhalten.}[gls:jee6] Anwendung entwickelt, die die aufbereiteten Verkehrsdaten der Stadt Darmstadt bereit stellt. Hierf"ur wurden die CSV-Dateien eingelesen und in eine MYSQL-Datenbank "uberf"uhrt. Die dort gesammelten Sensordaten wurden bereits mit Geoinformation des OpenStreetMap Projektes\footnote{Die Website des OpenStreetMap-Projektes ist unter \url{http://openstreetmap.org/} zu erreichen.} verkn"upft und erlauben es eine Position f"ur Kreuzungs- und Sensorknoten zu bestimmen.\\ \\ - (todo ER Diagramm) + \begin{figure} + \centering + \includegraphics[width=0.5\textwidth]{pic/er_jee} + \caption{"Ubersicht "uber die verwendeten Datenbanken der JEE6-Anwendung} + \label{abb:erjee} + \end{figure} 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{\textit{jee\_crmodel\_CrossroadDim}: In dieser Tabelle werden Kreuzungsname und -position abgespeichert.} @@ -59,8 +64,10 @@ In diesem Kapitel werden die Verkehrsdaten, die f"ur diese Arbeit zur Verf"ugung FROM `jee_crmodel_CrossroadDim` AS CD, `jee_crmodel_SensorDim` as SD WHERE CD.VALIDTO is null - AND CD.REALNAME IN - ('A 3','A 4',...todo,'A 59','A104') + AND CD.REALNAME IN + ('A 46','A 12','A 59', + 'A104','A 23','A 28', + 'A 29','A 3','A 4','A 5') AND SD.REALNAME LIKE 'D%' AND SD.CROSSROAD_ID = CD.ID AS sensors @@ -76,7 +83,10 @@ In diesem Kapitel werden die Verkehrsdaten, die f"ur diese Arbeit zur Verf"ugung FROM `jee_crmodel_CrossroadDim` AS CD, `jee_crmodel_SensorDim` as SD WHERE CD.VALIDTO is null - AND CD.REALNAME IN('A 3','A 4',...,'A104') + AND CD.REALNAME IN + ('A 46','A 12','A 59', + 'A104','A 23','A 28', + 'A 29','A 3','A 4','A 5') AND SD.REALNAME LIKE 'D%' AND SD.CROSSROAD_ID = CD.ID) AS sensors, `jee_traf?clight_rawevents` AS raw diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex index e98fc984..ba0b62c3 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex @@ -177,7 +177,12 @@ Um ein Verkehrsmodell zu entwickeln muss zuerst festgelegt werden, welche Art de \item{Die Abbiegewahrscheinlichkeit welche der richtigen Verbindungen zwischen Sensor und entsprechendem virtuellen Kreuzungsausgang zugordnet ist.} \item{Induktionsschleifwerte der Sensoren.} \end{enumerate} - [ER diagramm todo] + \begin{figure} + \centering + \includegraphics[width=0.95\textwidth]{pic/er_bt} + \caption{"Ubersicht "uber die entworfene Datenbankstruktur} + \label{abb:erbt} + \end{figure} F"ur Sensoren werden daf"ur folgende Daten in der Tabelle \textit{bt\_sensors} gespeichert: \begin{itemize} \item{Eindeutige ID des Sensors} @@ -214,16 +219,17 @@ Um ein Verkehrsmodell zu entwickeln muss zuerst festgelegt werden, welche Art de Eine Kreuzung wird mit der Klasse \textit{XR} modelliert. Sie enth"alt den, in \autoref{lst:sensorgraph} gezeigten Sensorgraph einer Kreuzung. Weiterhin werden f"ur die Kreuzungen eine Position in Latitude und Longitude abgespeichert, sowie alle verbundenen eingehenden Kreuzungen und alle ausgehenden Kreuzungen. Das Speichern von beiden, Vorg"anger- und Nachfolgerkreuzungen, ist zum Aufbau des Graphen nicht n"otig. Daf"ur w"urden entweder Ein- oder Ausg"ange ausreichen. Um Visualisierung und Berechnung zu vereinfachen wurden allerdings beide definiert. \\ \\ Eine Stra"se wird, wie in der Kreuzungsmodellierung mit der Klasse \textit{ST} beschrieben. Das Feld f"ur die Abbiegewahrscheinlichkeit kann allerdings nicht gef"ullt werden, da keine Abbiegewahrscheinlichkeiten au"serhalb von Kreuzungen bekannt sind. Das Feld wird sp"aterhin zum Speichern von Fl"ussen zwischen den Kreuzungen benutzt. \\ \\ Um den Graph mit der \textit{JGraphT}-Bibliothek zu modellieren, wurde die Klasse \textit{ListableDirectedGraph} benutzt (siehe \autoref{lst:sensorgraph}). Diese Klasse des Frameworks erlaubt gerichtete Graphen aufzubauen, die Struktur zur Berechnung zu verwenden und sp"ater zu visualisieren.\\ + \lstset{language=java} \begin{minipage}[t]{\dimexpr\textwidth-3\fboxsep-2\fboxrule-1em} - \begin{lstlisting}[caption={[abc] Die Kreuzungsklasse XR}, label={lst:sensorgraph}, captionpos=bsec] + \begin{lstlisting}[caption={[JGraphT-Definition des Kreuzungsgraphen] JGraphT-Definition des Kreuzungsgraphen}, label={lst:sensorgraph}, captionpos=bsec] public ListenableDirectedGraph sensorGraph = new ListenableDirectedGraph<>(ST.class); \end{lstlisting} - \begin{lstlisting}[caption={[abc] Die Kreuzungsklasse XR}, label={lst:streetgraph}, captionpos=bsec] + \begin{lstlisting}[caption={[JGraphT-Definition des Kreuzungs"ubersichtsgraphen] JGraphT-Definition des Kreuzungs"ubersichtsgraphen}, label={lst:streetgraph}, captionpos=bsec] private static ListenableDirectedGraph streetGraph = new ListenableDirectedGraph<>(ST.class); \end{lstlisting} - \end{minipage} + \end{minipage}\\ Die Klasse \textit{TrafficGraph} ist die Hauptklasse der JGraphT Modellierung. Sie enth"alt den Kreuzungs"ubersichtsgraphen (siehe \autoref{lst:streetgraph}) und "uber das Feld \textit{data\_timestamp} kann definiert werden welcher Datensatz aus der Datenbank selektiert wird. Die Funktion \textit{createGraph} der Klasse erzeugt den Kreuzungs"ubersichtsgraphen. Daf"ur werden zuerst alle Kreuzungsknoten aus der Datenbank selektiert und f"ur jeden ein neues \textit{XR}-Objekt angelegt und mit den Werten der Datenbank bef"ullt. Dieses wird daraufhin dem \textit{streeGraph} hinzugef"ugt. In einem zweiten Schritt werden alle Verbindungen der Knoten untersucht. Wird der angegebene Zielknoten gefunden, wird eine Kante zwischen den beiden Kreuzungen dem \textit{streeGraph}-Objekt hinzugef"ugt. W"ahrend des Anlegens des \textit{XR}-Objekt werden die Kreuzungsdaten in dieses nachgeladen. Hierf"ur werden alle Sensoren, welche zu der entsprechenden Kreuzung geh"oren aus der Datenbank geholt, diese dem \textit{sensorGraph} hinzugef"ugt, sowie Verbindungen zwischen den Sensoren annotiert.\\ \\ Die Funktion \textit{loadData} der \textit{TrafficGraph}-Klasse erlaubt das Laden der Daten f"ur den spezifizierten Zeitpunkt. Diese l"ad sowohl die Sensorwerte und schreibt diese in die einzelnen Sensorknoten des \textit{sensorGraph}, als auch die Abbiegewahrscheinlichkeiten, welche den dazugeh"origen Kanten "ubergeben wird. Daraufhin sind alle Daten geladen und der Graph ist komplett aufgebaut. \\ \\ diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex index c6c3f2f6..6c1b0a02 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex @@ -1,24 +1,18 @@ \section{Validierung}\label{sec:validierung} In diesem Kapitel wird die Validierung der berechneten Verkehrswerte beschrieben (siehe \autoref{sec:berechnung}). Dabei wird zun"achst ein angestrebtes Verfahren beschrieben und darauf eingegangen warum dieses Verfahren sich nicht eignet. Um die berechneten Werte dennoch validieren zu k"onnen, wurde eine Verkehrsz"ahlung im Rahmen dieser Arbeit vorgenommen. \subsection{Validierung durch Testdatenmenge} - Ein "ubliches Testverfahren ist es, einen Teil der Datenmenge aus der Berechnung au"senvorzulassen und durch die verwendete Berechnung diese fehlenden Daten zu reproduzieren. Die Datenmenge wird hierf"ur in die sog. Testdatenmenge und die Restdatenmenge aufgeteilt. Durch einen Vergleich der Testdaten und den zugeh"origen berechneten Daten, kann nun festgestellt werden wie genau die Berechnung ist.\\ \\ + Ein "ubliches Testverfahren ist es, einen Teil der Datenmenge aus der Berechnung au"senvorzulassen und durch die verwendete Berechnung diese fehlenden Daten zu reproduzieren. Die Datenmenge wird hierf"ur in die sog. Testdatenmenge und die Rechendatenmenge aufgeteilt. Durch einen Vergleich der Testdaten und den zugeh"origen berechneten Daten, kann nun festgestellt werden wie genau die Berechnung ist.\\ \\ Dieses Verfahren eignet sich hier allerdings nicht, da bei den vorliegenden Sensordaten das Auslassen von Sensorwerten, um diese als Testdaten zu verwenden, die Berechnung unm"oglich macht, da das LGS unl"osbar wird (vgl. \autoref{sec:berechnung:validate}). Das ist auf die geringe Menge an Sensoren zur"uckzuf"uhren.\\ \\ Um dieses Verfahren anwenden zu k"onnen m"ussen Vallidierungssensoren fl"achendeckend auf den Kreuzungen zur Verf"ugung stehen. Dann kann durch Weglassen der Sensor- oder der Validierungssensordaten die Berechnung erfolgen und die Ausgelassenen Daten k"onnen zur Validierung eingesetzt werden.\\ \\ Die vorliegenden Daten der Sensorwerte verbieten das Auslassen von Sensordaten, da die Berechnung ansonsten nicht erfolgen kann. Deshalb kann dieses Verfahren nicht verwendet werden, um die berechneten Daten zu validieren. \subsection{Verkehrsz"ahlung} - Da kein anderes Testverfahren gefunden wurde, welches eine Validierung der Daten erm"oglichen w"urde, wurde im Rahmen dieser Arbeit eine Verkehrsz"ahlung durchgef"uhrt. Diese Verkehrsz"ahlung wurde mit Hilfe von \textit{Scholz} \autoref{thesis:michael} durchgef"uhrt. Gez"ahlt wurde dabei mit Strichliste an den Kreuzungen [], [] und []. Dabei wurden in der einen Messreihe die Autos an den Ausg"angen gez"ahlt, um die berechneten Werte der virtuellen Kreuzungsausg"ange in dem Graphenmodell validieren zu k"onnen. Desweiteren wurden die Fahrzeuge gez"ahlt, die "uber die Sensoren [] und [] gefahren sind. Jeder Sensor bzw. Ausgang wurde daf"ur "uber einen Zeitraum von 15 Minuten beobachtet und der Verkehr gez"ahlt.\\ \\ - Es wurden dabei starke Unterschiede zwischen den gez"ahlten und den, von den Sensoren ermittelten, Werten festgestellt. Dies ist zum einen auf ungenaue und fehleranf"allige Sensorik(vgl. \autoref{sec:grundlagen}) zur"uckzuf"uhren, zum anderen muss f"ur adaptiv gesteuerte Ampelanlagen sichergestellt werden, dass alle Fahrzeuge erkannt werden, um diese "uber die Kreuzung zu lassen. Diese Vorgabe wird dadurch erf"ullt, dass die Sensorik leichter als n"otig ausl"ost, um wirklich jedes Fahrzeug zu erkennen. Dies wiederum erh"oht die Fehleranf"alligkeit des Sensors. [todo auswertung]\\ \\ - In einer weiteren Untersuchung wurde der Sensor [] im Minutentakt gez"ahlt, um eine genaueres Bild der Abweichung zu erhalten. Die gemessenen Werte lagen dabei bis zu 700\% von dem gez"ahlten Wert entfernt. Bei dieser Z"ahlung wurden neben der Anzahl der Verkehrsteilnehmer der Fahrzeugtyp untersucht, um die Fehleranf"alligkeit des Sensors f"ur die verschiedenen Fahrzeugtypen genauer zu bestimmen.[todo auswertung]\\ \\ - Die Erkenntnisse "uber die Ungenauigkeiten der Sensoren decken sich mit den Befunden der Arbeit [] von [][cite]. In dem dort Untersuchten Gebiet der Stadt Hannover wurde eine sehr starke Varianz der Messgenauigkeit der dort verbauten Induktionsschleifen festgestellt. + Da kein anderes Testverfahren gefunden wurde, welches eine Validierung der Daten erm"oglichen w"urde, wurde im Rahmen dieser Arbeit eine Verkehrsz"ahlung durchgef"uhrt. Diese Verkehrsz"ahlung wurde mit Hilfe von \textit{M. Scholz} \autoref{thesis:michael} durchgef"uhrt. Gez"ahlt wurde dabei mit Strichliste an den Kreuzungen A12, A23 und A4. Dabei wurden in der einen Messreihe die Fahrzeuge an den Ausg"angen gez"ahlt, um die berechneten Werte der virtuellen Kreuzungsausg"ange in dem Graphenmodell validieren zu k"onnen. Desweiteren wurden die Fahrzeuge gez"ahlt, die "uber die Sensoren A12.D31, A23.D3 und A23.D1 gefahren sind. Jeder Sensor bzw. Ausgang wurde daf"ur "uber einen Zeitraum von 15 Minuten beobachtet und der Verkehr gez"ahlt.\\ \\ + Es wurden dabei starke Unterschiede zwischen den gez"ahlten und den, von den Sensoren ermittelten, Werten festgestellt. Dies ist zum einen auf ungenaue und fehleranf"allige Sensorik(vgl. \autoref{sec:grundlagen}) zur"uckzuf"uhren, zum anderen muss f"ur adaptiv gesteuerte Ampelanlagen sichergestellt werden, dass alle Fahrzeuge erkannt werden, um diese "uber die Kreuzung zu lassen. Diese Vorgabe wird dadurch erf"ullt, dass die Sensorik leichter als n"otig ausl"ost, um wirklich jedes Fahrzeug zu erkennen. Dies wiederum erh"oht die Fehleranf"alligkeit des Sensors. Eine tabellarische Auswertung der Daten ist in Anhang zu finde [todo]\\ \\ + In einer weiteren Untersuchung wurde der Sensor D31 der Kreuzung A12 im Minutentakt gez"ahlt, um eine genaueres Bild der Abweichung zu erhalten. Die gemessenen Werte lagen dabei bis zu 700\% von dem gez"ahlten Wert entfernt. Bei dieser Z"ahlung wurden neben der Anzahl der Verkehrsteilnehmer der Fahrzeugtyp untersucht, um die Fehleranf"alligkeit des Sensors f"ur die verschiedenen Fahrzeugtypen genauer zu bestimmen.[todo auswertung]. Eine tabellarische Auswertung der Daten ist im Anhang zu finden.[todo]\\ \\ + Die Erkenntnisse "uber die Ungenauigkeiten der Sensoren decken sich mit den Befunden der Disseration von \textsc{N. Lehnhoff}\cite{thesis:lehnhoff}. In dem dort Untersuchten Gebiet der Stadt Hannover wurde eine sehr starke Varianz der Messgenauigkeit der dort verbauten Induktionsschleifen festgestellt. \subsection{Validierung der Berechneten Verkehrswerte} Eine Berechnung der Verkehrswerte mittels LGS mit jeweils den Sensorwerten und den gez"ahlten Werten ergabt eine Abweichung von bis zu x\%.[geht nicht - zeit] [todo -> rechnung, abweichung bestimmen] Da die Berechnung der Kreuzungsein- und Ausgangswerte direkt von der Genauigkeit der Sensorwerte abh"angt, ist die Genauigkeit der berechneten Werte entsprechend. Eine Verbesserung der Qualit"at der Sensordaten w"urde eine direkte Verbesserung der Berechneten Werte zur folge haben. - \subsection{"Uberpr"ufung des Modells} - [todo ausblick] - Das in Kapitel \autoref{sec:modell} entwickelte Modell muss auf seine G"ultigkeit "uberpr"uft werden. Hierzu wird "uberpr"uft, ob die f"ur das Modell getroffenen Annahmen mit einer realen Verkehrssituation angebracht sind. - [falschabbieger] - [spurwechsler] - [uturns] \newpage \ No newline at end of file

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