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Figures2_and_3.nb
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Figures2_and_3.nb
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Generating Figures 2 and 3 in the article \[OpenCurlyDoubleQuote]Obscuring \
digital route choice information prevents delay-induced congestion\
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Figure 2: Routing in a two-route network with delayed information\
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Solving the delay-differential equations by numerical integration\
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With this notebook, we solve the delayed differential equations of vehicle \
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To start, we first define our travel time, the corresponding in-rates and the \
differential equations for the two streets A and C.\
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Our differential equation has two fixed points, which we find by determining \
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Now we have all the tools to integrate the differential equations numerically \
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DisplayFunction -> Identity, Ticks -> {Automatic, Automatic},
AxesOrigin -> {0, 0}, FrameTicks -> {{Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
Charting`ScaledFrameTicks[{Identity, Identity}]}},
GridLines -> {{0}, {0}}, DisplayFunction -> Identity,
PlotRangePadding -> {{0, 0}, {0, 0}}, PlotRangeClipping -> True,
ImagePadding -> All, DisplayFunction -> Identity, AspectRatio ->
NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {False, False},
AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :>
Identity, Frame -> {{True, True}, {True, True}}, FrameLabel -> {{
FormBox["\"number of cars\"", TraditionalForm], None}, {
FormBox["\"time\"", TraditionalForm], None}}, FrameStyle -> Automatic,
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
GridLines -> {{0}, {0}}, GridLinesStyle -> Directive[
GrayLevel[0.5, 0.4]], LabelStyle -> {FontFamily -> "Times"},
Method -> {
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}}, PlotLabel ->
FormBox["\"\[Tau]=0\"", TraditionalForm],
PlotRange -> {{0, 100}, {0, 2}}, PlotRangeClipping -> True,
PlotRangePadding -> {{Automatic, Automatic}, {Automatic, Automatic}},
Ticks -> {Automatic, Automatic}}],FormBox[
FormBox[
TemplateBox[{"\"street 1\"", "\"street 2\""}, "LineLegend",
DisplayFunction -> (FormBox[
StyleBox[
StyleBox[
PaneBox[
TagBox[
GridBox[{{
TagBox[
GridBox[{{
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
RGBColor[0.9, 0.36, 0.054],
CapForm["Butt"],
AbsoluteThickness[1.6]], {
LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
RGBColor[0.9, 0.36, 0.054],
CapForm["Butt"],
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
RGBColor[0.365248, 0.427802, 0.758297],
CapForm["Butt"],
AbsoluteThickness[1.6]], {
LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
RGBColor[0.365248, 0.427802, 0.758297],
CapForm["Butt"],
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}},
GridBoxAlignment -> {
"Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
AutoDelete -> False,
GridBoxDividers -> {
"Columns" -> {{False}}, "Rows" -> {{False}}},
GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
GridBoxSpacings -> {
"Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
AutoDelete -> False,
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
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ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
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FontFamily -> "Times", FontFamily -> "Arial"}, Background ->
Automatic, StripOnInput -> False], TraditionalForm]& ),
InterpretationFunction :> (RowBox[{"LineLegend", "[",
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RowBox[{"{",
RowBox[{
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[0.9, 0.36, 0.054],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
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FrameStyle ->
RGBColor[0.6000000000000001, 0.24, 0.036000000000000004`],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
RowBox[{"0.9`", ",", "0.36`", ",", "0.054`"}], "]"}],
NumberMarks -> False]], Appearance -> None,
BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0.9, 0.36, 0.054];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[0.9, 0.36, 0.054], Editable -> False, Selectable ->
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RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
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RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[0.365248, 0.427802, 0.758297],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle ->
RGBColor[
0.2434986666666667, 0.28520133333333336`,
0.5055313333333333], FrameTicks -> None, PlotRangePadding ->
None, ImageSize ->
Dynamic[{
Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
RowBox[{"0.365248`", ",", "0.427802`", ",", "0.758297`"}],
"]"}], NumberMarks -> False]], Appearance -> None,
BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0.365248, 0.427802, 0.758297];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[0.365248, 0.427802, 0.758297], Editable -> False,
Selectable -> False], ",",
RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
"}"}], ",",
RowBox[{"{",
RowBox[{#, ",", #2}], "}"}], ",",
RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"{",
RowBox[{"FontFamily", "\[Rule]", "\"Times\""}], "}"}]}], ",",
RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
Editable -> True], TraditionalForm], TraditionalForm]},
"Legended",
DisplayFunction->(GridBox[{{
TagBox[
ItemBox[
PaneBox[