<p>Urban traffic systems are characterized by dynamic interactions between congestion and free-flow states, influenced by human activity and road topology. This study employs percolation theory to analyze traffic dynamics in Seoul, focusing on the transition point <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_\textrm{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mtext>c</mtext> </msub> </math></EquationSource> </InlineEquation> and Fisher exponent <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>. The transition point <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_\textrm{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mtext>c</mtext> </msub> </math></EquationSource> </InlineEquation> quantifies the robustness of the free-flow clusters, while the exponent <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> captures the spatial fragmentation of the traffic networks. Our analysis reveals temporal variations in these metrics, with lower <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_\textrm{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mtext>c</mtext> </msub> </math></EquationSource> </InlineEquation> and lower <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq6.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> values generally during rush hours representing low-dimensional behavior, within the broader context of the positive correlation between <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_\textrm{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mtext>c</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40042_2025_1328_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>. Weight–weight correlations are found to significantly impact cluster formation, driving the early onset of dominant traffic states. Comparisons with uncorrelated models highlight the role of real-world correlations. This approach provides a comprehensive framework for evaluating traffic resilience and informs strategies to optimize urban transportation systems.</p>

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Quantifying traffic patterns with percolation theory: a case study of Seoul roads

  • Yongsung Kwon,
  • Mi Jin Lee,
  • Seung-Woo Son

摘要

Urban traffic systems are characterized by dynamic interactions between congestion and free-flow states, influenced by human activity and road topology. This study employs percolation theory to analyze traffic dynamics in Seoul, focusing on the transition point \(q_\textrm{c}\) q c and Fisher exponent \(\tau\) τ . The transition point \(q_\textrm{c}\) q c quantifies the robustness of the free-flow clusters, while the exponent \(\tau\) τ captures the spatial fragmentation of the traffic networks. Our analysis reveals temporal variations in these metrics, with lower \(q_\textrm{c}\) q c and lower \(\tau\) τ values generally during rush hours representing low-dimensional behavior, within the broader context of the positive correlation between \(q_\textrm{c}\) q c and \(\tau\) τ . Weight–weight correlations are found to significantly impact cluster formation, driving the early onset of dominant traffic states. Comparisons with uncorrelated models highlight the role of real-world correlations. This approach provides a comprehensive framework for evaluating traffic resilience and informs strategies to optimize urban transportation systems.