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Braess’ paradox asserts that adding new roads to a congested networks can reduce overall performance. The question whether this paradox can be detected to a network is hard to answer. In this chapter, we consider a small network consisting of four nodes and four edges and one more edge is added. We further adopt the assumption that the time function of every edge of the network is linear. In this setting, the difference between the two equilibrium time durations is a multiparametric rational function, and it can be studied via algebraic or statistical tools. Our main result indicates that the Braess’ paradox occurs with probability \(50\%\) .

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A Mathematical Study of the Braess’s Paradox Within a Network Comprising Four Nodes, Five Edges, and Linear Time Functions

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  • 发表日期：

    2025年

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  • Costas Poulios,
  • Evangelos Melas,
  • Nick C. Poulios,
  • Maria Livada,
  • John Leventides

摘要

Braess’ paradox asserts that adding new roads to a congested networks can reduce overall performance. The question whether this paradox can be detected to a network is hard to answer. In this chapter, we consider a small network consisting of four nodes and four edges and one more edge is added. We further adopt the assumption that the time function of every edge of the network is linear. In this setting, the difference between the two equilibrium time durations is a multiparametric rational function, and it can be studied via algebraic or statistical tools. Our main result indicates that the Braess’ paradox occurs with probability \(50\%\) .