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

Costas Poulios (), Evangelos Melas (), Nick C. Poulios (), Maria Livada () and John Leventides ()
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Costas Poulios: National and Kapodistrian University of Athens
Evangelos Melas: National and Kapodistrian University of Athens
Nick C. Poulios: University of Leoben
Maria Livada: City University of London
John Leventides: National and Kapodistrian University of Athens

A chapter in Optimization, Discrete Mathematics and Applications to Data Sciences, 2025, pp 223-232 from Springer

Abstract: Abstract 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 % $$50\%$$ .

Date: 2025
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DOI: 10.1007/978-3-031-78369-2_12

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