Braess like Paradox on Ladder Network

TL;DR

This paper investigates the occurrence of Braess' paradox on Ladder networks through theoretical and numerical analysis, extending previous studies to complex network structures and providing insights for transportation network design.

Contribution

It introduces the first analysis of Braess' paradox on Ladder networks, extending models and providing phase diagrams and conditions for paradox occurrence.

Findings

Braess' paradox can occur on Ladder networks under certain conditions.

The phase diagram identifies parameter regions where the paradox is present or absent.

Simulation results suggest design guidelines for efficient transportation networks.

Abstract

Braess \cite{1} has been studied about a traffic flow on a diamond type network and found that introducing new edges to the networks always does not achieve the efficiency. Some researchers studied the Braess' paradox in similar type networks by introducing various types of cost functions. But whether such paradox occurs or not is not scarcely studied in complex networks except for Dorogovtsev-Mendes network\cite{2}. In this article, we study the paradox on Ladder type networks, as the first step to the research about Braess' paradox on Watts and Strogatz type small world network\cite{Watt1}\cite{Watt2}. %We theoretically and numerically studied Braess' paradox on Ladder networks. For the purpose, we construct $4 \times 3$ models as extensions of the original Braess' models. We analyze theoretically and numerically studied the models on Ladder networks. Last we give a phase diagram for (a) model, where the cost functions of bypasses are constant =0 or flow, base on two parameters $r$ and $p$ by numerical simulations. Simulation experiments also show some conditions that paradox can not occur. These facts give some sugestions for designing effective transportation networks.