Traffic network analysis via multidimensional split variational inequality problem with multiple output sets

Timilehin O. Alakoya; Bidisha Ghosh; Salissou Moutari; Vikram Pakrashi; Ranganatha B. Ramachandra; Timilehin O. Alakoya; Bidisha Ghosh; Salissou Moutari; Vikram Pakrashi; Ranganatha B. Ramachandra

doi:10.3934/nhm.2024008

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 169-195. doi: 10.3934/nhm.2024008

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Research article

Traffic network analysis via multidimensional split variational inequality problem with multiple output sets

1.
Mathematical Sciences Research Centre, School of Mathematics and Physics, Queen's University Belfast, University Road, Belfast BT71NN, United Kingdom
2.
QUANT Group, Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin, Ireland
3.
UCD Centre for Mechanics, Dynamical Systems and Risk Laboratory, School of Mechanical and Materials Engineering, University College Dublin, Dublin, Ireland

Received: 13 November 2023 Revised: 19 January 2024 Accepted: 24 January 2024 Published: 06 February 2024

In this study, we introduce and investigate a new class of split inverse problems, comprising a multidimensional parameter of evolution, which we call the multidimensional split variational inequality problem with multiple output sets. To demonstrate its applicability, we formulate the equilibrium flow of multidimensional traffic network models for an arbitrary number of locations. We define a multidimensional split Wardrop condition with multiple output sets and establish its equivalence with the formulated equilibrium flow of multidimensional traffic network models. We then establish the existence and uniqueness of equilibria for our proposed model. In addition, we propose a method for solving the introduced problem. We then validate our results using some numerical experiments.
Citation: Timilehin O. Alakoya, Bidisha Ghosh, Salissou Moutari, Vikram Pakrashi, Ranganatha B. Ramachandra. Traffic network analysis via multidimensional split variational inequality problem with multiple output sets[J]. Networks and Heterogeneous Media, 2024, 19(1): 169-195. doi: 10.3934/nhm.2024008

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Abstract

In this study, we introduce and investigate a new class of split inverse problems, comprising a multidimensional parameter of evolution, which we call the multidimensional split variational inequality problem with multiple output sets. To demonstrate its applicability, we formulate the equilibrium flow of multidimensional traffic network models for an arbitrary number of locations. We define a multidimensional split Wardrop condition with multiple output sets and establish its equivalence with the formulated equilibrium flow of multidimensional traffic network models. We then establish the existence and uniqueness of equilibria for our proposed model. In addition, we propose a method for solving the introduced problem. We then validate our results using some numerical experiments.

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