Applications of Systems of Linear Equations in the Analysis of Traffic Flow Equilibrium in Transportation Networks
Main Article Content
Abstract
This paper constructs several transportation network models in the form of directed graphs and presents the application of systems of linear equations to the analysis of traffic flow equilibrium in these transportation networks.
Keywords
Systems of linear equations, directed graphs, traffic flow, transportation networks.
Article Details
References
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[2] N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge University Press, 1993.
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[2] N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge University Press, 1993.
[3] B. Bollobás, Modern Graph Theory, Springer, 1998.
[4] R. Diestel, Graph Theory, 5th ed., Springer, 2017.
[5] M. E. J. Newman, Networks: An Introduction, Oxford University Press, 2010.
[6] J. de D. Ortúzar, L. G. Willumsen, Modelling Transport, 4th ed., Wiley, 2011.
[7] Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice Hall, 1985.
[8] G. Strang, Linear Algebra and Its Applications, 4th ed., Brooks/Cole, 2006.
[9] R. J. Vanderbei, Linear Programming: Foundations and Extensions, 5th ed., Springer, 2020.