Traffic assignment: on the interplay between optimization and equilibrium problems.

*(English)*Zbl 1453.90012Summary: Motorists often have to choose routes helping them to realize faster journey times. Route choices between an origin and a destination might involve direct main roads, shorter routes through narrow side streets, or longer but (potentially) faster journeys using motorways or ring-roads. In the absence of effective traffic control measures, an approximate equilibrium travel time may result between the routes available, which is generally expected to be far from optimal. In this paper, we investigate discrete and continuous optimization and equilibrium-type problems, for a simplified traffic assignment problem on a simple network with parallel links and fixed demand. We explore the interplay between solutions of certain optimization and equilibrium problems which can be solved by dynamic programming. The results are supported by numerical simulations, in which the price of anarchy is calculated to highlight the demand levels where there is a change in road choice and usage.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

90C39 | Dynamic programming |

90C29 | Multi-objective and goal programming |

##### Keywords:

traffic assignment problem; equilibrium state; discrete dynamic programming; multi-objective optimization
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\textit{O. Bagdasar} et al., Optimization 69, No. 7--8, 1773--1790 (2020; Zbl 1453.90012)

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##### References:

[1] | Dafermos, SC; Sparrow, FT., The traffic assignment problem for a general network, J Res NSB B Math Sci, 73B, 2, 91-118 (1969) · Zbl 0197.46003 |

[2] | Patriksson, M., The traffic assignment problem: models and methods (2015), Mineola (NY: Courier Dover Publications, Mineola (NY |

[3] | Lowndes, V, Berry, S, Parkes, C.2017. Further use of heuristic methods. In: Berry S, Lowndes V, Trovati M, editors. Guide to Computational Modelling for Decision Processes. Springer, Cham. |

[4] | Youn, H.; Gastner, MT; Jeong, H., Price of anarchy in transportation networks: efficiency and optimality control, Phys Rev Lett, 101 (2008) |

[5] | Bagdasar, O.; Berry, S.; O’Neill, S.; Popovici, N.; Raja, R., Traffic assignment: methods and simulations for an alternative formulation of the fixed demand problem, Math Comput Simulation, 155, 360-373 (2019) |

[6] | U.S. Bureau of Public Roads, Traffic assignment manual for application with a large, high speed computer, U.S. Dept. of Commerce, Bureau of Public Roads, Office of Planning, Urban Planning Division, Washington; 1964. Available from: http://catalog.hathitrust.org/Record/000968330. |

[7] | Koutsoupias, E.; Papadimitriou, C., Worst-case equilibria, Comput Sci Rev, 3, 65-69 (2009) · Zbl 1303.91012 |

[8] | Bellman, R., Dynamic programming (2003), Mineola (NY: Dover Publications, Mineola (NY · Zbl 1029.90076 |

[9] | Rockafellar, RT., Convex analysis (1970), Princeton (NJ): Princeton University Press, Princeton (NJ) |

[10] | Braess, D., Über ein Paradoxon aus der Verkehrsplanung, Unternehmensforschung, 12, 258-268 (1968) · Zbl 0167.48305 |

[11] | Bagdasar, O.; Popovici, N., Local maximizers of generalized convex vector-valued functions, J. Nonlinear Convex Anal, 18, 2229-2250 (2017) · Zbl 1387.90233 |

[12] | Göpfert, A.; Riahi, H.; Tammer, C.; Zălinescu, C., Variational methods in partially ordered spaces (2003), New York (NY): Springer, New York (NY) · Zbl 1140.90007 |

[13] | Jahn, J., Vector optimization: theory, applications, and extensions (2011), Berlin: Springer, Berlin · Zbl 1401.90206 |

[14] | Popovici, N., Pareto reducible multicriteria optimization problems, Optimization, 54, 253-263 (2005) · Zbl 1087.90070 |

[15] | Bar-Gera, H.; Hellman, F.; Patriksson, M., Computational precision of traffic equilibria sensitivities in automatic network design and road pricing, Transp Res B Meth, 57, 485-500 (2013) |

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