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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