Geodesic
Non-linear optimization for continuous travel demand estimation
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 40-46

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Models and methods of traffic distribution are being developed by researchers all over the world. The development of this scientific field contributes to both theory and practice. In this article, the non-linear optimization of traffic flow re-assignment is examined in order to solve continuously the travel demand estimation problem. An approach has been developed in the form of computational methodology to cope with the network optimization problem. A uniqueness theorem is proved for a certain type of road network. Explicit relations between travel demand and traffic flow are obtained for a single-commodity network of non-intersecting routes with special polynomial travel time functions. The obtained findings contribute to the theory and provide a fresh perspective on the problem for transportation engineers.
Keywords: travel demand estimation, traffic assignment problem, non-linear optimization, bi-level optimization. 
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     author = {A. P. Raevskaya and A. Yu. Krylatov},
     title = {Non-linear optimization for continuous travel demand estimation},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/}
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A. P. Raevskaya; A. Yu. Krylatov. Non-linear optimization for continuous travel demand estimation. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 40-46. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/