Mixed traffic optimization considering road reservation travel based on the bi-level programming mode

Abstract: Reservation travel has gradually become an important strategy to alleviate urban traffic congestion by finely matching traffic supply and demand. In order to quantify the effectiveness of the reservation travel strategy, ordinary vehicles and reservation vehicles are considered, The reservation travel problem is formulated as a Bi-level Programming (BP), where the upper-level objective is to maximize traffic demand, while the lower-level model considers the System Optimal-Stochastic User Equilibrium (SO-SUE) mixed traffic equilibrium. The equivalence of the mixed equilibrium problem and the existence of the solution are proved. On the basis of the WOA algorithm, combined with the lower-level Partan Frank-Wolfe algorithm, the traffic assignment solution process is connected to the upper-level as a function. A Whale Optimization Algorithm (WOA) nested Partan Frank-Wolfe algorithm is proposed to solve the model. Finally, the Sioux-Falls network numerical experiment proves that the reservation travel has a gratifying benefit in alleviating traffic congestion. By comparing the Vehicle-to-Capacity (V/C) ratio and cost before and after the implementation of reservation, it shows the effectiveness of reservation travel for urban traffic congestion management, and discusses the impact of the number of reserved roads and reservation trends on road network capacity, service level and travel cost under the implementation of reservation travel.

How to cite this paper

 Zheng, S., Wang, J & Lu, X. (2025). Mixed traffic optimization considering road reservation travel based on the bi-level programming mode.International Journal of Industrial Engineering Computations , 16(3), 521-534.

Refrences

Akahane, H., Kuwahara, M., & Sato, T. (2000). A basic study on trip reservation systems for recreational trips on motorways. Doboku Gakkai Ronbunshu, 2000(660), 79-87. Ben-Ayed, O. (1993). Bilevel linear programming. Computers & Operations Research, 20(5), 485-501. Chen, Y., Song, X., Cheng, Q., An, Q., & Zhang, Y. (2021). A cordon-based reservation system for urban traffic management. Physica A: Statistical Mechanics and its Applications, 582, 126276. Cheng, Q., Chen, Y., & Liu, Z. (2022). A bi-level programming model for the optimal lane reservation problem. Expert Systems with Applications, 189, 116147. Dobre, C. (2012). Intelligent lane reservation system for highways. International Journal of Vehicular Technology, 2012(1), 604965. Evans, S. P. (1973). A relationship between the gravity model for trip distribution and the transportation problem in linear programming. Transportation Research, 7(1), 39-61. Fisk, C. (1980). Some developments in equilibrium traffic assignment. Transportation Research Part B: Methodological, 14(3), 243-255. Kinderlehrer, D., & Stampacchia, G. (1980). An introduction to variational inequalities and their applications. SIAM. Li, N., Yang, H., & Ke, J. (2023). Booking cum rationing strategy for equitable travel demand management in road networks. Transportation Research Part B: Methodological, 167, 261-274. Liu, K., Chan, E., Lee, V., Kapitanova, K., & Son, S. H. (2013). Design and evaluation of token-based reservation for a roadway system. Transportation Research Part C: Emerging Technologies, 26, 184-202. Menelaou, C., Kolios, P., Timotheou, S., Panayiotou, C. G., & Polycarpou, M. P. (2017). Controlling road congestion via a low-complexity route reservation approach. Transportation Research Part C: Emerging Technologies, 81, 118-136. Menelaou, C., Timotheou, S., Kolios, P., & Panayiotou, C. G. (2017). Improved road usage through congestion-free route reservations. Transportation Research Record: Journal of the Transportation Research Board, 2621, 71-80. Menelaou, C., Timotheou, S., Kolios, P., Panayiotou, C. G., & Polycarpou, M. M. (2018). Minimizing traffic congestion through continuous-time route reservations with travel time predictions. IEEE Transactions on Intelligent Vehicles, 4(1), 141-153. Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51-67. Teodorović, D., Edara, P., & Via, C. E. (2005). Highway space inventory control system. In Transportation and Traffic Theory: Flow, Dynamics and Human Interaction: Proceedings of the 16th International Symposium on Transportation and Traffic Theory, University of Maryland, College Park. Vasirani, M., & Ossowski, S. (2012). A market-inspired approach for intersection management in urban road traffic networks. Journal of Artificial Intelligence Research, 43, 621-659. Wong, C.-T. (1997). Basic concepts for a system for advance booking for highway use. Transport Policy, 4(2), 109-114. Wu, P., Chu, F., Che, A., & Zhao, Y. (2018). Dual-objective optimization for lane reservation with residual capacity and budget constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(6), 2187-2197. Yang, H., Zhang, X., & Meng, Q. (2007). Stackelberg games and multiple equilibrium behaviors on networks. Transportation Research Part B: Methodological, 41(8), 841-861. Ye, J., Cao, R., He, B., Kuai, X., & Guo, R. (2024). Disaggregated spatiotemporal traffic assignment for road reservation service and supply-demand statistical analysis. Physica A: Statistical Mechanics and its Applications, 645, 129854. Zhang, K., & Nie, Y. M. (2018). Mitigating the impact of selfish routing: An optimal-ratio control scheme (ORCS) inspired by autonomous driving. Transportation Research Part C: Emerging Technologies, 87, 75-90. Zhao, Y., Triantis, K., Teodorović, D., & Edara, P. (2010). A travel demand management strategy: The downtown space reservation system. European Journal of Operational Research, 205(3), 584-594.