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Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System

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  • Lin Xiao
  • Hong Lo

Abstract

We formulate a joint dynamical traffic system that encompasses both route choice and traffic control in which the signal controller interacts with and adapts to the route choices of travelers, and vice versa. Travelers’ route choice dynamics are captured by a recurrence function, which governs the system evolution from day to day. Traffic control also adjusts its plan from day to day in response to the route choices of travelers. We show that this joint dynamical system has a set of fixed points in which both the user equilibrium is achieved and the traffic signal converges to a fixed-time plan. We address equilibrium stability and convergence of this joint dynamical system through analyzing the Jacobian matrix associated with each fixed point. We demonstrate the attraction domains of this joint problem and illustrate their importance and relevance for designing adaptive traffic control through some numerical examples. Copyright Springer Science+Business Media New York 2015

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  • Lin Xiao & Hong Lo, 2015. "Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System," Networks and Spatial Economics, Springer, vol. 15(3), pages 697-717, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:697-717
    DOI: 10.1007/s11067-014-9248-4
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    Cited by:

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    4. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    5. Liu, Wei & Geroliminis, Nikolas, 2017. "Doubly dynamics for multi-modal networks with park-and-ride and adaptive pricing," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 162-179.
    6. Meneguzzer, Claudio, 2022. "Day-to-day dynamics in a simple traffic network with mixed direct and contrarian route choice behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    7. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    8. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    9. Xiaozheng He & Jian Wang & Srinivas Peeta & Henry X. Liu, 2022. "Day-to-Day Signal Retiming Scheme for Single-Destination Traffic Networks Based on a Flow Splitting Approach," Networks and Spatial Economics, Springer, vol. 22(4), pages 855-882, December.
    10. Iryo, Takamasa, 2016. "Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 88-103.
    11. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    12. Wang, Guanfeng & Jia, Hongfei & Feng, Tao & Tian, Jingjing & Wu, Ruiyi & Gao, Heyao & Liu, Chao, 2024. "Modelling the dual dynamic traffic flow evolution with information perception differences between human-driven vehicles and connected autonomous vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).

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