TY - GEN
T1 - An optimal control framework for multi-region macroscopic fundamental diagram systems with time delay, considering route choice and departure time choice
AU - Zhong, Renxin
AU - Huang, Yunping
AU - Xiong, Jianhui
AU - Zheng, Nan
AU - Lam, William
AU - Sumalee, Agachai
PY - 2018/12/7
Y1 - 2018/12/7
N2 - Macroscopic fundamental diagram (MFD) has been used for aggregate modeling of urban traffic network dynamics under stationary traffic assumption for dynamic taxi dispatching, vehicle relocation and dynamic pricing schemes to tackle the dimensionality problem of microscopic approaches. A city is assumed to be partitioned into several regions with each admits a well-defined MFD. Integrating state-dependent regional travel time function as an endogenous time-varying delay, the MFD model with time delay, is adopted to describe the traffic dynamics within a region. On the other hand, it is necessary to enable simultaneous route choice and departure time choice under the MFD framework for various applications such as vehicle dispatching and relocation. This paper presents an optimal control framework to model dynamic user equilibria (DUE) with simultaneous route choice behavior and departure time choice for general urban networks. Necessary conditions for the DUE are analytically derived through the lens of Pontryagin minimum principle. In contrast to existing analytical methods, the proposed method is applicable for general MFD systems without approximation schemes of the equilibrium solution. Numerical examples by time discretization are conducted to illustrate the characteristics of DUE and corresponding dynamic external costs.
AB - Macroscopic fundamental diagram (MFD) has been used for aggregate modeling of urban traffic network dynamics under stationary traffic assumption for dynamic taxi dispatching, vehicle relocation and dynamic pricing schemes to tackle the dimensionality problem of microscopic approaches. A city is assumed to be partitioned into several regions with each admits a well-defined MFD. Integrating state-dependent regional travel time function as an endogenous time-varying delay, the MFD model with time delay, is adopted to describe the traffic dynamics within a region. On the other hand, it is necessary to enable simultaneous route choice and departure time choice under the MFD framework for various applications such as vehicle dispatching and relocation. This paper presents an optimal control framework to model dynamic user equilibria (DUE) with simultaneous route choice behavior and departure time choice for general urban networks. Necessary conditions for the DUE are analytically derived through the lens of Pontryagin minimum principle. In contrast to existing analytical methods, the proposed method is applicable for general MFD systems without approximation schemes of the equilibrium solution. Numerical examples by time discretization are conducted to illustrate the characteristics of DUE and corresponding dynamic external costs.
UR - http://www.scopus.com/inward/record.url?scp=85060435921&partnerID=8YFLogxK
U2 - 10.1109/ITSC.2018.8569905
DO - 10.1109/ITSC.2018.8569905
M3 - Conference article published in proceeding or book
AN - SCOPUS:85060435921
T3 - IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC
SP - 1962
EP - 1967
BT - 2018 IEEE Intelligent Transportation Systems Conference, ITSC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 21st IEEE International Conference on Intelligent Transportation Systems, ITSC 2018
Y2 - 4 November 2018 through 7 November 2018
ER -