Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives th...

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Vydáno v:Transportation research. Part B: methodological Ročník 45; číslo 7; s. 1035 - 1061
Hlavní autoři: Zhong, R.X., Sumalee, A., Friesz, T.L., Lam, William H.K.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 01.08.2011
Elsevier
Edice:Transportation Research Part B: Methodological
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ISSN:0191-2615, 1879-2367
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Abstract ► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives the analytical closed-form of the link control for ensuring that dynamic traffic volumes under DUE condition satisfy the side-constraint on link volumes. ► The paper proposed a computational algorithm for solving DUE-SC and deriving the link control parameters. This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
AbstractList This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives the analytical closed-form of the link control for ensuring that dynamic traffic volumes under DUE condition satisfy the side-constraint on link volumes. ► The paper proposed a computational algorithm for solving DUE-SC and deriving the link control parameters. This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.
Author Lam, William H.K.
Zhong, R.X.
Sumalee, A.
Friesz, T.L.
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Issue 7
Keywords Traffic volume control
Dynamic user equilibrium (DUE)
Traffic assignment with side constraint
Lagrange multiplier
Traffic management and control
Pontryagin minimum principle
Stress analysis
User
Transportation
Theoretical study
Algorithm
Equilibrium
Traffic assignment
Formulation
Traffic management
Example
Traffic control
Numerical simulation
Language English
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SSID ssj0003401
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Snippet ► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict...
This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not...
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elsevier
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StartPage 1035
SubjectTerms Applied sciences
Dynamic user equilibrium (DUE)
Dynamic user equilibrium (DUE) Traffic volume control Traffic management and control Traffic assignment with side constraint Pontryagin minimum principle Lagrange multiplier
Exact sciences and technology
Ground, air and sea transportation, marine construction
Lagrange multiplier
Pontryagin minimum principle
Traffic assignment with side constraint
Traffic management and control
Traffic volume control
Transportation planning, management and economics
Title Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm
URI https://dx.doi.org/10.1016/j.trb.2011.05.004
http://econpapers.repec.org/article/eeetransb/v_3a45_3ay_3a2011_3ai_3a7_3ap_3a1035-1061.htm
https://www.proquest.com/docview/896207619
Volume 45
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