Solving the dynamic network user equilibrium problem with state-dependent time shifts

Friesz, Terry L.; Mookherjee, Reetabrata

doi:10.1016/j.trb.2005.03.002

Cited by 89 publications

(70 citation statements)

References 6 publications

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“…As pointed out by Han (2013), there are two essential components within the notion of DUE: (i) the mathematical expression of Nashlike equilibrium conditions, and (ii) a network performance model, which is, in effect, an embedded dynamic network loading (DNL) problem. There are multiple means of expressing the Nash-like notion of a dynamic equilibrium mathematically, including a variational inequality (Friesz et al, 1993;Wisten, 1994, 1995), an evolutionary dynamic (Mounce, 2006;Smith and Wisten, 1995), a nonlinear complementarity problem (Wie et al, 2002;Han et al, 2011), a differential variational inequality (Friesz et al, 2011(Friesz et al, , 2013Friesz and Mookherjee, 2006), and a differential complementarity system (Pang et al, 2011). Clearly, another key component of the DUE is the path delay operator, typically obtained from dynamic network loading (DNL), which is a sub-problem of a complete DUE model.…”

Section: The Dynamic User Equilibrium As the Lower-level Problemmentioning

confidence: 99%

A bi-level model of dynamic traffic signal control with continuum approximation

Han

Sun

Liu

et al. 2015

Transportation Research Part C: Emerging Technologies

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This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955;Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in , which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.

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Section: The Dynamic User Equilibrium As the Lower-level Problemmentioning

confidence: 99%

A bi-level model of dynamic traffic signal control with continuum approximation

Han

Sun

Liu

et al. 2015

Transportation Research Part C: Emerging Technologies

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“…This study adopts the bottleneck model and discretises time. Friesz and Mookherjee (2006) also provided an algorithm that always converges for DUE assignments with route-and-departure-time choices and the whole-link model if the cost functions are strongly monotonic. Lo and Szeto (2002) proposed a solution algorithm for a cell-based DUE assignment model that converges to an equilibrium point if a route travel time functions with respect to route flow has a 'co-coercivity' property.…”

Section: Variational Inequality Approach and Monotonicity Of Route Comentioning

confidence: 99%

Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology

Iryo

2013

Transportmetrica B: Transport Dynamics

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This paper reviews studies that deal with properties of dynamic user equilibrium (DUE) solutions to understand the extent to which they have been resolved in past studies and indicate theoretical problems that remain to be addressed in future research. DUE assignment is an equilibrium-based methodology for dynamic traffic assignment. In conventional equilibriumbased static traffic assignment, the four desirable properties of solutions -existence, uniqueness, stability of solutions, and the existence of a robust solution methodology -are all guaranteed. These properties must be ensured for planners to obtain a reliable solution for equilibriumbased assignment. Meanwhile, for DUE assignment, although some of these properties have been proved, many issues regarding these properties remain unresolved. This paper reviews studies that deal with these properties to understand how far they have been investigated and discusses what is required from future research to improve the robustness of DUE assignment.

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“…These include variational inequality (Friesz et al 1993(Friesz et al , 2013Han et al 2013c;Szeto and Lo 2004); differential variational inequality (Freisz et al 2001(Freisz et al , 2010Friesz and Mookherjee 2006); nonlinear complementarity problem (Ukkusuri et al 2012;Wie et al 2002); and differential complementarity problem (Pang et al 2011). In addition, several extensions of the DUE problem pertaining to bounded user rationality (Han et al 2015b), demand elasticity (Friesz and Meimand 2014;Han et al 2015a) and en-route update (Kachroo andÖzbay 2005), have been formulated using (differential) variational inequalities (which are closely related to open-loop optimal control problems) and feedback (closed-loop) control formulations.…”

Section: Introductionmentioning

confidence: 99%

Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model

Han

Friesz

2017

Netw Spat Econ

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This paper is concerned with a dynamic traffic network performance model, known as dynamic network loading (DNL), that is frequently employed in the modeling and computation of analytical dynamic user equilibrium (DUE). As a key component of continuous-time DUE models, DNL aims at describing and predicting the spatial-temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers, by introducing appropriate dynamics to flow propagation, flow conservation, and travel delays. The DNL procedure gives rise to the path delay operator, which associates a vector of path flows (path departure rates) with the corresponding path travel costs. In this paper, we establish strong continuity of the path delay operator for networks whose , our continuity proof is constructed without assuming a priori uniform boundedness of the path flows. Such a more general continuity result has a few important implications to the existence of simultaneous route-and-departure-time DUE without a priori boundedness of path flows, and to any numerical algorithm that allows convergence to be rigorously analyzed.

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Solving the dynamic network user equilibrium problem with state-dependent time shifts

Cited by 89 publications

References 6 publications

A bi-level model of dynamic traffic signal control with continuum approximation

A bi-level model of dynamic traffic signal control with continuum approximation

Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology

Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model

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