Approximate network loading and dual-time-scale dynamic user equilibrium

Friesz, Terry L.; Kim, Taeil; Kwon, Changhyun; Rigdon, Matthew A.

doi:10.1016/j.trb.2010.05.003

Cited by 97 publications

(104 citation statements)

References 40 publications

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“…Existing studies dealing with a 'dual dynamic model' (i.e. a model considering both day-to-day and within-day dynamics) include Cascetta and Cantarella (1993), Mounce (2006), Iryo (2008), Carey (2011), andFriesz et al (2011). Another alternative to equilibrium is 'tolerance-based DUO' (Szeto and Lo 2006), in which a small gap is allowed between the travel cost of a used route and the minimum travel cost.…”

Section: Summary and Discussion On Future Research On Due Solution Pmentioning

confidence: 99%

“…The co-coercivity property is an intermediate concept between monotonicity and strong monotonicity (see Zhu and Marcotte (1996) for details). Further, Friesz et al(2011) showed that component-wise strongly pseudomonotone delay operators guarantee the convergence of the algorithm they proposed. However, note that no clear relationship has been identified between these mathematical properties and characteristics of transport networks such as network structure or demand pattern, excluding the single-bottleneck-per-route network case introduced above.…”

Section: Variational Inequality Approach and Monotonicity Of Route Comentioning

confidence: 99%

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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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Section: Summary and Discussion On Future Research On Due Solution Pmentioning

confidence: 99%

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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“…(1) The 19-arc network with 4 OD pairs and 24 paths, which is studied in Nguyen (1984) and Nie and Zhang (2010) and hereafter referred to as the Nguyen network; and (2) The Sioux Falls network (Friesz et al, 2011;Suwansirikul et al, 1987) with 60, 119, 201, and 501 paths, respectively.…”

Section: Test Scenariosmentioning

confidence: 99%

“…For example, the existence of dynamic user equilibrium (DUE), which is the most widely studied form of DTA problems, depends on the continuity of the delay operators (Han et al, 2013c;Smith and Wisten, 1995;Zhu and Marcotte, 2000), while the uniqueness of DUE is guaranteed by the monotonicity of the delay operator (Mounce and Smith, 2007). Moreover, all computational procedures for DUE problems rely on certain versions of continuity and monotonicity to converge (Friesz et al, 2011;Han et al, 2015;Long et al, 2013;Mounce, 2006;Szeto and Lo, 2004). Furthermore, differentiability is typically required for the delay operator for problems such as sensitivity analysis (Chung et al, 2014;Yang and Bell, 2007) and mathematical programs with equilibrium constraints .…”

Section: Introductionmentioning

confidence: 99%

Statistical metamodeling of dynamic network loading

Song

Han

Wang

2018

Transportation Research Part B: Methodological

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Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses the dynamics of flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times. It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult problem, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, while possessing closed-form Jacobians. The implications of these desirable properties for DTA research and model applications are discussed in depth.

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“…For an introduction to differential games and for recent applications to traffic flow on networks we refer to [6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Nash equilibria for a model of traffic flow with several groups of drivers

Bressan

Han

2012

ESAIM: COCV

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Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κ i drivers, sharing the same departure and arrival costs ϕ i (t), ψ i (t). For any given population sizes κ 1 , . . . , κ n , we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible nonuniqueness, and a characterization of this Nash equilibrium solution, are also discussed.

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Approximate network loading and dual-time-scale dynamic user equilibrium

Cited by 97 publications

References 40 publications

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

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

Statistical metamodeling of dynamic network loading

Nash equilibria for a model of traffic flow with several groups of drivers

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