On the equivalence between stationary link flow patterns and traffic network equilibria

Zhang, Ding; Nagurney, Anna; Wu, Jiahao

doi:10.1016/s0191-2615(00)00020-5

Cited by 61 publications

(28 citation statements)

References 20 publications

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“…This property was noticed by Zhang et al (2001) and Yang and Zhang (2009), and was named as the "rational behavior adjustment process" (RBAP) by the latter. Guo et al (2013Guo et al ( , 2015 pointed out that the same feature can be found in the link-based models such as He et al (2010), Han and Du (2012) and Smith and Mounce (2011).…”

Section: Rational Behavior Adjustment Processmentioning

confidence: 99%

Exploration of day-to-day route choice models by a virtual experiment

Xiao

Yang

2018

Transportation Research Part C: Emerging Technologies

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This paper examines existing day-to-day models based on a virtual day-to-day route choice experiment using the latest mobile internet techniques. With the realized day-to-day path flows and path travel times in the experiment, we calibrate several welldesigned path-based day-to-day models who take the Wardrop's user equilibrium as (part of) their stationary states. The nonlinear effects of path flows and path time differences on the path swapping are then investigated. Participants' path preferences, time-varying sensitivity and learning behavior in the day-to-day process are also examined. The prediction power of various models with various settings (nonlinear effects, time-varying sensitivity, and learning) is compared. Assumption of rational behavior adjustment process in Yang and Zhang (2009) is further verified. Finally, evolutions of different Lyapunov functions used in the literature are plotted and no obvious diversity is observed.

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Section: Rational Behavior Adjustment Processmentioning

confidence: 99%

Exploration of day-to-day route choice models by a virtual experiment

Xiao

Yang

2018

Transportation Research Part C: Emerging Technologies

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“…We refer to Assumption 2 in Zhang et al (2001) to establish a special group of BRUE-RBAP models in Eq. (27).…”

Section: A Special Group Of Brue-rbap Modelsmentioning

confidence: 99%

“…(27). The readers may note that the original assumption in Zhang et al (2001) violated the flow conservation, which assumed that under a fixed-demand day-to-day dynamics, traffic flows on paths with costs higher than the minimum cost would decrease, while flows on the minimum-cost paths would keep unchanged. It is easy to verify that BRUE-PSAP and BRUE-NTP do not necessarily satisfy condition (27), although they are BRUE-RBAP.…”

Section: A Special Group Of Brue-rbap Modelsmentioning

confidence: 99%

“…RBAP is a type of fixed-demand day-to-day dynamics summarized by Zhang et al (2001) and Yang and Zhang (2009), which includes the day-to-day models in Smith (1984), Friesz et al (1994) and Nagurney and Zhang (1997) as its special cases. There are also day-to-day models that can be treated as the link-based version of RBAP (Guo et al, , 2015aHan and Du, 2012;He et al, 2010;Smith and Mounce, 2011) or as the extension of RBAP under elastic demand (Guo et al, , 2015aLi et al, 2012;Sandholm, 2002Sandholm, , 2005.…”

Section: Introductionmentioning

confidence: 99%

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Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium

Yang

2017

Transportation Science

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This paper extends the framework of "rational behavior adjustment process" (RBAP) to incorporating the "boundedly rational user equilibrium" (BRUE). The proportional-switch adjustment process (PSAP) and the network tatonnement process (NTP) are extended to the BRUE case, and their dynamical equations are shown to be Lipschitz continuous, which guarantees the global uniqueness of the classical solutions. A special group of the BRUE-RBAP is proposed, for which the path flows would increase if the paths are in the acceptable path set, and would decrease otherwise. Classical solutions to this special group of models may not exist. Stability of the BRUE-RBAP with classical solutions is proved with separable link travel cost functions. For non-separable link travel cost functions, the stability of the BRUE-PSAP is proved. Numerical examples are presented to demonstrate the evolution processes of BRUE-PSAP and BRUE-NTP under various bounded rationality thresholds and various initial states. The applicability of BRUE-PSAP in larger networks with asymmetric link travel cost functions is also illustrated.

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“…In Nagurney and Zhang (1996) and Zhang and Nagurney (1996), systematic definitions and discussions of the stability of a user equilibrium was given with a projected dynamical system. Existing studies yield quite consistent results on stability: for symmetric or monotone traffic assignment problems, the unique user equilibrium is always stable (Smith, 1979(Smith, , 1984bNagurney and Zhang, 1996;Zhang and Nagurney, 1996;Zhang et al, 2001); for non-monotone problems, there could exist multiple or unstable user equilibria (Netter, 1972;Watling, 1996;Marcotte and Wynter, 2004;Yang, 2005).…”

Section: Introductionmentioning

confidence: 96%

On the Stability of User Equilibria in Static Transportation Networks

Jin¹

2008

Transportmetrica

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The stability of a user equilibrium determines whether it could be realized or sustained in a transportation network, when subject to perturbations in traffic conditions and drivers' route choice behaviors. In this paper, with a simple deterministic dynamical system model of the traffic assignment problem, we first develop a systematic approach to analyzing asymptotic stability and instability of user equilibria in static transportation networks with fixed demand. We then discuss two examples of non-monotone traffic assignment problem. Compared with existing approaches, the new approach is simpler to use and leads to results consistent with the former. This study could be helpful for analysis and design of real transportation networks.

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On the equivalence between stationary link flow patterns and traffic network equilibria

Cited by 61 publications

References 20 publications

Exploration of day-to-day route choice models by a virtual experiment

Exploration of day-to-day route choice models by a virtual experiment

Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium

On the Stability of User Equilibria in Static Transportation Networks

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