2015
DOI: 10.1016/j.trb.2015.06.005
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Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition

Abstract: a b s t r a c t Hoogendoorn and Bovy (2004) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton-Jacobi-Bellman (HJB) equation that contains a minimum value problem. However, only an isotropic application example was given in their paper. We claim that the HJB equation is difficult to c… Show more

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Cited by 9 publications
(9 citation statements)
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“…Surprisingly, we found that among more than 20 studied papers in the continuum-space literature, only three of them have briefly mentioned MFD as a justification for the speed-density relationship [10,11,40], but no attempts can be found in the literature to verify whether or not the assumptions of MFD theory are met. This is perhaps because in existing models travelers do not exit within the region except at discrete destinations.…”
Section: From Mfd To the Conservation Lawmentioning
confidence: 90%
See 1 more Smart Citation
“…Surprisingly, we found that among more than 20 studied papers in the continuum-space literature, only three of them have briefly mentioned MFD as a justification for the speed-density relationship [10,11,40], but no attempts can be found in the literature to verify whether or not the assumptions of MFD theory are met. This is perhaps because in existing models travelers do not exit within the region except at discrete destinations.…”
Section: From Mfd To the Conservation Lawmentioning
confidence: 90%
“…Thus, the minimum value problem has to be solved twice in each iteration. Du et al [11] revisit Hoogendoorn and Bovy's (2004) model for vehicular traffic for the sake of simplifying the numerical solution. They reduce the HJB equation to a HJ equation by removing the minimum value problem from the solution procedure and computing the actual travel cost when the velocity vector is known.…”
Section: Predictive Route Choicementioning
confidence: 99%
“…where V(ρ) is the speed-density relationship and u ≡ u 2 1 + u 2 2 is the norm of the velocity vector. Notice that Q(ρ) in the continuum models is in units of flux and V(ρ) plays the role of MFD in the literature as mentioned in Du et al (2013Du et al ( , 2015, Long et al (2017).…”
Section: Continuum Models For Citiesmentioning
confidence: 99%
“…There is now extensive literature analysing and modelling the extent to which traffic flows systematically vary within a day, due to time-of-day variations in demand, time-of-day variations in capacity (e.g. due to traffic signals), and the temporal and spatial interactions of congestion (Ukkusuri et al, 2012, Du et al, 2015, Han et al, 2015, Long et al, 2016, Ngoduy et al, 2016, Wang and Du, 2016 A corresponding body of work has additionally sought to address the considerable variation observed in traffic flows between days, known as day-to-day variability (Watling and Cantarella, 2013a, Watling and Cantarella, 2013b, Guo et al, 2015, Hazelton and Parry, 2015, Kumar and Peeta, 2015, Xiao et al, 2016. This twin focus, on within-day and day-to-day variation, is the topic of the present paper.…”
Section: Introductionmentioning
confidence: 99%