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

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Title: Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model
Author(s): Han, K
Friesz, TL
Item Type: Journal Article
Abstract: 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 arc flows are described by the link delay model (Friesz et al., Oper Res 41(1):80–91, 1993; Carey, Networks and Spatial Economics 1(3):349–375, 2001). Unlike the result established in Zhu and Marcotte (Transp Sci 34(4):402–414, 2000), 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.
Publication Date: 14-Dec-2017
Date of Acceptance: 24-Oct-2017
URI: http://hdl.handle.net/10044/1/55571
DOI: https://dx.doi.org/10.1007/s11067-017-9379-5
ISSN: 1566-113X
Publisher: Springer Verlag
Start Page: 1095
End Page: 1110
Journal / Book Title: Networks and Spatial Economics
Volume: 17
Issue: 4
Copyright Statement: © The Author(s) 2017. This article is an open access publication
Keywords: dynamic traffic assignment
dynamic user equilibrium
dynamic network loading
effective delay operator
link delay model
0102 Applied Mathematics
Logistics & Transportation
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/s11067-017-9379-5
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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