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Title: Mathematical foundations of dynamic user equilibrium
This paper is pedagogic in nature, meant to provide researchers a single reference for learning how to apply the emerging literature on differential variational inequalities to the study of dynamic traffic assignment problems that are Cournot-like noncooperative games. The paper is presented in a style that makes it accessible to the widest possible audience. In particular, we apply the theory of differential variational inequalities (DVIs) to the dy- namic user equilibrium (DUE) problem. We first show that there is a variational inequality whose necessary conditions describe a DUE. We restate the flow conservation constraint associated with each origin-destination pair as a first-order two-point boundary value problem, thereby leading to a DVI representation of DUE; then we employ Pontryagin-type necessary conditions to show that any DVI solution is a DUE. We also show that the DVI formulation leads directly to a fixed-point algorithm. We explain the fixed-point algorithm by showing the calculations intrinsic to each of its steps when applied to simple examples.  more » « less
Award ID(s):
1662968
NSF-PAR ID:
10122277
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Transportation research. Part B, Methodological
Volume:
126
Issue:
219
ISSN:
1879-2367
Page Range / eLocation ID:
309-328
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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