Imperial College London

Dr Ke Han

Faculty of EngineeringDepartment of Civil and Environmental Engineering

Senior Lecturer



+44 (0)20 7594 5682k.han Website CV




Mrs Maya Mistry +44 (0)20 7594 6100




605Skempton BuildingSouth Kensington Campus






BibTex format

author = {Friesz, TL and Han, K},
doi = {10.1016/j.trb.2018.08.015},
journal = {Transportation Research Part B: Methodological},
title = {The mathematical foundations of dynamic user equilibrium},
url = {},
year = {2018}

RIS format (EndNote, RefMan)

AB - 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 dynamic 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.
AU - Friesz,TL
AU - Han,K
DO - 10.1016/j.trb.2018.08.015
PY - 2018///
SN - 0191-2615
TI - The mathematical foundations of dynamic user equilibrium
T2 - Transportation Research Part B: Methodological
UR -
UR -
UR -
ER -