Solving the dynamic network user equilibrium problem with state-dependent time shifts

Terry L. Friesz; Reetabrata Mookherjee

doi:10.1016/j.trb.2005.03.002

Solving the dynamic network user equilibrium problem with state-dependent time shifts

Terry L. Friesz, Reetabrata Mookherjee

Research output: Contribution to journal › Article › peer-review

70 Scopus citations

Abstract

In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.

Original language	English (US)
Pages (from-to)	207-229
Number of pages	23
Journal	Transportation Research Part B: Methodological
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.trb.2005.03.002
State	Published - Mar 2006

All Science Journal Classification (ASJC) codes

Civil and Structural Engineering
Transportation

Access to Document

10.1016/j.trb.2005.03.002

Cite this

@article{b16b212746fd44e2b179b98a654f5f94,

title = "Solving the dynamic network user equilibrium problem with state-dependent time shifts",

abstract = "In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.",

author = "Friesz, {Terry L.} and Reetabrata Mookherjee",

year = "2006",

month = mar,

doi = "10.1016/j.trb.2005.03.002",

language = "English (US)",

volume = "40",

pages = "207--229",

journal = "Transportation Research Part B: Methodological",

issn = "0191-2615",

publisher = "Elsevier Ltd",

number = "3",

}

TY - JOUR

T1 - Solving the dynamic network user equilibrium problem with state-dependent time shifts

AU - Friesz, Terry L.

AU - Mookherjee, Reetabrata

PY - 2006/3

Y1 - 2006/3

N2 - In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.

AB - In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.

UR - http://www.scopus.com/inward/record.url?scp=28844505600&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844505600&partnerID=8YFLogxK

U2 - 10.1016/j.trb.2005.03.002

DO - 10.1016/j.trb.2005.03.002

M3 - Article

AN - SCOPUS:28844505600

SN - 0191-2615

VL - 40

SP - 207

EP - 229

JO - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

IS - 3

ER -

Solving the dynamic network user equilibrium problem with state-dependent time shifts

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this