A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control

Mike Smith

A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

A two direction method of solving variable demand equilibrium models is considered. Throughout an equilibration using this method, if the first direction fails to reduce disequilibrium, use the second. A proof of convergence under fairly weak conditions is provided. The paper shows how the method works on models without and with responsive signal controls. In the former case the method may replace the iteration of an assignment and a demand model. In the latter case the method may replace the iteration of an assignment and a control model; and may then be utilized to design new fixed time signal timings suitable for a variety of situations. In both cases there will be a reasonable convergence guarantee if the two-direction method is utilized.

Original language	English
Title of host publication	Transportation and Traffic Theory 2009: Golden Jubilee
Subtitle of host publication	Papers selected for presentation at ISTTT18
Editors	William H. K. Lam, S.C. Wong, Hong K. Lo
Place of Publication	NEW YORK
Publisher	Springer
Pages	365-386
Number of pages	22
ISBN (Electronic)	978-1-4419-0820-9
ISBN (Print)	978-1-4419-0819-3
Publication status	Published - 2009
Event	18th International Symposium on Transportation and Traffic Theory - Hong Kong Duration: 16 Jul 2009 → 18 Jul 2009

Conference

Conference	18th International Symposium on Transportation and Traffic Theory
City	Hong Kong
Period	16/07/09 → 18/07/09

Keywords

PROXIMAL POINT ALGORITHM
MONOTONE-OPERATORS
TRAFFIC CONTROL
ASSIGNMENT

Access to Document

http://www.springerlink.com/content/978-1-4419-0819-3#section=277821&page=1&locus=0

Cite this

Smith, M. (2009). A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control. In W. H. K. Lam, S. C. Wong, & H. K. Lo (Eds.), Transportation and Traffic Theory 2009: Golden Jubilee: Papers selected for presentation at ISTTT18 (pp. 365-386). Springer. http://www.springerlink.com/content/978-1-4419-0819-3#section=277821&page=1&locus=0

@inproceedings{a590b86cdc524fa79fbc56fd7f081b41,

title = "A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control",

abstract = "A two direction method of solving variable demand equilibrium models is considered. Throughout an equilibration using this method, if the first direction fails to reduce disequilibrium, use the second. A proof of convergence under fairly weak conditions is provided. The paper shows how the method works on models without and with responsive signal controls. In the former case the method may replace the iteration of an assignment and a demand model. In the latter case the method may replace the iteration of an assignment and a control model; and may then be utilized to design new fixed time signal timings suitable for a variety of situations. In both cases there will be a reasonable convergence guarantee if the two-direction method is utilized.",

keywords = "PROXIMAL POINT ALGORITHM, MONOTONE-OPERATORS, TRAFFIC CONTROL, ASSIGNMENT",

author = "Mike Smith",

year = "2009",

language = "English",

isbn = "978-1-4419-0819-3",

pages = "365--386",

editor = "Lam, {William H. K.} and S.C. Wong and Lo, {Hong K.}",

booktitle = "Transportation and Traffic Theory 2009: Golden Jubilee",

publisher = "Springer",

address = "Germany",

note = "18th International Symposium on Transportation and Traffic Theory ; Conference date: 16-07-2009 Through 18-07-2009",

}

Smith, M 2009, A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control. in WHK Lam, SC Wong & HK Lo (eds), Transportation and Traffic Theory 2009: Golden Jubilee: Papers selected for presentation at ISTTT18. Springer, NEW YORK, pp. 365-386, 18th International Symposium on Transportation and Traffic Theory, Hong Kong, 16/07/09. <http://www.springerlink.com/content/978-1-4419-0819-3#section=277821&page=1&locus=0>

A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control. / Smith, Mike.
Transportation and Traffic Theory 2009: Golden Jubilee: Papers selected for presentation at ISTTT18. ed. / William H. K. Lam; S.C. Wong; Hong K. Lo. NEW YORK: Springer, 2009. p. 365-386.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control

AU - Smith, Mike

PY - 2009

Y1 - 2009

N2 - A two direction method of solving variable demand equilibrium models is considered. Throughout an equilibration using this method, if the first direction fails to reduce disequilibrium, use the second. A proof of convergence under fairly weak conditions is provided. The paper shows how the method works on models without and with responsive signal controls. In the former case the method may replace the iteration of an assignment and a demand model. In the latter case the method may replace the iteration of an assignment and a control model; and may then be utilized to design new fixed time signal timings suitable for a variety of situations. In both cases there will be a reasonable convergence guarantee if the two-direction method is utilized.

AB - A two direction method of solving variable demand equilibrium models is considered. Throughout an equilibration using this method, if the first direction fails to reduce disequilibrium, use the second. A proof of convergence under fairly weak conditions is provided. The paper shows how the method works on models without and with responsive signal controls. In the former case the method may replace the iteration of an assignment and a demand model. In the latter case the method may replace the iteration of an assignment and a control model; and may then be utilized to design new fixed time signal timings suitable for a variety of situations. In both cases there will be a reasonable convergence guarantee if the two-direction method is utilized.

KW - PROXIMAL POINT ALGORITHM

KW - MONOTONE-OPERATORS

KW - TRAFFIC CONTROL

KW - ASSIGNMENT

M3 - Conference contribution

SN - 978-1-4419-0819-3

SP - 365

EP - 386

BT - Transportation and Traffic Theory 2009: Golden Jubilee

A2 - Lam, William H. K.

A2 - Wong, S.C.

A2 - Lo, Hong K.

PB - Springer

CY - NEW YORK

T2 - 18th International Symposium on Transportation and Traffic Theory

Y2 - 16 July 2009 through 18 July 2009

ER -