Award Abstract # 1024647
BECS Collaborative Research: Modeling the Dynamics of Traffic User Equilibria Using Differential Variational Inequalities

NSF Org: EFMA
Office of Emerging Frontiers in Research and Innovation (EFRI)
Recipient: RENSSELAER POLYTECHNIC INSTITUTE
Initial Amendment Date: August 24, 2010
Latest Amendment Date: August 24, 2010
Award Number: 1024647
Award Instrument: Standard Grant
Program Manager: Eduardo Misawa
emisawa@nsf.gov
 (703)292-5353
EFMA
 Office of Emerging Frontiers in Research and Innovation (EFRI)
ENG
 Directorate for Engineering
Start Date: September 1, 2010
End Date: August 31, 2014 (Estimated)
Total Intended Award Amount: $100,000.00
Total Awarded Amount to Date: $100,000.00
Funds Obligated to Date: FY 2010 = $100,000.00
History of Investigator:
  • Xuegang Ban (Principal Investigator)
    banx@uw.edu
Recipient Sponsored Research Office: Rensselaer Polytechnic Institute
110 8TH ST
TROY
NY  US  12180-3590
(518)276-6000
Sponsor Congressional District: 20
Primary Place of Performance: Rensselaer Polytechnic Institute
110 8TH ST
TROY
NY  US  12180-3590
Primary Place of Performance
Congressional District:
20
Unique Entity Identifier (UEI): U5WBFKEBLMX3
Parent UEI:
NSF Program(s): OFFICE OF MULTIDISCIPLINARY AC,
DYNAMICAL SYSTEMS,
COFFES,
EFRI Research Projects
Primary Program Source: 01001011DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 7722
Program Element Code(s): 125300, 747800, 755200, 763300
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.041

ABSTRACT

The goal of this project is to employ a novel mathematical paradigm, known as a differential variational inequality (DVI), to study two fundamental problems in transportation analysis, namely, the continue-time dynamic user equilibrium with flow propagation and delays, and the problem of traffic disequilibrium in the face of network disruption. Our aim is to develop a nonlinear dynamical system theory that combines classical ordinary differential equation (ODE) methods with contemporary mathematical programming advances to study the equilibrium of short-time (e.g. within-day dynamics) and the equilibration process of longer-time (e.g. transient dynamics) traffic flows, answering questions such as: how to compute dynamic user equilibria, how traffic evolves from a disequilibrium state, due to network disruptions, toward an equilibrium, and how close the current traffic state is to an equilibrium. Results from this study will lead to a new paradigm integrating traffic network analysis methods with recent advances in mathematical science, and bridge the gaps between current practice of traffic analysis and the needs to consider short-term and long-term traffic dynamics in a holistic manner.

The research will be the first step to develop a mathematical framework for traffic dynamic analysis that, in a long term, has the potential to revolutionize the traditional way of conducting transportation analyses such as network signal optimization, dynamic congestion pricing, emergency management after disruptions, among others. Since equilibrium analysis and system dynamics are widely used in other science and engineering fields, the concepts and methodologies developed in this research can also provide new perspectives for equilibrium based analysis in these fields. The research team plans to integrate research findings to undergraduate and graduate courses, and involve undergraduate and graduate students with multidisciplinary backgrounds in this research. The team also plans to reach out to policy makers and practitioners at various transportation management agencies for whom findings from the proposed research will enable them to better manage transportation systems.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Ban, X., Pang, J.S., Liu, X., and Ma, R. "Continuous-time Point-Queue Models in Dynamic Network Loading" Transportation Research Part B , v.46(3) , 2012 , p.360
Ban, X., Pang, J.S., Liu, X., and Ma, R. "Modeling and Solution of Continuous-Time Instantaneous Dynamic User Equilibria: A Differential Complementarity Systems Approach" Transportation Research Part B , v.46(3) , 2012 , p.389
Di, X., Liu, H., Ban, X., and Yu, J.W. "One the stability of a boundedly rational day to day dynamic" Networks and Spatial Economics , 2013
Xuegang Ban, Jong-Shi Pang, and Henry Liu, and Rui Ma "Continuous-time Point-Queue Models in Dynamic Network Loading" Transportation Research Part B , v.46 , 2012 , p.36 http://dx.doi.org/10.1016/j.trb.2011.11.004
Xuegang Ban, Jong-Shi Pang, and Henry Liu, and Rui Ma "Modeling and Solution of Continuous-Time Instantaneous Dynamic User Equilibria: A Differential Complementarity Systems Approach" Transportation Research Part B , v.46 , 2012 http://dx.doi.org/10.1016/j.trb.2011.11.002

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

This project studied the fundamental issues of dynamic traffic networks (such as the dynamic user equilibrium (DUE) problem) in continuous time using a novel mathematical paradigm known as differential variational inequality (DVI). The research developed new traffic flow and dynamic network optimization models for DUE, and investigated issues that are critical for the stability, convergence, and computationally efficiency of the solution process of the models.

 The research was conducted as a multidisciplinary collaboration between transportation experts and applied mathematicians, which benefited many audiences, including graduate students and researchers in various disciplines. Graduate students, especially those from the underrepresented groups, participated in the research. Results from this research were used to enhance graduate level courses. The PI made his best effort to convey research findings to transportation decision makers and engineers, and the academic communities.

Major findings of the research are summarized as follows:

  • A point-queue traffic flow model widely used in the dynamic traffic network analysis literature contains some flaws that may produce negative network flows when being discretized. A modification to the model was proposed which can correct the flaws; some basic properties of the model were established.
  • The modified model was employed as a key building block in an instantaneous dynamic user equilibrium (IDUE) model. Convergence conditions were established for the discretization and solution process of the IDUE model.
  • Complex real world traffic dynamics especially realistic queuing behavior of traffic flow can be incorporated into the continuous-time DUE framework. The new formulation incorporates several novel modeling techniques, including: (i) a double-queue model and associated slack variables to capture queue spillbacks and storage capacities; (ii) a node model that is based on merging properties; and (iii) bounded disutility to capture flow departure time choices. Ultimately, a differential complexity system (DCS) is developed as a comprehensive continuous-time model that integrates all the above key components for the predictive DUE problem.
  • The predictive DUE problem contains time-varyinmg, state-dependent delays. An approximation scheme, called the psuedo-derivative, was developed to approximate such delays. After the approximation, time-varying, state-dependent delays reduce to constant time delays.
  • Discrete-time DUE models, although widely studied in the past, cannot help reveal certain fundamental issues of modeling and solving DUE, such as the convergence of the discretization and solution process. The study of continuous-time DUE problems can help address these and other related issues.

Major outcomes of the research are summarized as follows:

  • Research activities and results: this research produced seven (7) journal papers, one (1) book chapter, and three (3) conference proceeding papers.
  • Teaching activities: integrated research results to multiple courses the PI taught in the last three years, including: Transportation Network Analysis; and developed a new course on Advanced Transportation Models.
  • Student advising: one (1) Ph.D. student was (partially) supported by this research, who graduated in the December of 2013; one (female) Ph.D. student was partially supported by this research, who plans to graduate in 2016. The project has helped the graduate students who worked on thi...

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