Traffic Assignment Using a Density-Based Travel-Time Function for Intelligent Transportation Systems

This paper presents and shows why density-based travel-time function is consistent with the fundamental diagram from traffic theory and then reviews the applications of travel time in intelligent transportation systems. This paper presents a density-based travel-time function that does not have the ill-posedness that is present in flow-based travel-time functions. The classic steady-state traffic assignment is cast using this new travel-time function, and corresponding mathematical programming formulations are proposed. It is shown that the modified Beckman formulation based on the density-based travel-time function provides a unique solution for link flows and link densities where the Wardrop condition has nonunique values for arc traffic densities.

[1]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[2]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[3]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[4]  Kaan Ozbay,et al.  Solution to the user equilibrium dynamic traffic routing problem using feedback linearization , 1998 .

[5]  S. Shankar Sastry,et al.  Travel Time Dynamics for Intelligent Transportation Systems: Theory and Applications , 2016, IEEE Transactions on Intelligent Transportation Systems.

[6]  Sanghoon Bae,et al.  Proactive travel time predictions under interrupted flow condition , 1995, Pacific Rim TransTech Conference. 1995 Vehicle Navigation and Information Systems Conference Proceedings. 6th International VNIS. A Ride into the Future.

[7]  Pushkin Kachroo,et al.  Feedback Control Solutions to Network Level User-Equilibrium Real-Time Dynamic Traffic Assignment Problems , 2005 .

[8]  黒田 孝次,et al.  Highway Capacity Manual改訂の動向--テイラ-教授の講演より , 1984 .

[9]  Kaan Ozbay,et al.  Feedback Control Theory for Dynamic Traffic Assignment , 1998 .

[10]  R Akcelik,et al.  Travel time functions for transport planning purposes: Davidson's function, its time dependent form and alternative travel time function , 1991 .

[11]  R. Cleary.  Mathematical Models , 2009 .

[12]  David Branston,et al.  LINK CAPACITY FUNCTIONS: A REVIEW , 1976 .

[13]  Kaan Ozbay,et al.  System dynamics and feedback control problem formulations for real time dynamic traffic routing , 1998 .

[14]  Y. She.  Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods , 1985 .

[15]  Pushkin Kachroo,et al.  Dynamic Traffic Assignment: A Survey of Mathematical Models and Techniques , 2013 .

[16]  Heinz Spiess,et al.  Technical Note - Conical Volume-Delay Functions , 1990, Transp. Sci..

[17]  H. Greenberg.  An Analysis of Traffic Flow , 1959 .

[18]  K B Davidson,et al.  THE THEORETICAL BASIS OF A FLOW-TRAVEL TIME RELATIONSHIP FOR USE IN TRANSPORTATION PLANNING , 1978 .

[19]  Mauro Garavello,et al.  Traffic Flow on Networks , 2006 .

[20]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[21]  Kaan Ozbay,et al.  Feedback Ramp Metering in Intelligent Transportation Systems , 2003 .

[22]  Haitham Al-Deek,et al.  Travel-Time Prediction for Freeway Corridors , 1999 .

[23]  William R. McShane,et al.  A review of pedestrian safety models for urban areas in Low and Middle Income Countries , 2016 .

[24]  P. Kachroo,et al.  Real-time travel time estimation using macroscopic traffic flow models , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[25]  Pushkin Kachroo,et al.  Modeling of Network Level System-Optimal Real-Time Dynamic Traffic Routing Problem Using Nonlinear H∞Feedback Control Theoretic Approach , 2006, J. Intell. Transp. Syst..

[26]  Peter J. Bickel,et al.  Day-to-Day Travel-Time Trends and Travel-Time Prediction from Loop-Detector Data , 2000 .

[27]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[28]  William L Eisele,et al.  TRAVEL TIME DATA COLLECTION HANDBOOK , 1998 .

[29]  J G Wardrop,et al.  CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[30]  Satish V. Ukkusuri,et al.  Advances in Dynamic Network Modeling in Complex Transportation Systems , 2013 .

[31]  S. Spraggs,et al.  Traffic Engineering , 2000 .