A Study on Travel Demand Models and Associated Solution Algorithms(1/3)

Traffic assignment (TA) is the core element of travel demand forecasting, or morebroadly, of transportation planning. Assuming drivers’ behavior of searching for shortest paths,and depending on the quality/type of travel information made available to travelers, a varietyof traffic assignment models – such as deterministic (Beckman et al., 1956; Sheffi, 1985),stochastic (Dial, 1971; Sheffi and Powell, 1981, 1982), and dynamic (Ran and Boyce, 1996;Chen, 1999) – have been developed and, subsequently, solved using the so-called traditionaltraffic assignment solution algorithms including Frank-and-Wolfe, parallel tangent (PARTAN),gradient projection (GP) methods among others.In the past decade, two important TA relevant issues have been raised and indeedattracted a lot of attention from both researchers and practitioners. The first issue is concernedwith the behavior assumptions on rational travelers. The second notable issue is about theunsatisfactory computational efficiency of the traditional TA solution algorithms. To well treatthe above two important issues and make a natural extension to a more complicated andpossibly more useful combined model application, i.e., entropy-based distribution/assignmentcombined model, this research proposal will be conducted in three years.In the first year, a generalized traffic assignment model formulation will be proposed(which includes most, if not all, of current traffic assignment models as special cases), theTAPAS (Traffic Assignment by Paired Alternative Segments) solution algorithm for theMEUE (maximum entropy user equilibrium) model will be coded into a computer programand the associated algorithmic drawbacks (appeared in the searching of paired alternativesegments (PASs) and redistributing PAS flows among relevant origins) will be improved anddemonstrated with numerical examples.In the second year, the EBTA (entropy-based traffic assignment) problem will beelaborately tackled in several aspects: (1) the associated equilibrium conditions will bederived and analyzed. (2) A workable solution algorithm that employs an “origin-basedgeneralized link cost function” will be proposed. (Note: The big advantage of the“origin-based generalized link cost function” will become apparent later because thedimensional curse of path enumeration can be avoided.) (3) Furthermore, the detection andremoval of negative cycles in an EBTA network will also be addressed.In the third year, the experience and lesson learned from the first two years will becarried over and applied to tackle a more complicated combined model called entropy-baseddoubly constrained distribution/assignment problem. The associated supernetworkrepresentation techniques and the innovative concept of “extended traffic assignment” for themodified traffic assignment solution algorithms will be adopted to efficiently solve the doublyconstrained distribution/assignment problem with large transportation networks.