A General Equilibrium Model, a Two-direction Solution Method, and a Convergence Guarantee

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A variable demand equilibrium model is specified. This model has a reasonably general cost function and a reasonably general demand function. The model represents the generation and distribution of equilibrium travel flows between different OD pairs as a function of OD travel costs and equilibrium route choices as a function of the travel costs along the various routes. A two-direction method of solving the model is presented; in this method two search directions are followed instead of the usual one. It will be demonstrated that the two-direction method is guaranteed to converge under natural and rather weak conditions.
The underlying equilibrium model here was originally called “DREAM”; a Demand Responsive Equilibrium Assignment Model. The DREAM model was originally developed with Yanling Xiang in partnership with Miles Logie at MVA Systematica and Ben Heydecker at UCL. The two direction method described here has been specified in route-flow terms in Lv et al (2007) and Smith (2010); here it is specified in link flow terms.
Original languageEnglish
Number of pages9
JournalAET Papers Repository
Publication statusPublished - 2010

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