Multi-commodity traffic assignment by continuum approximation of network flow with variable demand

Consider a city with several highly compact central business districts (CBD ), and the commuters' destinations from each of them are dispersed over the whole city. Since at a particular location inside the city the traffic mov ements from different CBDs share the same space and do not cancel out each other as in conventional fluid flow problems albeit travelling in different directions, the traffic flows from a CBD to the destinations over the city are considered as one commodity. The interaction of the traffic flows amon g different commodities is governed by a cost-flow relationship. The case o f variable demand is considered. The primal formulation of the continuum eq uilibrium model is given and proved to satisfy the user optimal conditions, and the dual formulation of the problem and its complementary conditions a re also discussed. A finite element method is then employed to solve the co ntinuum problem. A numerical example is given to illustrate the effectivene ss of the proposed method. (C) 1998 Elsevier Science Ltd. All rights reserv ed.