UC Irvine Institute of Transportation Studies

Most of the equilibrium traffic assignment models used nowadays, are based on aggregate link performance functions. These flow-delay functions represent a crude abstraction of real dependence of travel time on actual traffic volumes and physical conditions of the transportation network elements. These link performance functions reflect the travel impedance associated with the links and intersections. In many applications, especial those which are concerned with detailed microscopic traffic analysis, the performance of these simplified flow-delay relationship might be too crude and thus unsatisfactory. When such analysis is desired, detailed flow-delay models, or simulation models, have to be used. Furthermore in many investigations different levels of detail are necessary for various components of the network. The flow-delay characteristics of some network elements can be represented by crude aggregate relations while other elements need to be represented in great detail and accuracy. When some, or all, of the network elements are not represented by mathematically defined flow-delay function it becomes very difficult to solve for user equilibrium in a transportation network. Similar difficulties might arise in the investigation of system optimum of transportation, communication or other networks. 

In the framework of this work, a traffic assignment model is developed that can be based on functions, whose exact mathematical form is not known. The proposed solution method applies to steady state network flow problems. This solution will be valid as long as the flow-delay curve is non deceasing when traffic flow increases. The flow-delay function can be numeric pointwise function or a set of simulation-generated values. The empirical analysis and derivation of the proposed solution methods follows the user equilibrium, traffic assignment model, developed by Leblanc [7].