Multi-Commodity Discrete/ContinuUM Model for a Traffic Equilibrium System

This paper will consider a city with several highly compact central business districts (CBDs). The commuters’ origins are continuously dispersed. The travel demand to each CBD, which is considered as a distinct commodity of traffic movements, is dependent on the total travel cost to that CBD. The transportation system is divided into two layers: major freeways and dense surface streets. Whereas the major freeway network is modeled according to the conventional discrete network approach, the dense surface streets are approximated as a continuum. Travelers to each CBD can either travel in the continuum (surface streets) and then exchange to the discrete network (freeways) at an interchange (ramp) before moving to the CBD on the discrete network, or travel directly to the CBD in the continuum. Specific travel cost-flow relationships for the two layers of transportation facilities are considered. The paper will develop a traffic equilibrium model for this discrete/continuum transportation system, in which for each origin-destination pair no traveler can reduce their individual travel cost by unilaterally changing routes. The problem is formulated as a simultaneous optimization program with two sub-problems. One sub-problem is a traffic assignment problem from the interchanges to the CBD in the discrete network, and the other is a traffic assignment problem in the continuum system with multiple centers (i.e. the interchange points and the CBDs). A Newtonian algorithm that is based on the sensitivity analysis of the two sub-problems is proposed to solve the resultant simultaneous optimization program. A numerical example is given to demonstrate the effectiveness of the proposed methodology