A Road Network Design Model Considering Node Capacity

Abstract

Optimal road network design models have been investigated in order to generate alternatives of road network planning. Most of the previous works assume that the decision variables of the planners are the attributes of the links. The actual road network, however, consists of links and nodes, and it is useful to distinguish links and nodes explicitly. Planning models should involve the attributes of nodes in decision variables as well as the link attributes. We formulate a road network design model considering the nodal capacity. The frame of the proposed model is interpreted as a two level optimal problem, which is a system optimizing problem including an optimal problem as its constraint. Before the formulation of a two level problem, the structure of a node is simplified, and a nodal passing time function is introduced, which represents the performance of a node. As a user equilibrium is the most relevant assumption for the description of road network flow, the lower problem is formulated as a fixed demand user equilibrium problem, using nodal passing time functions as well as link travel time functions. Given the total investment cost constraint, the higher problem decides the link and nodal capacities in order to optimize a measure of the whole network performance. The lower problem describes the traffic flow on a network for given capacities. The structure of the model is explained by using the frame of the Stackelberg differential game, whose players are planner (leader) and aggregate term of network user (follower). In order to solve the formulated problem, a heuristic algorithm is proposed. This is the input/outputiterativemethod, and it is expected to be effective for a normal size problem. The convergence of the algorithm is numerically confirmed through an example for simple and hypothetical datum. A sensitivity analysis for the value of the cost constraint is executed to determine the effective value of an investment. Remaining problems are extensively discussed for further research.