Optimal urban development density along a multimodal linear travel corridor with time-distance toll scheme
Consider a travel corridor with a multimodal transport system (highway and railway) that connects continuous residential locations to the city center. All commuters travel along the corridor from home to work in the morning peak hour. The spatial dynamics of the traffic congestion on both transportation systems are determined by the trip-timing condition. The flow dynamics on the highway will be considered by applying the Lighthill-Whitham-Richards model. A time-distance road pricing scheme is applied to achieve the system optimal condition. The urban population is assumed to be located continuously along the corridor. This study aims to find the optimal urban population density distribution leading to optimal transportation system performance, with a basic assumption that it follows some given distribution pattern. The problem is eventually formulated into a mathematical program with complementarity constraints and an efficient solution algorithm is applied. Finally, numerical examples are applied to test the validity of the model formulation.