Robust transit network design under demand uncertainty considering development density

This paper analyzes the influence of unban density on transit network design under demand uncertainty by considering two types of services, rapid transit services and dial-a-ride services. Rapid transit services are operated on dedicated lanes, whereas dial-a-ride services can make use of the existing road ways hence are much more economical to implement. It is obvious that the absolute minimum urban density which makes these two services types financially sustainable is different. This study integrates the two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium passenger flow. The absolute minimum unban density at which the first rapid transit line phases in is investigated. A robust formulation is proposed to address the stochastic demand as captured in a polyhedral uncertainty set. User equilibrium (UE) principle is represented by a set of variational inequality (VI) constraints. An example is provided to illustrate the performance of this formulation and solution algorithm.