Investment timing and length choice for a rail transit line under demand uncertainty

This paper is motivated by the inadequate treatment of uncertainty in public transit infrastructure investments. As observed in the past, rare but dramatic events can heavily disrupt public transit system operations and negatively affect the transit riders. For example, the COVID-19 pandemic caused an 80%-90% transit demand decline in March 2020 in the U.S. However, the existing transit infrastructure planning studies have not modeled such sudden demand shocks. We thus improve the modeling realism of uncertain transit demand by formulating demand evolution as a jump-diffusion process, which is a combination of continuous-time Brownian motion and a discrete counting process, namely Poisson process, and present analytical optimization models for the development of a rail transit line under such uncertainty. We jointly optimize two related decisions, namely the timing for introducing rail transit to a commuter corridor and length choice for the rail line. We refute a misconception that investment in a project should always start immediately if a positive cost saving over the planning horizon is expected. We also find that investment timing and sizing decisions are closely related and behave quite differently for the same change in some parameters, such as the infrastructure construction period. The developed modeling and analysis framework should be transferable to other civil infrastructure development and investment problems under uncertainty.