A bi-level frequency setting and passenger assignment model for complying with pandemic capacity limits

Pubic transport is one of the most impacted sectors by the COVID-19 pandemic. Public transport services have experienced a reduction in passenger demand. Notwithstanding this, the social distancing regulations that require public transport service providers to operate under reduced passenger loads stretch the available operational resources. As a consequence, there is an urgent need for new public transport planning tools that can adapt the service supply to the passenger demand. This study proposes a bi-level model for setting the frequencies of public transport lines while accounting for the reduced vehicle capacities due to the pandemic. The upper-level model is a mixed-integer quadratic programming model that sets the line frequencies while accounting for the in-vehicle crowding, whereas the lower-level model is a nonlinear model that performs a probabilistic user-equilibrium passenger assignment. We demonstrate the benefits of our approach for two bus lines in Twente, the Netherlands, using smart card data from the early stages of the pandemic.