Using the transportation problem to build a congestion/threshold constrained spatial accessibility model

As the COVID-19 pandemic has shown, congestion is an important component in access to medical care. This study expands congestion-based accessibility research by imposing upper limits on demand levels and introducing minimum demand thresholds at individual facilities using the bounded transportation problem to develop different variants of congestion/threshold constrained accessibility metrics. The results of these models were compared against the rational agent access model (RAAM) (Saxon and Snow, 2020) for measuring access to intensive care unit (ICU) beds in the state of Illinois. First, congestion constrained models have more demand sites with a flow link to a single facility resulting in more equalization of costs at these demand sites. Second, one form of these models is guaranteed to have lower objective costs with respect to congestion and travel times than the RAAM model. Third, these methods can flatten the congestion curve across facilities more than the RAAM model. Finally, the inclusion of a lower threshold on the number of potential patients is viewed as a more realistic assumption as hospital services must operate at a minimum operating level to be economically feasible. Congestion/threshold constrained accessibility metrics show important tradeoffs between the even distribution of congestion/thresholds at facilities and travel times with respect to demand sites.