  Parking infrastructure is pervasive and occupies large swaths of land in
cities. However, on-demand (OD) mobility -- such as commercial services Uber,
Grab or Didi -- has started reducing parking needs in urban areas around the
world. This trend is expected to grow significantly with the advent of
autonomous driving, which might render on-demand mobility predominant. Recent
studies have started looking at expected parking reductions with on-demand
mobility, but a systematic framework is still lacking. In this paper, we apply
a data-driven methodology based on shareability networks to address what we
call the "minimum parking" problem: what is the minimum parking infrastructure
needed in a city for given on-demand mobility needs? While solving the problem,
we also identify a critical tradeoff between two public policy goals: less
parking means increased vehicle travel from deadheading between trips. By
applying our methodology to the city of Singapore we discover that parking
infrastructure reduction of up to 86% is possible, but at the expense of a 24%
increase in traffic measured as vehicle kilometers travelled (VKT). However, a
more modest 57% reduction in parking is achievable with only a 1.3% increase in
VKT. We find that the tradeoff between parking and traffic obeys an inverse
exponential law which is invariant with the size of the vehicle fleet, leading
to a simple methodology to estimate aggregate parking demand in a city.
Finally, we analyze parking requirements due to passenger pick-ups and show
that increasing convenience produces a substantial increase in parking for
passenger pickup/dropoff. The above mathematical findings can inform
policy-makers, mobility operators, and society at large on the tradeoffs
required in the transition towards pervasive on-demand mobility.
