  Ridesourcing platforms recently introduced the ``schedule a ride'' service
where passengers may reserve (book-ahead) a ride in advance of their trip.
Reservations give platforms precise information that describes the start time
and location of anticipated future trips; in turn, platforms can use this
information to adjust the availability and spatial distribution of the driver
supply. In this article, we propose a framework for modeling/analyzing
reservations in time-varying stochastic ridesourcing systems. We consider that
the driver supply is distributed over a network of geographic regions and that
book-ahead rides have reach time priority over non-reserved rides. First, we
propose a state-dependent admission control policy that assigns drivers to
passengers; this policy ensures that the reach time service requirement would
be attained for book-ahead rides. Second, given the admission control policy
and reservations information in each region, we predict the ``target" number of
drivers that is required (in the future) to probabilistically guarantee the
reach time service requirement for stochastic non-reserved rides. Third, we
propose a reactive dispatching/rebalancing mechanism that determines the
adjustments to the driver supply that are needed to maintain the targets across
regions. For a specific reach time quality of service, simulation results using
data from Lyft rides in Manhattan exhibit how the number of idle drivers
decreases with the fraction of book-ahead rides. We also observe that the
non-stationary demand (ride request) rate varies significantly across time;
this rapid variation further illustrates that time-dependent models are needed
for operational analysis of ridesourcing systems.
