  One of the most relevant challenges regarding on-demand ridepooling relates
to the spatial imbalances of the demand, which induce a mismatch between the
position of the vehicles and the origins of the emerging requests. Most
ridepooling models face this problem through rebalancing methods only, i.e.,
moving idle vehicles towards areas with high rejections rate, which is done
independently from routing and vehicle-to-orders assignments, so that vehicles
serving passengers (a large portion of the total fleet) remain unaffected. This
paper introduces two types of techniques for anticipatory routing that affect
how vehicles are assigned to users and how to route vehicles to serve such
users, so that the whole operation of the system is modified to reach more
efficient states for future requests. Both techniques do not require any
assumption or exogenous knowledge about the future demand, as they depend only
on current and recent requests. Firstly, we introduce rewards that reduce the
cost of an assignment between a vehicle and a group of passengers if the
vehicle gets routed towards a high-demand zone. Secondly, we include a small
set of artificial requests, whose request times are in the near future and
whose origins are sampled from a probability distribution that mimics observed
generation rates. These artificial requests are to be assigned together with
the real requests.
  We test these techniques using a set of real rides from Manhattan.
Introducing rewards can diminish the rejection rate to about nine-tenths of its
original value. On the other hand, including future requests can reduce users'
traveling times by about one-fifth, but increasing rejections. Both methods
increase the vehicles-hour-traveled by about 10%. Spatial analysis reveals that
vehicles are indeed moved towards the most demanded areas, such that the
reduction in rejections rate is achieved mostly there.
