  This paper presents a time-invariant network flow model capturing two-person
ride-pooling that can be integrated within design and planning frameworks for
Mobility-on-Demand systems. In these type of models, the arrival process of
travel requests is described by a Poisson process, meaning that there is only
statistical insight into request times, including the probability that two
requests may be pooled together. Taking advantage of this feature, we devise a
method to capture ride-pooling from a stochastic mesoscopic perspective. This
way, we are able to transform the original set of requests into an equivalent
set including pooled ones which can be integrated within standard network flow
problems, which in turn can be efficiently solved with off-the-shelf LP solvers
for a given ride-pooling request assignment. Thereby, to compute such an
assignment, we devise a polynomial-time algorithm that is optimal w.r.t. an
approximated version of the problem. Finally, we perform a case study of Sioux
Falls, South Dakota, USA, where we quantify the effects that waiting time and
experienced delay have on the vehicle-hours traveled. Our results suggest that
the higher the demands per unit time, the lower the waiting time and delay
experienced by users. In addition, for a sufficiently large number of demands
per unit time, with a maximum waiting time and experienced delay of 5 minutes,
more than 90% of the requests can be pooled.
