  "An advanced city is not a place where the poor move about in cars, rather
it's where even the rich use public transportation". This is what Enrique
Penalosa, the celebrated ex-mayor of Bogota once said. However, in order to
achieve this objective, one of the crucial properties that the public
transportation systems need to satisfy is reliability. While reliability is
often referenced with respect to on-schedule arrivals and departures, in this
study we are interested in the ability of the system to satisfy the total
passenger demand. This is crucial, since if the capacity of the system is not
enough to satisfy all the passengers, then ridership will inevitably drop.
However, quantifying this excess demand is not straightforward since public
transit data, and in particular data from bus systems that we focus on in this
study, only include information for people that got on the bus, and not those
that were left behind at a stop due to a full bus. In this work, we design a
framework for estimating this excess demand. Our framework includes a mechanism
for identifying instances of potential excess demand, and a Poisson regression
model for the demand for a given bus route and stop. These instances of
potential excess demand are filtered out from the training phase of the Poisson
regression. We show through simulated data that this filtering is able to
remove the bias introduced by the censored data logged by the system. Failure
to remove these data points leads to an underestimation of the excess demand.
We then apply our approach on real data collected from the Pittsburgh Port
Authority and estimate the excess demand over an one-year period.
