  Ubiquitous taxi trajectory data has made it possible to apply it to different
types of travel analysis. Of interest is the need to allow someone to monitor
travel momentum and associated congestion in any location in space in real
time. However, despite an abundant literature in taxi data visualization and
its applicability to travel analysis, no easy method exists. To measure taxi
travel momentum at a location, current methods require filtering taxi
trajectories that stop at a location at a particular time range, which is
computationally expensive. We propose an alternative, computationally cheaper
way based on pre-processing vector fields from the trajectories. Algorithms are
formalized for generating vector kernel density to estimate a travel-model-free
vector field-based representation of travel momentum in an urban space. The
algorithms are shared online as an open source GIS 3D extension called
VectorKD. Using 17 million daily taxi GPS points within Beijing over a four-day
period, we demonstrate how to generate in real time a series of projections
from a continuously updated vector field of taxi travel momentum to query a
point of interest anywhere in a city, such as the CBD or the airport. This
method allows a policy-maker to automatically identify temporal net influxes of
travel demand to a location. The proposed methodology is shown to be over
twenty times faster than a conventional selection query of trajectories. We
also demonstrate, using taxi data entering the Beijing Capital International
Airport and the CBD, how we can quantify in nearly real time the occurrence and
magnitude of inbound or outbound queueing and congestion periods due to taxis
cruising or waiting for passengers, all without having to fit any mathematical
queueing model to the data.
