  This paper leverages macroscopic models and multi-source spatiotemporal data
collected from automatic traffic counters and probe vehicles to accurately
estimate traffic flow and travel time in links where these measurements are
unavailable. This problem is critical in transportation planning applications
where the sensor coverage is low and the planned interventions have
network-wide impacts. The proposed model, named the Macroscopic Traffic
Estimator (MaTE), can perform network-wide estimations of traffic flow and
travel time only using the set of observed measurements of these quantities.
Because MaTE is grounded in macroscopic flow theory, all parameters and
variables are interpretable. The estimated traffic flow satisfies fundamental
flow conservation constraints and exhibits an increasing monotonic relationship
with the estimated travel time. Using logit-based stochastic traffic assignment
as the principle for routing flow behavior makes the model fully differentiable
with respect to the model parameters. This property facilitates the application
of computational graphs to learn parameters from vast amounts of spatiotemporal
data. We also integrate neural networks and polynomial kernel functions to
capture link flow interactions and enrich the mapping of traffic flows into
travel times. MaTE also adds a destination choice model and a trip generation
model that uses historical data on the number of trips generated by location.
Experiments on synthetic data show that the model can accurately estimate
travel time and traffic flow in out-of-sample links. Results obtained using
real-world multi-source data from a large-scale transportation network suggest
that MaTE outperforms data-driven benchmarks, especially in travel time
estimation. The estimated parameters of MaTE are also informative about the
hourly change in travel demand and supply characteristics of the transportation
network.
