  Traffic assignment is one of the key approaches used to model the congestion
patterns that arise in transportation networks. Since static traffic assignment
does not have a notion of time dynamics, it is not designed to represent the
complex dynamics of transportation networks as usage changes throughout the
day. Dynamic traffic assignment methods attempt to resolve these dynamics, but
require significant computational resources if modeling urban-scale regions and
often take days of compute time to complete. The focus of this work is
two-fold: 1) to introduce a new traffic assignment approach: a quasi-dynamic
traffic assignment (QDTA) model and 2) to describe how we parallelized the QDTA
algorithms to leverage High-Performance Computing (HPC) capabilities and scale
to large metropolitan areas while dramatically reducing compute time. We
examine and compare the user-equilibrium model (UET) to a baseline static
traffic assignment (STA) model. Results are presented for the San Francisco Bay
Area which accounts for 19M trips/day and an urban road network of 1M links and
is validated against multiple data sources. In order to select the gradient
descent step size, we use a line search using Newton's method with parallelized
cost function evaluations and compare it to the method of successive averages
(MSA). Using the parallelized line search provides a 49 percent reduction in
total execution time due to a reduction in the number of gradient descent
iterations required for convergence. The full day simulation using results of
96 optimization steps over 15 minute intervals runs in \textasciitilde6 minutes
utilizing 1,024 compute cores on the NERSC Cori computer, representing a
speedup of over 34x versus serial execution. To our knowledge, this compute
time is significantly lower than any other traffic assignment solutions for a
problem of this scale.
