  We study the problem of computing public transit traffic assignments in a
multi-modal setting: Given a public transit timetable, an additional
unrestricted transfer mode (in our case walking), and a set of
origin-destination pairs, we aim to compute the utilization of every vehicle in
the network. While it has been shown that considering unrestricted transfers
can significantly improve journeys, computing such journeys efficiently remains
algorithmically challenging. Since traffic assignments require the computation
of millions of shortest paths, using a multi-modal network has previously not
been feasible. A recently proposed approach (ULTRA) enables efficient
algorithms with UnLimited TRAnsfers at the cost of a short preprocessing phase.
In this work we combine the ULTRA approach with a state-of-the-art assignment
algorithm, making multi-modal assignments practical. Careful algorithm
engineering results in a new public transit traffic assignment algorithm that
even outperforms the algorithm it builds upon, while enabling unlimited walking
which has not been considered previously. We conclude our work with an
extensive evaluation of the algorithm, showing its versatility and efficiency.
On our real world instance, the algorithm computes over 15 million unique
journeys in less than 17 seconds.
