  We study journey planning in multimodal networks consisting of public transit
plus an unrestricted transfer mode (e.g., walking or cycling). In order to
provide good results in practice, algorithms must account for vehicle delays.
Delay-responsive algorithms receive a continuous stream of delay updates and
must return optimal journeys in the currently known delay scenario. Updates are
incorporated in an update phase, which must be fast (e.g., a few seconds). The
fastest known approach for multimodal journey planning is ULTRA, which
precomputes shortcuts representing transfers between vehicles. This allows
query algorithms to find Pareto-optimal journeys regarding arrival time and the
number of public transit trips without any performance loss compared to pure
public transit networks. However, the precomputation phase does not account for
delays and is too slow to rerun during the update phase. We present
Delay-ULTRA, a delay-responsive variant of ULTRA. Since accounting for all
theoretically possible delays would yield an impractically large set of
shortcuts, our approach precomputes shortcuts that are provably sufficient as
long as delays do not exceed a configurable limit (e.g., 5 minutes). To handle
delays above the limit (which are less frequent in practice), we propose a
heuristic search for missing shortcuts that is fast enough to be run during the
update phase. Our experimental evaluation on real-world data shows that
Delay-ULTRA fails to find less than 0.02% of optimal journeys on metropolitan
and mid-sized country networks, and 0.16% on the much larger Germany network.
Considering that the available delay information in realistic applications is
never perfectly accurate, these error rates are negligible. Query speed is at
most twice as slow as ULTRA without delay information, and up to 8 times faster
than the fastest exact algorithm, which does not require a preprocessing phase.
