  We study a new modification of the Arrival problem, which allows for nodes
that exhibit random as well as controlled behaviour, in addition to switching
nodes. We study the computational complexity of these extensions, building on
existing work on Reachability Switching Games. In particular, we show for
versions of the arrival problem involving just switching and random nodes it is
\PP{}-hard to decide if their value is greater than a half and we give a PSPACE
decision algorithm.
