The Stochastic Arrival Problem

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.