We show that the bounded context-switching reachability problem for concurrent finite systems communicating using unbounded FIFO queues is decidable, where in each context a process reads from only one queue (but is allowed to write onto all other queues). Our result also holds when individual processes are finite-state recursive programs provided a process dequeues messages only when its local stack is empty. We then proceed to classify architectures that admit a decidable (unbounded context switching) reachability problem, using the decidability of bounded context switching. We show that the precise class of decidable architectures for recursive programs are the forest architectures, while the decidable architectures for non-recursive programs are those that do not have an undirected cycle.