We consider a system of parallel queues with the constraint that only one queue can be served at a time. Each queue can be served through a wireless channel with intermittent connectivity. We propose a policy which serves the longest connected queue when the lengths of all connected are below a given threshold, and serves the connected queue that exceeds the threshold and has received the least service so far, otherwise. We prove that this simple policy (a) maximizes the aggregate service rate of all queues (b) maximizes the minimum service rate attained by any queue and (c) attains the stability region of the network.