We consider the problem of task assignment for a multi-robot system where each robot must attend to one or more queues of tasks. We assume that individual robots have no knowledge of tasks in the environment that are not in their queue. Robots in communication with each other may share information about active tasks and exchange queues to achieve lower cost for the system. We show that allowing this kind of task switching causes tasks to be completed more efficiently. In addition, we present conditions under which queues can be guaranteed to make progress, and we support these claims with simulation and experimental results. This work has potential applications in manufacturing, environmental exploration, and pickup-delivery tasks.