Robotic message ferrying for wireless networks using coarse-grained backpressure control

We formulate the problem of robots ferrying messages between statically-placed source and sink pairs that they can communicate with wirelessly. We first analyze the capacity region for this problem under both ideal (arbitrarily high velocity, long scheduling periods) and realistic conditions. We indicate how robots could be scheduled optimally to satisfy any arrival rate in the capacity region given prior knowledge about arrival rates. We then consider the setting where the arrival rates are unknown and present a coarse-grained backpressure message ferrying algorithm (CBMF) for it. In CBMF, the robots are matched to sources and sinks once every epoch to maximize a queue-differential-based weight. The matching controls both motion and transmission for each robot: if a robot is matched to a source, it moves towards that source and collects data from it; and if it is matched to a sink, it moves towards that sink and transmits data to it. We show through analysis and simulations the conditions under which CBMF can stabilize the network. We show that the maximum achievable stable throughput with this policy tends to the ideal capacity as the schedule duration and robot velocity increase.