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 ideal conditions. We indicate how robots could be scheduled optimally to satisfy any arrival rate in the capacity region, given prior knowledge about arrival rate. We then consider the setting where the arrival rate is 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. We show through analysis and simulations the conditions under which CBMF can stabilize the network, and its corresponding delay performance. From a practical point of view, we propose a heuristic approach to adapt the epoch duration according to network conditions that can improve the end-to-end delay while guaranteeing the network stability at the same time. We also study the structural properties with its explicit delay performance of the CBMF algorithm in a homogeneous network.