Minimal delay in controlled mobile relay networks

Abstract—We consider a network in which a set of vehicles is responsible for picking up and delivering messages that arrive according to Poisson process with pickup and delivery location distributed in certain region uniformly at random. The vehicles are required to pickup and deliver the messages so that the average delay is minimized. In our previous work, we examined the benefits of vehicle control on the message delay. Specifically, we obtained optimal delay scaling where each message was required to be picked up and delivered by the same vehicle. Motivated by application to wireless networks, in this paper we remove this restriction and allow the vehicles to relay message between them. Specifically, we consider two relay methods. The first requires vehicles to relay messages directly to each other using a synchronous rendezvous schedule while the other utilizes an infinite capacity depot to store relayed messages. Under both relay models, we characterize the minimal delay scaling which demonstrates that relaying helps in reducing delay further. Surprisingly, the optimal delay scaling is achieved with only one relay per message. We note that our results naturally apply to the classical vehicle routing setup as well as to a wireless communication network. Specifically, our results suggest that the delay reduction can be very significant in a controlled relay network. I