Exact speed and transmission cost in a simple one-dimensional wireless delay-tolerant network

We study a simple one-dimensional, discrete-time network model that consists of two nodes moving on a discrete circle, changing their direction of movement randomly, and a single packet travelling in the clockwise direction, using combinations of transmissions between the two nodes (when they are co-located) and physical transports on their buffers. In this setting, we provide exact, explicit expressions for the long-term averages of the packet speed and the wireless transmission cost. Our work is a first step towards providing simple and exact results for more realistic wireless delay-tolerant network models.