Synchronising Energy Harvesting and Data Packets in a Wireless Sensor

We consider a wireless sensor node that gathers energy through harvesting and reaps data through sensing. The node has a wireless transmitter that sends out a data packet whenever there is at least one "energy packet" and one "data packet", where an energy packet represents the amount of accumulated energy at the node that can allow the transmission of a data packet. We show that such a system is unstable when both the energy storage space and the data backlog buffer approach infinity, and we obtain the stable stationary solution when both buffers are finite. We then show that if a single energy packet is not sufficient to transmit a data packet, there are conditions under which the system is stable, and we provide the explicit expression for the joint probability distribution of the number of energy and data packets in the system. Since the two flows of energy and data can be viewed as flows that are instantaneously synchronised, this paper also provides a mathematical analysis of a fundamental problem in computer science related to the stability of the "join" synchronisation primitive.