Big Data Transmission in Industrial IoT Systems With Small Capacitor Supplying Energy

Transmission is crucial for big data analysis and learning in industrial Internet of Things (IoT) systems. To transmit data with limited energy is a challenge. This paper studies the problem of data transmission in energy harvesting systems with capacitor to supply energy where the energy receiving rate varies over time. The energy receiving rate is slower when the capacitor receives more energy. Based on this characteristic, we study the problem of how to transmit more data when the energy receiving time is not continuous. Given many packets that arrive at different time instances, there is a tradeoff between transmitting the packet right now or saving the energy to transmit the future arriving packets. We formalize two types of problems. The first one is how to minimize the total completion time when there is enough energy to transmit all the packets. The second one is how to transmit as many packets as possible when the energy is not enough to transmit all the packets. For the first problem, we give a $1+\alpha$ approximation offline algorithm when all the information of the packets and the energy receiving periods is known in advance, and a $\max \lbrace 2,\beta \rbrace$ competitive ratio online algorithm where the information is not known in advance. For the second problem, we study three cases and give a $6+\lceil \frac{h}{b/R} \rceil$ approximation offline algorithm for the general situation. We also prove that there does not exit a constant competitive ratio online algorithm.