Timely Status Update in Internet of Things Monitoring Systems: An Age-Energy Tradeoff

We consider an Internet of Things (IoT) monitoring system, in which an IoT device monitors a physical process and transmits randomly generated status updates to its associated access point (AP) as timely as possible. The timeliness of the status updates is characterized by a recently introduced metric, termed the age of information (AoI), which is defined as the time elapsed since the generation of the last successfully received status update. The channel between the IoT device and the AP is considered to be error-prone and thus the status updates suffer from packet loss. Assuming that the AP provides no feedback to the IoT device, we adopt a practical truncated automatic repeat request (TARQ) scheme: the IoT device keeps transmitting the current status update repeatedly until the maximum allowable transmission times is reached or a new status update is generated. We characterize the inherent age-energy tradeoff for the considered IoT monitoring system. Specifically, a larger value of the maximum allowable transmission times reduces the average AoI, at the cost of incurring higher average energy consumption at the IoT device. Based on the evolution of AoI, we derive the closed-form expressions of the average AoI, the average peak AoI, and the average energy consumption. We then minimize the average AoI by optimizing the transmit power of the IoT device and the maximum allowable transmission times under an average transmit power constraint. Simulations validate the theoretical analysis and reveal that under the same average transmit power constraint, the adopted TARQ scheme achieves a lower average AoI than the classical ARQ scheme that allows an infinite number of retransmission times.