# Lyapunov-Guided Energy Scheduling and Computation Offloading for Solar-Powered WSN
## 1 Introduction
[30] considered the battery queue stability and quality of service (QoS) constraints of renewable energy-powered MEC systems and proposed a joint optimization strategy for partial offloading decision and resource allocation based on Lyapunov optimization to minimize the long-term average energy consumption and discard rate of computational tasks in the network. The study, however, fully deploys renewable energy harvesting devices in sensing terminals, which are not friendly to HD video monitoring terminals with small scale in remote and harsh environments, such as substations and transmission lines. Based on the above analysis, we investigate the solar-powered MEC system with the partial offloading scenario, where the hybrid access point (HAP) with a built-in MEC server wirelessly charges and handles the offloading task for its sensor by using the \"harvest-store-use\" protocol. Each sensor uses the harvested energy from RF signals to complete local computing and remote offloading. Considering the stochastic nature of solar arrival and channel state, we construct a model for maximizing network long-term energy efficiency under energy/task queue stability, transmit power, and local computation frequency constraints, and propose a joint optimization algorithm for online computation offloading and resource allocation based on Lyapunov optimization, which balancing the long-term energy efficiency and queue backlog for the network by optimizing the terminal calculation frequency, solar energy broadcast power, and time allocation. In this paper, the innovation points and specific work are as follows:  
1. We integrate solar power provision and multi-access edge computing to formulate a multi-terminal MEC framework for partial offloading with solar energy to provide a continuous energy provision to the terminal nodes, adapting to the high energy consumption and high computation requirements for remote video monitoring networks in remote areas, such as isolated microgrids and high-voltage transmission and distribution systems. 2. We define a long-term offloading energy efficiency function to measure the benefits of solar-powered offloading by considering the long-term offloading computations and long-term energy provision. Considering the stochastic nature of the solar energy arrival and channel state, we developed a long-term stochastic optimization problem to maximize network energy efficiency under the constraints of energy queue stability, task queue stability, peak transmission power, and maximum CPU cycle frequency for each user. 3. We propose a Lyapunov-based online computational offloading and resource allocation algorithm to find the optimal solution to the long-term energy efficiency and queueing backlog problems, which does not require a priori knowledge of the channel state and energy arrival and therefore is a more realistic solution for practical solar-powered MEC systems. The rest of the paper is organized as follows. Section 2 introduces the system model and assumption. Section 3 formulates a long-term stochastic optimization problem to maximize network energy efficiency for multi-terminal solar-powered MEC wireless sensing networks. Section 4 presents the details of Lyapunov theory-based online computational offloading and resource allocation joint optimization algorithm for the non-convex problem mentioned above. Section 5 evaluates the simulation results and Section 6 concludes the paper.