Maximum throughput analysis in hybrid energy harvesting wireless communication systems based on martingale theory

In this article, based on martingale theory, we investigate the problem of maximum throughput in hybrid energy harvesting wireless communication systems (EH-WCSs) under energy storage and delay (or backlog) constraints. Specifically, the energy supply and data transmission of the hybrid EH-WCS are modeled as two queuing systems. For the first energy supply queueing system, we construct corresponding martingales for each type of energy harvesting (EH) process and the system's energy consumption process. Leveraging the multiplicativity of martingales, the stochastic characteristics of the hybrid EH process are described in the martingale domain. On this foundation, a closed-form expression for the energy depletion probability bound (EDPB) under various energy storage constraints is derived. In the second data transmission queueing system, to capture the impact of channel fading on the system's service, we map the arrival and service processes to the signal-to-noise ratio (SNR) domain and construct the corresponding martingales. A martingale parameter is proposed that connects the martingales of the arrival and service processes with the system's EDPB. Based on this, the closed-form expressions for the delay violation probability bound and backlog violation probability bound are derived. Utilizing these derived performance bounds, we address the maximum throughput optimization problems under the energy storage and delay (or backlog) constraints. Furthermore, we instantiate a scenario and provide guidance on the impact of resource allocation on maximum throughput through simulation and validation, offering insights for achieving green communication networks.