Modeling Energy Packets Networks in the Presence of Failures

We model networks of Energy Packets which have been previously introduced by Gelenbe and his colleagues to represent the interactions between communication units and energy units in data processing networks with energy harvesting. We consider failures of batteries and the network structure models the connectivity. The model explicitly represents the amount of Energy Packets needed to transfer a Data Packet. We consider both Data Packets and Jumbo Data Packets which require distinct amounts of energy to be transmitted. Unlike previous models, our approach is based on the assumption that the transmission time of a Data Packet can be neglected when we model Energy Packets harvesting and Leakage which are operating on a larger time scale. We prove that the network of queues associated with the batteries has a product form steady-state distribution under usual Markovian assumptions. An important feature of our model is the ability to study Data Packet losses due to the lack of energy at certain nodes or to the failure of the components which cannot be obtained in previous models with closed form solutions.