Product-Form Solution for Cascade Networks With Intermittent Energy

The power needs of digital devices, their installation in locations where it is difficult to connect them to the power grid and the difficulty of frequently replacing batteries, create the need to operate digital systems with harvested energy. In such cases, local storage batteries must overcome the intermittent nature of the energy supply. System performance then depends on the intermittent energy supply, possible energy leakage, and system workload. Queueing networks with product-form solution (PFS) are standard tools for analyzing the performance of interconnected systems, and predicting relevant performance metrics including job queue lengths, throughput, and system turnaround times and delays. However, existing queueing network models assume unlimited energy availability, whereas intermittently harvested energy can affect system performance due to insufficient energy supply. Thus, this paper develops a new PFS for the joint probability distribution of energy availability, and job queue length for an N-node tandem system. Such models can represent production lines in manufacturing systems, supply chains, cascaded repeaters for optical links, or a data link with multiple input data ports that feeds into a switch or server. Our result enables the rigorous computation of the relevant performance metrics of such systems operating with intermittent energy.