Abstract
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.
Highlights
We have introduced a mathematical model of a cascaded multihop network or a service system where each node gathers energy through harvesting
If a data packets (DPs) encounters a node that does not have at least one energy packets (EPs), the DP must wait for the arrival of enough energy through harvesting at that node
We assume that EPs are lost at each node due to leakage and that DPs may be lost at nodes due to timeouts or errors
Summary
T HE growing energy needs of devices in the wired backbone of mobile networks, the Internet, and the Internet of Things [1]–[4], the need to power them even when they are not plugged into permanent sources of electricity [5], and the inconvenience of changing batteries have motivated the research regarding systems that are powered with harvested energy sources [6], [7]. Mathematical performance models are needed to combine the effect of both the arrival of energy (EPs) and the flow of DPs when the service units are network nodes, or jobs when the service units are computer servers Progress in such analytical models has always happened in steps, and the general results in [10] were preceded by an earlier solution technique that only considered tandem queueing systems [12]. To avoid using different terminologies, a unit will be called a node, and rather than say “DP or job” we shall refer to DPs. our model applies just as well to computer jobs, or to jobs in a manufacturing system, or to items that area being forwarded in a supply chain, and that are processed with the help of intermittent energy in each of the successive nodes
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