## 4 An Architecture for Edge-Fog-Cloud Offloading
It is noted that a higher battery usage is required when D1 uses C1 than if it uses F1, as we would expect. Experiment 5 showed that a device (i.e., D1) offloading to a fog node (F1) and cloud node (C1) can achieve a speed up of 4.85. However, because less work is performed by D1, even though it is transmitting jobs to the other devices, its battery usage decreased. Experiment 6 showed that a device (i.e., D1) offloading to a a peer node (D2), a fog node (F1), and a cloud node (C1) can achieve a speed up of 7.5. However, because even less work is performed by D1, even though it is transmitting jobs to the other devices, its battery usage decreased. Experiment 9 shows that the more powerful (relative to workers) a device is, the less advantage there is in delegating, e.g., it shows that since D2 is more powerful, the speedup from delegation is less than would be gained if D1 was the delegator. RQ2: Impact of task sharing configuration parameters in an edge, fog, cloud collaboration setup

Experiment 7 shows that delegation parameters such as chunk size have a significant impact on performance, increasing speedup by as much as 3-5% (e.g., in a 10 h job, that would be 30 min of savings), and that parameter optimisation should be tailored to the specific requirements of each tier. RQ3: Dynamically adding/removing or slowing down worker nodes

Experiment 8 shows that there are limits to delegation--employing more cloud workers does not always mean improvements to speedup due to increasing transmission times \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Exp.** & **Configuration: D1 as Delegator** & **Avg Battery Saving \%** & **Avg Speedup** \\ \hline
1 & D1 monolithic & - & 1.00 \\



\hline Exp. & Configuration: D2 as delegator & Avg. Battery Saving\% & Avg Speedup \\ \hline
9 & D2 monolithic & - & 1.00 \\
9 & offload to D1 & \(-\)162.51 & 0.17 \\
9 & offload to F1 & 37.71 & 0.85 \\
9 & offload to C1 & 17.80 & 0.56 \\
9 & D2 + D1 + F1 + C1 & 44.38 & 2.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experiment summary. and the delegator's limitations in managing multiple workers. The speedup saturates at around 4.1 even with eight cloud nodes or more. There are also diminishing returns so that the gain in speedup with each additional node is less. Experiment 10 demonstrates the ability of the Honeybee framework to compensate and adapt to nodes disconnecting or slowing down across diverse tiers of edge, fog, and cloud--other nodes automatically do more jobs and do so in a way where the additional jobs are distributed fairly uniformly among the remaining nodes so that no particular node suddenly increases in job uptake (the increases in cumulative jobs across different devices over time remain fairly linear). Conversely, the addition of a new worker reduces load or completed jobs on all nodes fairly uniformly. Overall, for Honeybee-based work stealing style offloading computations, we note that, with the current networking technology, offloading (especially to nearby nodes, i.e., fog or peer nodes) becomes a way to reduce battery consumption on the delegator, i.e., with \(D1\) as delegator, we have: \(\mathit{batt}(D1,D2,F1,C1)<\mathit{batt}(D1,F1,C1)<\mathit{batt}(D1,D2)< \mathit{batt}(D1,F1)<\mathit{batt}(D1,C1)\), where \(\mathit{batt}\) is the battery usage on the delegator.