# Digital Twins, Virtual Devices, and Augmentations for Self-Organising Cyber-Physical Collectives +
## 5 Evaluation
### Experiment Setup
#### 5.2.2 Parameters  
We let the system run varying the following parameters, whose meaning and set of tested values are also summarised in Table 4. We run a simulation for each combination of the variable values (we test the Cartesian product of the parameters values). * _Logical communication range_\(R\): the maximum distance as the crow flies at which communication between devices is allowed. We explore the system behaviour with a large range of options, exploring the possible space approximately geometrically, ranging from 10 m to 2000 m. The former option builds a logical network that behaves similarly to an opportunistic network with short range radio systems (e.g., Bluetooth 2.0); the latter option, considering the map size of the town centre of Urbino, implies a fully connected map. We experiment by (approximately) doubling \(R\) in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Meaning** & **Unit** & **Values** \\ \hline \(\delta_{j}\) & distance error for device \(j\) & \(m\) & n.a. (metric) \\ \hline \(\overline{\delta}\) & mean distance error: & \(m\) & n.a. (metric) \\  & \(\sum_{j\in H}\delta_{j}N_{r}\) & & \\ \hline \(I\) & isolated devices & devices & n.a. (metric) \\ \hline \(M_{j}\) & comm. cost for device \(j\) & \begin{tabular}{c} _messages_ \\ _round_ \\ \end{tabular} & n.a. (metric) \\ \hline \(H\) & set of physical devices UIDs & adim. & n.a. (\(H\subset\mathbb{N}\)) \\ \hline \(\sum_{j\in H}M_{j}\) & total communication cost & \
\begin{tabular}{c} _messages_ \\ _round_ \\ \end{tabular} & n.a. (metric) \\ \hline \(\overline{M}\) & mean comm. cost: \(\sum_{j\in H}M_{j}N_{r}\) &
\begin{tabular}{c} _messages_ \\ _round_ \\ \end{tabular} & n.a. (metric) \\ \hline \(N_{v}\) & virtual device count & devices & n.a. (metric) \\ \hline \(N_{r}\) & physical devices (explorers) & devices & \(5,15,50,158,500\) (\(N_{r}=|H|\)) \\ \hline \(R\) & logical communication range & \(m\) & \(10\cdot(1,2,5,10,20,50,100,200)\) \\ \hline \(R_{v}R\) & relative spawn range & adim. & \(0.25,0.5,0.75,1,1.25,1.5,\infty\) \\ \hline \(R_{v}\) & virtual device spawn range & \(m\) & n.a. (derived as \(R\cdot R_{v}R\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of all symbols used in the evaluation. each simulation set. Since the performance of the system is largely unknown, we preferred to investigate using an approximately geometric progression in place of a linear progression. * _Virtual device spawn range_\(R_{v}\): the maximum distance from the closest virtual device than a physical device tolerates before spawning a new virtual device in its current position, when set to \(\infty\) disables spawning new devices entirely. We decided to control this parameter indirectly by tuning the relative span range \(R_{v}R\). The decision was taken after an initial exploratory testing which showed that varying \(R\) and \(R_{v}\) independently produced results of little significance and/or extremely expensive simulations; for instance, setting \(R=2000\) m and \(R_{v}=10\) m quickly produced a fully connected network of tens of thousands virtual devices, which had extremely high distance error \(\delta\) and cost (both in terms of virtual device count \(N_{v}\) and communication cost \(M_{j}\)), and also resulting in a simulation that required tens of gigabytes in memory and weeks of computation to terminate. The opposite extreme situation, with \(R=10\) m and \(R_{v}=2000\) m (but we obtained similar results values of \(R_{v}\) larger than few times \(R\)) resulted in the same results fo setting \(R_{v}=\infty m\), de-facto disabling the virtual device generation. We concluded that what really matters for the system performance and cost is the ratio \(R_{v}R\) and one between \(R_{v}\) and \(R\) (of course, the interested reader may experiment with the provided kit for reproducing the experiments, and explore the system behaviour with these or even more extreme settings).