## 3 Model Validation
### Mobility Scenarios
#### 3.1.1 Real-World (Human-Based) Mobility Model  
The real-world mobility model used in our study is based on a trace that includes Bluetooth sightings collected by iMotes (the iMote is a low-power, Bluetooth-enabled sensor node designed to log contact events with other devices by detecting Bluetooth signals) devices during the five days of the IEEE INFOCOM'06 conference [36], which is publicly available in the CRAWDAD archive ([[https://ieee-dataport.org/open-access/crawdad-cambridgeheaggle-v-2006-09-15](https://ieee-dataport.org/open-access/crawdad-cambridgeheaggle-v-2006-09-15)]([https://ieee-dataport.org/open-access/crawdad-cambridgeheaggle-v-2006-09-15](https://ieee-dataport.org/open-access/crawdad-cambridgeheaggle-v-2006-09-15)) (accessed on 21 December 2024)). To collect this trace, 78 iMotes were distributed among the conference attendees, while 17 nodes were static long-range iMotes deployed throughout the area, and 3 nodes were long-range iMotes that were placed in the elevators of the hotel. The iMotes log contact events every 120 s using Bluetooth sightings. The contacts with other iMotes were classified as \"internal\" contacts, while the sightings of other types of Bluetooth devices were classified as \"external\" contacts. The trace consists of five days of logs, but in our study we consider a single segment of four consecutive hours, which shows a stable number of contact events over time. As shown in the following, the duration of the mobility trace is long enough to ensure that all nodes' content requests are satisfied before the simulation ends. In this time segment, 65 iMotes are active (i.e., each logs at least three contact events), with a total number of 2811 contacts. Figure 5 shows the empirical complementary cumulative distribution function (CCDF) of the aggregate inter-any-contact time--the time elapsed between two successive contacts of a device with any other device--on a log-linear plot, comparing it with an exponential distribution of the same mean. As a reminder, we use 'inter-contact time' and 'inter-any-contact time' interchangeably.  
The results clearly show that the empirical distribution has a slower decay rate than the exponential distribution, with the empirical inter-contact times deviating considerably from the exponential distribution, especially in the tail [37]. In the figure, we have also expanded the initial section of the CCDF. We observe that the lower end of the inter-contact time distribution is heavier than that of an exponential distribution with the same mean, indicating a higher concentration of probability mass at smaller inter-contact times. For instance, we find that 10% and 30% of the inter-contact times are shorter than 2 s and 40 s, respectively, while the same percentages are reached at 18 s and 60 s in the exponential distribution with the same mean. An interesting behaviour also emerges when examining directly the probability density function (PDF) of inter-contact times (not shown here due to space constraints). Specifically, the PDF exhibits regular peaks at two-minute intervals. This is likely due to Bluetooth sightings being recorded every 120 s in this trace; however, if the Bluetooth scanning processes are not synchronised across nodes, this interval affects the distribution, especially for shorter contact times.