# Collecting Sensed Data with Opportunistic Networks: The Case of Contact Information Overhead
## 3 A Model for Contact Information Overhead
### Impact of Contact Information Size on Message Forwarding
#### 3.2.2. Energy Utilized in Exchanging Contact Information  
When two nodes encounter each other, they exchange summary vectors that contain \(C\), the set of contact information. The energy expended in exchanging contact information per encounter, \(E_{x}\) Joules, is the sum of energy consumed in sending \(S_{tx}\) bits, \(E_{tx}\) Joules, and receiving \(S_{rx}\) bits, \(E_{rx}\) Joules. As shown in Equation (3), we assume that \(S_{tx}=S_{rx}=S_{C}\) bits, since the number of nodes for which contact information is maintained eventually converges with the total number of nodes in the network.  
\[E_{C}=S_{C}(E_{x})=S_{C}(E_{tx}+E_{rx}) \tag{3}\]  
We assume that node batteries are not recharged until an observation period of \(T\) seconds has elapsed. The energy consumed within this period, \(E_{C}(T)\) Joules, is obtained by multiplying the energy expended in exchanging contact information for an encounter, \(E_{C}\) Joules, by the number of encounters within the period, \(N_{T}\) (cf. Equation (4)).  
\[E_{C}(T)=E_{C}N_{T} \tag{4}\]  
Take the energy consumed to send or receive a byte of data through the available wireless communication interface as \(E_{tx}\) Joules and \(E_{rx}\) Joules, respectively. Also, take the energy on a portable handheld device battery as \(E_{B}\) Joules, and the percentage users are willing to allocate to the OppNet as \(P_{A}\%\) (i.e., allocated energy = \(E_{B}\times P_{A}/100\) Joules). The percentage of allocated energy utilized in exchanging contact information after an observation period of \(T\) seconds is given by Equation (5).  
\[P_{E}=\frac{E_{C}(T)}{P_{A}E_{B}}\times 10^{4} \tag{5}\]  
Again, consider the UTM campus IoT scenario with a total of 24,000 networking nodes. The number of encounters a node experiences depends on its popularity in the network. Let us assume that for a wireless transmission range of 10 m, the average number of encounters (with repetition) experienced by a node during an observation period of 24 h is 500. Since smartphones are energy constrained due to various applications running on them, we assume that users would be willing to allocate only an unnoticeable amount of their battery to the OppNet. Let us take this value as 3%. Let us also assume that devices communicate through Bluetooth (v4.1) and consume 1.225 micro Joules to send or receive a byte of data [57]. From Equation (5), 38.5% of the allocated energy on a smartphone battery of 12.705 Wh or 45,738 Joules (e.g., 3.85 V and 3300 mAh for SAMSUNG Galaxy J7) would be utilized in exchanging contact information alone. In that case, only 61.5% of the allocated energy would be remaining for other network operations, which include device discovery, exchanging other portions of the summary vector, sending and receiving data messages in the device buffer and computations! Table 2 shows the percentage of allocated energy utilized in exchanging contact information for a different number of encounters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Contact Info. Size** & **Remaining Encounter Duration** & **Max. Transferable Data** & **Data Exchange Success** \\ \hline
0 KB & 5.00 s & 1250 KB & 100\% \\
10 KB & 4.92 s & 1230 KB & 98.4\% \\
20 KB & 4.84 s & 1210 KB & 96.8\% \\
30 KB & 4.76 s & 1190 KB & 95.2\% \\
40 KB & 4.68 s & 1170 KB & 93.6\% \\
50 KB & 4.60 s & 1150 KB & 92.0\% \\
0.432 MB & 0.00 s & 0 KB & 0.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data exchange success for different amounts of contact information.