# Value of Information Based Data Retrieval in UWSNs
## 3 Value of Information in Underwater Sensor Networks
### UWSN Deployment Scenario  
We consider a UWSN that has been deployed for monitoring the sea and its surface from below. This UWSN records video data. We assume that the UWSN has been deployed to monitor disasters such as oil spills and leaks from vessels or pipelines. Sensor nodes in the UWSN have the ability to detect and classify such disasters. Therefore, we have two classes of information reported; one is normal routine data while the other is data pertaining to disasters. Both classes of information are mapped to separate infotentials. The information for high-priority events such as oil leaks is mappedto the function \(v_{H}(t)\) while normal routine information is classified as low-priority and is mapped to \(v_{L}(t)\). The UWSN considered in our simulation study is illustrated in Figure 1. We assume a UWSN with \(n\) sensor nodes  
\[S=\{s_{1},s_{2},\ldots,s_{i},\ldots,s_{n}\} \tag{6}\]  
Figure 1: The UWSN mesh setting used for the simulation study. The same arrangement will be used for simulation and experimentation in the results section. The blue colored path is of the AUV that uses LPP, red of the AUV that uses GPP and green of the AUV that uses GIPP. The GPP visits one hot-spot after another. Notice how LPP stumbles upon a hot-spot, i.e., discovers it by chance. Also, observe how GIPP visits intermediate nodes in-between hot-spot visits. These nodes are equipped with sensors that collect high-quality video data which makes their transmission over acoustic channels unfeasible. An AUV is deployed to gather data from these sensor nodes. The sensor nodes have acoustic communication modules for long distance communication such as transmitting signaling and configuration messages while optical communication modules are used for short distance transmissions such as offloading the data from the sensor nodes to the AUVs. The sensor nodes have the ability to classify data into \(q\) different information classes  
\[C=\{c_{1},c_{2},\ldots,c_{p},\ldots,c_{q}\} \tag{7}\]  
Each information class is characterized by a unique infotential. The VoI functions that we use, as discussed earlier, are of the form  
\[v(t)=Ae^{-B(t-\tau_{o})} \tag{8}\]  
In this case, the infotentials for the high-priority and low-priority information classes are as follows respectively  
\[v_{H}(t)=A_{H}e^{-B_{H}(t-\tau_{iH})} \tag{9}\]  
\[v_{L}(t)=A_{L}e^{-B_{L}(t-\tau_{el})} \tag{10}\]  
The sensor nodes process and save the data in the form of data reports. After time \(t\) the \(i_{th}\) sensor node has \(k\) data reports  
\[D_{i}=\{d_{i1},d_{i2},\ldots,d_{ij},\ldots,d_{ik}\} \tag{11}\]  
Data reports are mapped to specific information classes such that the mapping is surjective. This means that a classification function \(\alpha\) (a computational procedure in the sensor node) may assign more than one data report to the same information class  
\[\alpha:D\to C \tag{12}\]  
In terms of the \(i\)th sensor node and \(j\)th data report, the infotentials are denoted with subscripts as  
\[v_{ij}(t)=A_{ij}e^{-B_{ij}(t-\tau_{ij})} \tag{13}\]  
The information class identity is stored in a tag associated with each data report. This tag contains the necessary information required to reconstruct the infotential at the remote user's end. The tag in our case is completely characterized by constants A, B and time stamp \(\tau_{o}\) where \(\tau_{o}\) is the time at which the data report was recorded by the sensor node. A tag is a 3-tuple entity. The tag for the \(j\)th data report at the \(i\)th sensor node is  
\[S=\{s_{1},s_{2},\ldots,s_{i},\ldots,s_{n}\} \tag{6}\]0  
Because the data reports are large in size, therefore, it is not possible to transmit them over the acoustic channel as stated earlier. The acoustic channel will be used for broadcasting the \(\lambda_{ij}\) tags residing at a sensor node. The tags will be transmitted to a sink node. On the other hand, the optical channel will be used for transmitting the actual data reports to the AUV during its tour.