# An Improved Forwarding of Diverse Events with Mobile Sinks in Underwater Wireless Sensor Networks
## 5 ESDR: Event Segregation Based Delay Sensitive Routing
### Mobility of Mobile Sinks
#### 5.6.2 Adaptive Mobility of Courier Nodes  
In this mobility pattern, nodes may accelerate or decelerate their speed on the basis of node density and data generated by the upcoming nodes. In this motion, nodes move up and down on a vertical line and their speed is influenced by node density and traffic generation rate of normal nodes. Courier nodes move in pairs as mobility of \(CN_{1}\) and \(CN_{3}\) is in one direction while \(CN_{2}\) and \(CN_{4}\) move towards other direction. This type of motion pattern ensures that these nodes must overlap and communicate with each other at the overlapping area. In order to illustrate the motion of a courier node \(c\) consider it is at position \(y_{c}\); its new position \(y_{t}\) after time \(t\) can be determined by following equation.  
\[\frac{dy_{c}^{2}}{dt^{2}}+\frac{1}{t}\frac{dy_{c}}{dt}+y_{c}=\frac{1}{t^{2}} \times y_{t} \tag{25}\]  
In this equation left term (second degree differential term) corresponds the acceleration of courier node \(c\). If this value is set to zero motion becomes uniform. For adaptive mobility of the nodes, this factor is dependent on the node density in the upcoming coverage region of courier node \(c\). Upcoming coverage regions is double of the transmission range of courier node. This process is explained as follows: Initially a courier node \(c\) increases its transmission range to double of the present value and broadcast its arrival to its future region. Receiving nodes acknowledge with their depth information, rate of data generation and elapsed time since their previous transfer of data to any courier node. The courier node calculates the mean of the depth information of only those nodes  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(i\) & \(h_{i}\) & \(k_{i}\) \\ \hline
1 & 0 & 140 \\
2 & 0 & 380 \\
3 & 0 & 620 \\
4 & 0 & 860 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Centers of elliptical paths.  
which are currently not in its range. This provides that spatial information to estimate its next possible location in its sojourn tour. It also utilizes elapsed time data to calculate the allowed time to reach the estimated location. Using the depth difference between current depth and calculated depth; and remaining time node courier node \(c\) decides new velocity to reach at next location. Courier nodes keep the record of this location and utilizes it in its next sojourn tour. Hence location estimation of courier nodes is a gradually improving process.  
\[y_{t}=\frac{1}{N_{d}}\sum_{1}^{N_{d}}D_{i} \tag{26}\]  
where \(N_{d}\) represents total number of data generating nodes farther than current transmission range of courier node. Node utilizes elapsed time and average traffic generation of all nodes \(N_{d}\) to determine remaining time \(t_{r}\) to reach new location. This remaining time \(t_{r}\) along with new location distance \(y_{t}\) are utilized to estimate the optimum velocity for next part of tour.  
\[v_{c}=\frac{y_{t}}{t_{r}} \tag{27}\]  
Variations of \(v_{c}\) during its sojourn tour make sure the adaptive and accelerated mobility of courier nodes for reaching at optimum new location with in the appropriate time.