# An Improved Forwarding of Diverse Events with Mobile Sinks in Underwater Wireless Sensor Networks
## 4 Problem Statement and Motivation
### Forwarding Functions Analysis  
Some important aspects of communication in underwater are neighbor selection, forwarding process (function) and holding time calculation. In order to predict the forwarding behaviour in network and its impact on holding time of nodes, it is convenient to have knowledge of domain and range of the forwarding functions. We have done comprehensive analysis on the respective forwarding functions defined in [40; 41]. The upper and lower bounds on the affecting metrics are given in Table 1. If the deepest layer of network is considered as reference level, \(h_{i}=D_{max}-D_{i}\) gives the information about the height of node. DBR and other depth based protocols select neighbors on the base of depth difference \(\Delta d\) between the depth of previous (\(d_{p}\)) and current node (\(d_{c}\)). Holding time in DBR is also function of depth. Depth of broadcasting nodes can have range from; transmission range \(R_{T}\) to maximum depth \(D_{max}\), which directly affects the holding time calculations. So this fails to explain the upper and lower bounds on possible holding time values while considering the delay and packet suppression tradeoff. EEDBR selects next forwarders on the basis of depth and residual energy. A node during its lifetime can have energy between 0 and \(E_{o}\). Hence the range of forwarding function in EEDBR is between 0 to \(E_{o}\). Weight based forwarding function in AMCTD is dependent on both remaining energy and depth difference and is given in following equations:  
\[W_{1}=\frac{p_{v}\times E_{r}}{D_{max}-D_{i}}\] (14a) where \[E_{r}\] and \[D_{i}\] are the residual energy and absolute depth of \[i\] th node respectively, \[p_{v}\] is priority value which is a system parameter. \[D_{max}\] is the maximum depth of underwater network. Weight \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Properties**} & \multicolumn{4}{c}{**Minimum Values**} & \multirow{2}{*}{**Maximum Value**} \\ \cline{2-2} \cline{4-5}  & \(d_{th}=20\) m & \(d_{th}=40\) m & \(d_{th}=60\) m & \\ \hline Depth Difference (\(l_{i}\)) & 20 m & 40 m & 60 m & 100 m \\ \hline Absolute Depth (\(D_{i}\)) & 100 m & 100 m & 100 m & 500 m \\ \hline Absorption Coefficient (Abc) (km) & 0.1990 dB & 0.3980 dB & 0.5969 dB & 0.9949 dB \\ \hline Scattering Coefficient (Sc) (km) & \(-25.485\) dB & \(-20.969\) dB & \(-18.328\) dB & \(-15\) dB \\ (Scm) & 19.5154 dB & 24.0309 dB & 26.6723 dB & 30 dB \\ \hline Total Attenuation (At) & \(-25.286\) dB & \(-20.571\) dB & \(-17.731\) dB & \(-14.005\) dB \\  & 19.7144 dB & 24.4289 dB & 27.2692 dB & 30.9949 dB \\ \hline Attenuation A(l,f) & 0.003 & 0.0088 & 0.0169 & 0.0398 \\  & 93.6 m\({}^{-1}\) & 277.3 m\({}^{-1}\) & 533.2 m\({}^{-1}\) & 1245.4 m\({}^{-1}\) \\ \hline Noise \(N(f)\) & \multicolumn{4}{c}{20.925 dBreuPa or 1.12 \(\times 10^{-5}\) Pa} \\ \hline  & \(3.29\times 10^{-8}\) & \(9.75\times 10^{-8}\) & \(1.87\times 10^{-7}\) & \(4.42\times 10^{-7}\) \\ Attenuation Noise Product A(l,f)\(\times N(f)\) & \(1\times 10^{-3}\) & \(3.1\times 10^{-3}\) & \(5.9\times 10^{-3}\) & \(14.1\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Ranges w.r.t Threshold. calculation in AMCTD is updated and shifted more on remaining energy after 2% death of total nodes using following equation. \[W_{2}=\frac{p_{v}\times D_{i}}{E_{r}} \tag{14b}\]  
In order to prolong the lifetime in sparse conditions, weight calculation is updated after 80% death of total nodes by Equation (14c). \[W_{3}=\frac{E_{r}}{p_{v}\times D_{i}} \tag{14c}\]  
For a unit value of \(p_{v}\) all the forwarding function \(W_{i}\) calculated for AMCTD using Equation (14) has range in interval \([0,\infty)\). Holding time values depending on this forwarding function would vary abruptly and would not meet the optimum delay and reduced redundant transmission requirements. In AMCTD depth threshold \(d_{th}\) is also updated after certain percentage of deaths, but weights are independent of \(d_{th}\) and transmission range \(R_{T}\) of nodes.