## 2 Related Work
### System Modelling
\begin{table}
\begin{tabular}{c c} \hline \(SN_{Net}\) & It represents the set of SNs in EH – WSN where SNs stands for source nodes/sensor nodes and \\  & \(SN_{Net}=\{SN_{1},SN_{2},..........,SN_{c}\}\) \\ \hline \(|SN_{Net}|\) & The number of SNs in EH-WSN \\ \hline \(R_{SN_{Net}}\) & The set of node-disjoint routes which are existing between all the SNs and BS. \\ \hline \(\left|R_{SN_{Net}}\right|\) & The number of node – disjoint routes in EH – WSN. Also, \(\left|R_{SN_{Net}}\right|=|SN_{Net}|*k\) with \(k\geq 2\). \\ \hline \(RN_{Net}\) & It represents the set of relay nodes and \(RN_{Net}=\{RN_{1},RN_{2},...,RN_{d}\}\), \(d<c\) \\ \hline \(|RN_{Net}|\) & The number of RNs in EH-WSN \\ \hline \(SN_{i}\) & One of the sensor node/source node in \(SN_{Net}\) \\ \hline \(BS\) & Sink Node/Base Station in EH-WSN \\ \hline \(RN_{CL}\) & A set representing candidate locations for RNs placement \\ \hline \(Energy_{shared}^{max}\) & Maximum harvested energy by the RN \\ \hline \(Weight_{KN}^{CL}\) & It represents the weight of RN for a particular candidate location and \(CL\in RN_{CL}\) \\ \hline \(SN_{state}\) & The state information of all the sensor nodes/source nodes in EH-WSN \\ \hline \(R_{set(SN_{i},BS)}\) & The set of all the node – disjoint routes between sensor node/source node \(SN_{i}\) and BS \\ \hline \(\left|R_{set(SN_{i},BS)}\right|\) & The number of node – disjoint routes between sensor node/source node \(SN_{i}\) and BS and \(\left|R_{set(SN_{i},BS)}\right|\leq k\) \\ \hline \(k\) & \(k\) is an integer and \(k\geq 2\), node – disjoint routes between each sensor node/source node \(SN_{i}\) and BS \\ \hline \(R_{j}(SN_{i},BS)\) & The _jth_ node – disjoint route between sensor node/source node \(SN_{i}\) and BS and \(\left(1\leq i\leq|SN_{Net}|\right)\), \(\left(1\leq j\leq k\right)\) \\ \hline \(SN_{e}\) & A sensor node in \(R_{j}(SN_{i},BS)\) and \(SN_{e}\in R_{j}(SN_{i},\ BS)\) \\ \hline \(l\) & The direct edge between any two adjacent sensor nodes in \(R_{j}(SN_{i},BS)\) and \(l\in R_{j}(SN_{i},\ BS)\) \\ \hline \(RN_{(BS)}\) & Base Station neighboring relay nodes \\ \hline \(A(RN_{(BS)})\) & The approximate number of base station neighboring relay nodes \\ \hline \(RN_{(SN_{i})}\) & Source Node/Sensor Node \((SN_{i})\) neighboring relay nodes \\ \hline \(A\big{(}RN_{(SN_{i})}\big{)}\) & The approximate number of source node/sensor node \((SN_{i})\) neighboring relay nodes \\ \hline CL & Candidate Location \\ \hline \(Energy^{CL}\) & Energy harvested at particular candidate location \\ \hline \(Range_{SN}\) & Range of sensor node \\ \hline \(Range_{RN}\) & Range of relay node \\ \hline \(CM_{(SN_{i},SN_{j})}\) & Connectivity matrix between _ith_ sensor node \(SN_{i}\) and _jth_ sensor node \(SN_{j}\) \\ \hline \(RE_{Adj}\) & Remaining available energy \\ \hline \(Energy_{\text{-}}\)\(Consumption_{l}\) & Energy \\ \hline \(hop(k_{j}(SN_{i},BS))\) & The hop counts in _jth_ node – disjoint route between _ith_ source node \(SN_{i}\) and BS \\ \hline \(hop(R_{\text{-}(SN_{i},BS)})\) & The hop counts in the set of all the node – disjoint routes between _ith_ source node \(SN_{i}\) and BS \\ \hline \(delay(SN_{e})\) & Delay in communication for the sensor node \(SN_{e},SN_{e}\in R_{j}(SN_{i},BS)\) \\ \hline \(delay(SN)\) & Delay in communication for the sensor node \(SN,SN\in R_{set(SN_{i},BS)}\) \\ \hline RI & Reliability Index \\ \hline \(Reliability_{l}\) & Link Reliability \\ \hline BSRI & Best Suitable Route Index \\ \hline \end{tabular}
\end{table} 
Table 1: Symbols with descriptions. The EH-WSN is deployed in a two-dimensional area and the single-tiered network topology is considered for deploying EH-WSN. The collector node/sink node or base station is placed at predetermined location in EH-WSN. The positions of the SNs are also fixed in EH-WSN; we are trying to get the optimal locations by deploying the relay nodes. Consider \(RN_{CL}\) for representing the set of candidate locations for RN placement, and where \(Energy_{harvest}^{max}\) represents the maximum energy that RN can harvest.