# Energy Efficient Multipath Routing Algorithm for Wireless Multimedia Sensor Network
## 3 System Model
### Network Model  
The WMSN consists of \(n\) battery-powered multimedia wireless sensor (MWS) nodes and a BS, as shown in Figure 1. We use a weighted undirected graph \(G=(V,\,E,\,W)\) to represent WMSN where \(V=\ \{v_{1},\,v_{2},\,v_{3},\,\ldots,\,v_{N}\}\) is the vertex set representing the MWS nodes in the network, \(E=\ \{e_{1},\,e_{2},\,e_{3},\,\ldots,\,e_{n}\}\) represents the set of all bidirectional links and \(W=\ \{w_{1},\,w_{2},\,w_{3},\,\ldots,\,w_{n}\}\) is the set of weights on the links. Each MWS node, \(v_{i}\in V\), consists of a sensing unit to monitor the environment, a processing unit to process information, a transceiver unit to transmit and receive the information wirelessly, and a power supply unit. The sensor nodes are randomly deployed in a square sensing field to monitor and detect, and collect information on dynamic events. BS collects information gathered by the MWS nodes to be stored or further processed. \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & \multicolumn{1}{c}{**Explanation**} \\ \hline \(v_{i}\) & A sensor node in WMSN \\ \hline \(e_{ij}\) & The bidirectional wireless link between \(v_{i}\) and \(v_{j}\) in WMSN \\ \hline \(w_{ij}\) & Energy consumed during data transmission between \(v_{i}\) and \(v_{j}\) in WMSN \\ \hline \(d\Big{(}v_{i},\ v_{j}\Big{)}\) & The distance between the node \(v_{i}\) and \(v_{j}\) \\ \hline \(S_{event}\) & Set of sensor nodes in the event area \\ \hline \(N\) & The total number of sensor nodes in the sensing field \\ \hline \(M\) & The total number of sensor nodes in the event area \\ \hline \(N_{r}\) & The set of neighboring nodes to node \(v_{r}\) \\ \hline \(d_{o}\) & The thresholdvaletoselect apply transmission model \\ \hline \(\varepsilon_{fs}\) & Transmission ability in free space model \\ \hline \(\varepsilon_{mp}\) & Transmission ability in multipath fading model \\ \hline \(k\) & Size of data to be transmitted or received by a node \\ \hline \(E(k,d)_{TX}\) & Energy consumed to send \(k\) bits data to a node at a distance \(d\) \\ \hline \(E(k)_{RX}\) & Energy consumed to receive \(k\) bits from another node \\ \hline \(d\) & The distance which the data traveled \\ \hline \(E_{cpu}\) & Energy consumed for processing data \\ \hline \(E_{elec}\) & Electronic energy \\ \hline  
Each multimedia wireless sensor has a unique ID, a communication radius, R, and a set of neighboring nodes defined as \(N(v_{i})=\big{\{}v_{j}/d\big{(}v_{i},v_{j}\big{)}\leq R\text{ and }v_{j}\varepsilon V \big{\}}\), where \(d\big{(}v_{i},v_{j}\big{)}\) is the distance between the node \(v_{i}\) and node \(v_{j}\). We assume that the \(n\) sensor nodes do not know their location, but they are capable of estimating the distance of their neighbor nodes. There exists a bidirectional wireless link, \(e_{ij}\in E\), between two sensor nodes, \(v_{i}\in V\) and \(v_{j}\in V\), such that \(v_{i}\
eq v_{j}\) and \(d\big{(}v_{i},\ v_{j}\big{)}\leq R\). The weight, \(w_{ij}\), on a given link, \(e_{ij}\in E\), denotes the energy consumed when data are being transmitted from node \(v_{i}\) to node \(v_{j}\), such that \(v_{i}\
eq v_{j}\). The sensor nodes are battery-powered and assumed to be deployed in an area where it is very difficult to reach every node and replace their sensor batteries. In order to prolong the lifetime of the network, the energy consumed by each sensor node should be minimized. To address this problem, multimedia sensor nodes are organized into clusters using a clustering mechanism (Section 4.1) with each cluster containing a set of cluster members and a cluster head (CH). The main purpose of the CH is to coordinate the cluster activities and the CH is dynamically elected. The cluster members have direct access to only one CH. Thus, each communication initiated by a cluster member to a destination inside the cluster must pass by the CH. WMSNs also experience failures for a variety of reasons such as network hole problems [39; 40], which have a great impact on the network during data transmission from source to destination.