# Energy Efficient and Reliable Routing Algorithm for Wireless Sensors Networks
## 3 Network Model and Evidence Theory  
### Network Model  
The wireless sensor network studied in this paper is mainly used for event discovery and information collection. Due to the limited communication distance between sensor nodes, the nodes usually transmit data to the base station through multi-hops. How to find the path with the least energy consumption from a source node to a sink node is a priority for routing algorithms.  
The topology of WSN is shown in Figure 1. The information collection terminals are regarded as common nodes, which transmit the collected data to a sink node through multi-hop forwarding. Suppose in the sensor network with an area of \(L\times L\), there are a number of common nodes and a single sink node located in the center, and all nodes are no longer moved after deployment. The location between nodes is determined in [26]. All sensor nodes are isomorphic, with routing, sending and receiving functions, any two nodes can communicate in single-hop or multi-hop, and the initial state is the same. The initial load of the nodes is 0, and the initial energy is \(E_{0}\).  
The information exchange method between nodes is as [27]. That is, each node has a unique identifier (ID), which maintains a buffer to store information such as residual energy, packet ID, next-hop ID, sender IDs etc. This information is updated in real-time as the forward neighbor changes. It is noted that the traffic queue length of the nodes is limited, and the data packet is processed in first-in first-out (FIFO) mode.  
To more clearly describe the algorithm, this paper makes the related definitions as follows:  
**Definition 1**.: _Network lifetime: network lifetime is defined as the round number when the first dead node appears due to the energy exhaustion._  
**Definition 2**.: _Forward neighbor node set: In order to avoid data backhaul, it is necessary to ensure that data is forwarded in the direction of the sink node. The forward neighbor node set includes the neighbor nodes in the forward semicircle region of node \(i\) within maximum communication radius \(R\). Based on the nodes spatial relationship in Figure 1 and forward transmission model in [12], the forward neighbor node set is defined as follows:_  
\[FN(i)=\{a|d_{ia}\leq R,d_{as}<d_{is}\}. \tag{1}\]  
_where node \(a\) is any forward neighbor node of node \(i\), \(d_{ia}\) is the distance from node \(i\) to node \(a\), \(d_{as}\) and \(d_{is}\) are the distances from node \(i\) and node \(a\) to the sink node respectively, \(R\) is the maximum communication radius of node \(i\)._  
**Definition 3**.: _Forward energy consumption: for any node \(a\in FN(i)\), the energy consumption during the communication between node \(a\) and sink node is the forward energy consumption which denoted as \(e_{as}\)._  
**Definition 4**.: _Candidate node set: for any node \(i\), the candidate node set \(CN_{next}(i)\) is the nodes \(inFN(i)\) that satisfy the criterion in Algorithm 1, which will be detailed in Section 4._  
In the WSN routing decision, the selection of the next hop is affected by the environment and the performance of a node (such as energy status and queue length). The optimal routings determined under different attribute indexes are different and even conflict. As a classical multi-attribute decision-making method, DS evidence theory can effectively deal with uncertain and incomplete information, which can provide a theoretical basis and fusion rules for the comprehensive judgment of sensor node performance. The following will introduce the fusion rules of DS evidence theory.