# Joint Balanced Routing and Energy Harvesting Strategy for Maximizing Network Lifetime in WSNs
## 3 Problem Statement and Motivation
### Motivation  
With the same link weight in each path, the Dijkstra algorithm computes the shortest path for all nodes of multi-hop network initially. After that, the routing path of each node changes as the path cost variation. To mitigate the power consumption of the hotspot nodes, the nodes with lighter traffic can share the forwarding packets if the hotspot nodes increase their path costs. At the same time, because the packet forwarding amount of hotspots next to the sink is very large, the packet forwarding rate is much higher than other nodes. Therefore, it is possible to design an energy balanced routing strategy by the amount of packet forwarding in each node and the packet forwarding rate can be utilized as a  
Figure 2: An illustrated example of packet forwarding amount for the sink connection area (SCA).  
forward awareness factor of path cost or link weight. It can be expected that after several transmission cycles, the SCA and other nodes in each communication layer centered at the sink can achieve the effect of load balance in terms of the energy balance of each network layer.  
In Figure 2, four main forwarding nodes directly connected to the sink can be observed that the number of forwarding packets via node 32 is nine times than that of node 50. We aimed to design a method with the packet forwarding rate for the path cost and to achieve the effect of load balancing of the four main forwarding nodes. Taking node 9 as an example in Figure 1, node 9 can reach sink 41 either from the primary node 32 or 42. Originally, the resulting shortest path is 9\(\rightarrow\)8\(\rightarrow\)7\(\rightarrow\)6\(\rightarrow\)5\(\rightarrow\)14\(\rightarrow\)23\(\rightarrow\)32 by the Dijkstra algorithm. After a certain period of operation, if the forwarding amount of node 32 is greater than the other primary nodes in SCA, the path cost of node 32 is increased and an alternative path 9\(\rightarrow\)8\(\rightarrow\)7\(\rightarrow\)15\(\rightarrow\)25\(\rightarrow\)34\(\rightarrow\)33\(\rightarrow\)42 could be generated. Thus, the packets originally forwarded by the node 32 will be forwarded by the node 42 afterward and the traffic load of node 32 can be mitigated. After that, when the forwarding amount of the node 42 is relatively increased and the path cost of the node 42 will be increased. As a result, the shortest path for node 9 can be alternative switched either via node 32 or node 42.  
On the other hand, the forwarding traffic load via node 42 such as nodes 78 to 81 will also be transferred to node 50, since it has a small number of forwarding packets than node 42. After changing the path cost of hotspots to update the new routing paths of other sensors, our first aim is to design a uniform forwarding packet rate for the main forwarding nodes and all the other communication layers. In addition, the hotspot nodes location can be transferred from the irregular distributed area into the SCA intra-layer. Finally, the ideal balanced shortest tree of multi-hop networks can be seen in Figure 3. Based on the balanced shortest tree routing, the energy harvest capability is jointly deployed for each sensor to effectively utilize the harvested energy and towards to achieve the main goal for an immortal WSN.  
Figure 3: The ideal balanced shortest tree of multi-hop networks.