# Joint Balanced Routing and Energy Harvesting Strategy for Maximizing Network Lifetime in WSNs
## 3 Problem Statement and Motivation  
### Problem Statement  
When considering traditional multi-hop routing with many-to-one traffic patterns, unbalanced energy consumption is an inherent problem in WSNs. However, the multi-hop routing method can achieve better energy efficiency than the single-hop routing method in networks. In the multi-hop routing method, each sensor node can transmit and forward packets to the data sink through the shortest path, either occasionally or periodically. After a period of operation, hotspot nodes will be generated when the high traffic routing paths are converged and most of the traffic load congested at some specific nodes. Typically, sensors near the sink forward a larger amount of traffic load than sensors that are far from the sink. Therefore, the hotspot nodes near the data sink deplete the battery faster than other sensors. Since the network operation lifecycle is usually defined as the occasion when a battery of the first node is exhausted, the remaining energy capacity of other sensors can be regardedas underutilized energy, and the energy consumption discrepancy results in the considerable network lifetime degradation. A traditional hierarchical WSN routing scenario that includes 81 clusters with one data sink and an evenly distributed two-dimensional network is shown in Figure 1. According to the energy capacity, a cluster head (CH) is selected from the sensors in each cluster. In the cluster, each CH is responsible to manage the sensors, merges all the sensing data from sensors, and sends the collected data to the sink. In order to achieve balance energy utilization, the node with the largest remaining battery capacity is designated as a CH in turn. In the WSNs example, it is assumed that the nodes are deployed in a uniform distribution; the communication distance between two adjacent nodes is \(d\). Each node transmits the sensing data to the sink through the forwarding node along the shortest path. The power consumption is assumed to be proportional to \(d^{2}\) in the path loss model. Note that the shortest path from each node to the sink is calculated by the Dijkstra algorithm. From the perspective of data application, the traffic generated in each node is periodically sent to the target sink. After a specific network operation cycle, each node calculates the number of sending and forwarding packets, and then sends the statistics of the total transmitted packets along with data packets to the sink. Finally, the statistics of each node are calculated by the sink to estimate the number of paths forwarded. In Figure 2, the average forwarding path load amount is illustrated. The 36 nodes in the red area are mainly forwarded through the node 32, the 20 nodes in the blue area are mainly forwarded by the node 40, the 20 nodes in the green area are mainly forwarded via the node 42, and the four nodes in the purple area are mainly forwarded by the node 50. Even though both nodes 32 and 50 are directly connected to the sink, the number of packets forwarding via node 32 is nine times that of node 50. Therefore, an interesting phenomenon is observed which leads to uneven traffic load among the sink in the network even with a uniform node distribution and each node has a uniform packet transmission rate. Specifically, the power consumption rate is unbalanced in the sink connectivity area (SCA), where  
Figure 1: An 81-cluster example illustration for wireless sensor networks (WSN) deployment. the power consumption rate can be calculated by the total number of packets sent and forwarded in the period of each node. In the SCA, it is expected that the four primary forwarding nodes 32, 40, 42, and 50 achieve the approximate power consumption rate per operation cycle. Unfortunately, the Dijkstra algorithm uses the first shortest path and does not consider the following shortest paths; a non-uniform forwarding packet load distribution phenomenon was found in the SCA.