# rSEM: System-Entropy-Measure-Guided Routing Algorithm for Industrial Wireless Sensor Networks
###### Abstract  
In this paper, a new system entropy measure is used to optimize the routing algorithm in power consumption. We introduce the system entropy measure into the problem of industrial wireless sensor networks (iWSNs) routing and propose a high-performance routing algorithm guided by the system entropy measure (rSEM). Based on the cluster iWSNs architecture, the rSEM selects the cluster heads and cluster member nodes successively, according to the system entropy measure, and constructs the iWSNs with the minimum system entropy. The method of the cluster head selection is traversal, while the method of the cluster member selection is a greedy algorithm to reduce the complexity. The experiments show that the power consumption of the iWSNs generated by the rSEM is in the same order of magnitude as that of Dijkstra in both 2D and 3D scenarios. In addition, the delay of the rSEM is slightly higher than that of LEACH. Therefore, the rSEM is suitable for networks that are sensitive to both the delay and power consumption. The rSEM puts forward a new idea for the design of routing for the next-generation iWSNs, which improves the overall network performance according to the network topology, instead of relying on the power consumption or delay performance only. system entropy; routing; energy saving; reducing the delay 202  
effectively compressed the average number of hops lower than two to achieve a trade-off between the energy consumption and the delay. This two-hop restriction is very suitable for delay-sensitive iWSNs. In addition, in order to balance the load, the round-robin mechanism of the cluster heads is introduced to ensure the load balance of each node. However, in the process of rotating cluster heads, some isolated or severely off-center nodes [8; 9; 10], in the sense of the geographical location, also have the chance to become cluster heads, which is undesirable in a practical application. Obviously, the performance of the network is affected by the topology. The reason why it will go to the two extremes is the lack of a systematic network measure. The concept of system entropy is proposed in [11], which measures the comprehensive performance of a network by its topology. There is only one variable, i.e., the Laplace matrix, in the expression of the system entropy measure, and the network topology matrix is used to evaluate the network performance in a more abstract way. The system entropy measure points out a new way for a future network. This paper introduces the system entropy measure into the problem of routing and proposes a high-performance routing algorithm based on the system entropy measure (rSEM). The algorithm is also used for routing in a two-hop cluster network. One of the differences between LEACH and the rSEM is that once the cluster head is selected, it does not change, and so is the cluster member (the round-robin mechanism of cluster heads is abandoned). Moreover, the selection of cluster heads by the rSEM is not random. Firstly, a group of nodes suitable for a cluster head is selected by minimizing the system entropy measure. So, the high-layer network composed of cluster head nodes and a sinknode has the minimum system entropy. Then, according to the system entropy measure, the cluster head suitable for the remaining cluster member nodes (in the basic layer) is selected, and the final result also meets the effect of the minimum system entropy measure. The experiments show that the power consumption of an iWSN generated by the rSEM is moderately higher but in the same order of magnitude as that of the Dijkstra algorithm in both 2D and 3D scenarios. In addition, the experiments also show that the hops the network generated by the rSEM are slightly higher than the LEACH algorithm but strictly lower than two hops. Therefore, the rSEM is suitable for networks that are sensitive to both a delay and power consumption. The rSEM algorithm is a reference for the routing algorithm design of the next-generation iWSNs.