# PDTR: Probabilistic and Deterministic Tree-based Routing for Wireless Sensor Networks
## 1 Introduction
Reference [15] proposed a tree-based protocol that considers both the number of intermediate nodes to the sink, and the residual energy for each node. The proposed protocol increases the network lifetime comparatively than the previously designed protocols; this may be explained by the fact that it reduces the energy of the excessive messages between nodes. Hence, the importance of the last factor, the residual energy, for the lifetime extension is demonstrated here. The authors in [11; 16; 17] also considered this factor in their presented protocols. The main purpose of tree-based protocols is to ensure that no loops will be created when we have redundant paths in the network; with tree-based protocols, it is possible to avoid packet collisions. In [18], the authors proposed a new tree-based routing algorithm that reduces energy consumption. The presented algorithm is a new cluster-based that uses a tree structure for packet transmission. It was designed in the manner to first minimize the used hop-lengths for data transmission inside the clusters, and then select the nearest cluster head to the base station. Reference [19] proposed PLCTA, a probabilistic load-balancing converge-cast tree, which considers the impact of sensors heterogeneities. It uses a weight assignment method, and for each link (node-node's candidate parent) there is a weight assignment, and over time this weight is adjusted according to local information. From the simulation, PLCTA achieved better performance in both energy efficiency and lifetime. In tree-based protocols, each time the node has to send the received data to a fixed next hop, which may cause quick energy depletion for some nodes. In consequence, updating the tree is required in order to save their batteries [15]. In this work, we propose a Probabilistic and Deterministic Tree-based Routing protocol (PDTR), which considers both the optimal routing path and energy balance between nodes. It consists of three different stages: tree construction, data transmission, and residual energy saving. PDTR starts with the selection of the optimal paths to root the packets via unicast, in order to optimize energy consumption. Rooting the packets via a deterministic tree reduces the energy consumption in comparison to the probabilistic tree. However, it may cause a quick depletion of the energy for some nodes. To fix this problem, PDTR is proposed to save the energy of any node which loses of its energy, in order to balance the energy in the network. This strategy will probabilistically root the packets, from this node to the forwarder (anycast). The protocol with the two strategies, the deterministic and probabilistic tree, has provided better results when compared with other protocols: DHA, DRP, and DAPR. The rest of this paper is organized as follows. Section 2 introduces some related work of the WSN designed routing protocols. Section 3 presents the used Radio Model. In Section 4, a description of the proposed PDTR is presented. Performance evaluation and comparison are given in Sections 5 and 6, respectively, while Section 7 concludes this paper.