# PDTR: Probabilistic and Deterministic Tree-based Routing for Wireless Sensor Networks
## 6 Simulation Results
### Performance Comparison of the Proposed PDTR to the State-of-the-Art Routing Protocols  
To prove the performance of our proposed approach PDTR, we compare it to the following protocols. In Deterministic Routing Protocols (DRP), such as Tree Routing (TR) and Enhanced Tree Routing (ETR) the paths are predefined, and each node has a fixed forwarder node. Thus, the protocol does not need more energy to be updated, unlike the case of probabilistic protocols; consequently, the DRP consumes less energy and provides better performance in terms of energy consumption in comparison to the probabilistic protocols, as we can see in Figures 8 and 9. Moreover, DPR, with its unicast routing, is the worst in terms of energy balancing and lifetime, since some nodes will be more loaded than others (see Figures 10 and 11). However, the fact that each node has only one fixed forwarder means that each time the sender node sends data to its parent if its parent is in sleep mode, the sender node has to wait, which means an increase in the waiting time delay, thus an increase in the sending time delay, and a decrease in the number of generated packets in comparison to probabilistic protocols, (see Figures 12 and 13). Our proposed approach with the parent probabilistic selection decreases the delay in both the waiting time and sending time. The PDTR at the update phase offers for the node needing a parent a set of candidate parents with different probabilities, and the node has to choose the suitable awake parent through a tree structure. PDTR also improves on DRP in terms of energy efficiency since it builds the tree based on three probability distributions (hops count, transmission distance and residual energy). Since the node's initial energy is the same in our case, we do not consider this criterion. Based on these criteria, PDTR starts generating packets through best-selected paths, and over time the network loading will be high for some nodes (node loses \(\ell_{e}\) =20% of its energy for this scenario (Network size = 100)), and the PDTR starts the probabilistic update; thus it achieves better performance than DRPs in term of energy balancing and energy efficiency. In Probabilistic Routing Protocols (PRP), such as Distributed Adaptive Probabilistic Routing (DAPR) and Distributed Heuristic Algorithm (DHA)), unlike the DRP, the sender in PRP has a set of candidate parent nodes, thus transmitting packets via different paths and distributing the network load and the energy consumption among nodes; consequently, PRPs improved on DRPs in terms of network balancing and lifetime, (see Figures 10 and 11). Moreover, the fact that the nodes have more candidate nodes when sending the packets means that the problem of the forwarder being in sleep mode does not affect the transmission, because the node has to choose another appropriate awake forwarder, thus decreasing both the waiting time and sending time in comparison to the DRPs, and increasing the number of generated packets (see Figures 12 and 13). However, in term of energy consumption, PRPs need more energy than DRPs, first because the packets may travel via longer paths, and second due to the updating, these protocols are built with the probabilities that need to be adjusted according to the transmission process; for these reasons, PRPs need more energy consumption than DRPs (see Figures 8 and 9). PDTR improved on PRPs in term of energy consumption by the fact that it processes via a tree structure based on 3 PD probability distributions (Hops distribution, transmission distance distribution, and residual energy distribution), and packets traveling via the tree structure built from optimal paths need less energy consumption than traveling via anycast structure. Moreover, PDTR has to be updated each time the node meets the high network loading, in order to save the energy and prolong the lifetime; thus, the PDTR increases the lifetime of DRP and PRP cited above (see Figures 10-13).