## 5 Performance Evaluation
### Quality of Service and Impact of Node Density  
The performance of this proposal was evaluated by estimating the Node Density (ND) impact, in order to measure the Quality of Service (QoS). Then, the proposed algorithm performance was estimated in terms of Packet Delivery ratio (PDR) and the End-to-End Delay (E2 ED). This performance was compared with similar protocols:  
1. Reliable Routing with Distributed Learning Automaton (RRDLA) [15]: The RRDLA is composed of four steps: 1. Initialization: Network of learning automaton is formed in a distributed way, namely each IoT device supports one learning automaton. In addition, the learning automaton of entire action plan or topology is calculated. 2. Acquisition: Selection of a scarce nodes' number with high packet delivery ratio is carried out. Figure 6: IISN distribution in an Industrial Plant using the Peano fractal curve: (**a**) ideal connection representation; and (**b**) actual connection representation. * Broadcasting: Transmitting information by means of selected nodes is performed. * Forwarding: Undelivered information is transmitted to the sink node. That algorithm presents both iteration and delay thresholds, thereby flooding the network with hello messages and putting all the nodes on listening for these messages. Then, it randomly chooses a learning automaton, to which a consecutive index is assigned. Hence, by using a QoS rule and network requirements, it generates a topology. Since certain nodes are disabled, this algorithm saves energy by using residuals from inactive nodes. * Delay-Energy Tradeoff in wireless sensor networks with Reliable communication (DETR) [9]: This algorithm creates \(F_{1}\), which is the set of devices inside the radio range and sends a broadcast message to all nodes. Then, that algorithm calculates information delay time at the same time it calculates its power consumption. Thus, by means of probabilities, it calculates what node has the maximum tradeoff energy rate, thus it forwards this information to the entire network. Hence, the DETR algorithm can be expressed as follows:
* Define \(F_{1}\). * Broadcast _HELLO_ message. * For each j IoT-device, \(jeF_{i}\). * Estimate the delay time of each package. * Calculate Energy Consumption for each node. * IF this device obtains the best delay-energy tradeoff, choose it as the main device. * ELSE Choose it as the sink device. * Reliable and Energy-Efficient Routing (REER) [8]: This algorithm assumes that certain nodes have a certain preset power, thus it generates multi-point communication through multicast. This algorithm bases its savings on energy consumption when choosing the most optimal linear route, comparing the best available options. Other features that can be highlighted are the following:
* A multicast routing protocol is performed with the purpose of energy consumption saving
* Two times of the minimum in a one-to-one communication mode
* Estimation of optimal or near optimal power assignments and communication routes
* Minimization of expected total energy
* Decide communication routing  
Hence, all these algorithms, including ours, send messages to know the existing number of nodes. However, our proposal is based on fractal-production rules, offering the best interconnection route to form a topology which does not apply any thresholds or comparisons until finding the best option recursively. The same network parameters, proposed by [PERSON] and [PERSON] [27] and [PERSON] and [PERSON] [28], were employed to make a real comparison to the state-of-the-art algorithms. To understand the experiments carried out, first we define E2 ED as the time it takes for a packet to reach the receiver from the moment it is emitted until it is received, being then the average sum of the differences between the delays sending and receiving [29]. PDR is defined as the probability of recovery from the original packets by receiver before their lifetime expires [30].