# Sigma Routing Metric for RPL Protocol
## 3 Related Works  
Traditionally, only one metric is used to select the route. However, this metric cannot satisfy the Quality of Service (QoS) requirements [18; 19] of different applications. Therefore, some proposals [12; 16; 20] present methods that combine metric types to satisfy the needs of the applications. For example, the Hop Count (HC) [9; 10] selects the route with the lowest number of hops, while the Expected Transmission Count (_ETX_) selects the route with the least number of expected transmissions [21; 22; 23]. The _ETX_ metric is the number of transmissions a node expects to make to a destination in order to successfully deliver a packet, and it can be represented by the following formula:  
\[ETX=\frac{1}{Df\times Dr}\]  
where _Df_ is the measured probability that a packet is received by the neighbor, and _Dr_ is the measured probability that the acknowledgment packet is successfully received [10]. The high number and sheer diversity of applications in networks such as WSN imposes challenges and different requirements with respect to the criteria of delay, loss, and energy. In terms of energy, [PERSON] et al. [24] define Residual Energy (RE) in the RPL protocol, where RE metric represents the available energy at one node. In LLNs, nodes are usually battery-powered, therefore, it is necessary to choose the nodes with the most available energy for routing. In another proposal published by [PERSON] et al. [15; 16], the authors describe a novel energy-efficient region-based routing protocol called ER-RPL that uses the ETX metric for calculating the rank. Additionally, [PERSON] [25] presents an RPL protocol for the mesh-based multi-gateway Advanced Metering Infrastructure (AMI) of the Smart Grid, where they define the Expected Transmission Time (ETT): this metric is based on ETX according to the packet size and the link transmission capacity. This technique enables the distribution of a small packet followed by a big packet to each neighbor, after which each neighbor measures the arrival time between the two packets and informs the sender of that time. Finally, the sender calculates the link capacity by dividing the size of the biggest packet delay by the smallest packet delay [26]. In other research [27] an \"optimization model to minimize the expected end-to-end transmission time in wireless mesh networks\", this model is based on the Weighted Cumulative ETT (WCETT)metric, has been proposed by [PERSON] et al. WCETT focuses on fixed nodes of local networks, where the goal is to select a high-throughput path to avoid any loss of information between the source and its destination. The metric assigns weights to the individual links, which are called Expected Transmission Time (ETT). WCETT is a value that increases depending on the number of links in the network where ETT is an estimation of the end-to-end delay that a packet experiences while traveling along a path between two nodes [28; 29]. In Table 1, the target performance of these metrics are introduced. In [30], the authors have presented the design of a path weight structure for wireless routing and some guidelines that identify the specific properties that a routing metric must have. This work describes the Bamer metric, which is a proposed structure to capture power consumption for more reliable communications of wireless links with packet loss. Bamer is suitable to source routing protocols combined with the discovery of routes based on floods (e.g., DSR Protocol) or the Dijkstra algorithm. If using Bamer with routing protocols based on the Bellman-Ford algorithm (e.g., DSDV), the routing protocol is not optimal, but it is still coherent and free of loops. Therefore, Bamer is still usable, although its performance can be degraded [24]. [PERSON] et al. propose the mRPL protocol, a solution to cope with mobility as one of the challenging issues for future IoT applications [31]. This research integrates a proactive hand-off mechanism (dubbed smart-HOP) within RPL [31].