# A New Linear Model for the Calculation of Routing Metrics in 802.11s Using ns-3 and RStudio
## 1 Introduction
### Contributions  
This research presents a new methodology for routing metric calculation in WMNs, particularly for the implementation of HWMP in ns-3.  
A lot of research has gone into understanding and evaluating the performance of WMNs with different scenarios, and [9] presents a new metric for the HWMP protocol based on two criteria: the diversity of the two-hop channel and the hop delay. This new metric, called NMH, has been tested, simulated, and compared with the WCETT metric using ns-2, resulting in a decrease in the end-to-end delay of the network and increment of the throughput.  
The information in [10] proposes a metric calculation based on the following parameters: hop count, energy cost, and network traffic, which employ a linear combination as follows:  
\[cost=cost+\sum\alpha_{i}\times metric_{i} \tag{2}\]  
Simulation analysis shows that the approach outperforms single-metric routing protocols while supporting flexible service criteria, including load balancing at access points.  
In [11], an improvement in the metric of the HWMP protocol is presented. This new metric takes the traffic flow into account and allocates network resources efficiently. In addition, this model manages the link quality historically, as well as in real-time, so it becomes more sensitive to variations in link quality.  
The model in [12] uses EXT (expected transmission count) as a metric and compares it with the HWMP metric based on hops. It then utilizes ns-2, which results in a decrease in network latency. Conversely, the overhead is increased.  
The model in [13] presents a metric called ETX-3 hop because it comprises three nodes for metric calculation. It includes a more precise method to obtain the link quality and it also shows improvements in the network throughput regarding ETX.  
In [14], an analytic hierarchy process (AHP) is applied to calculate the two new metric calculations within four parameters of the QoS: delay, bandwidth, security, and packet loss probability. The results of this paper are focused on demonstrating the effects of metric prioritization on the routing decisions.  
In [15], presented herein is an improved routing metrics algorithm for WMNs that use the page rank (PR) theory and linear regression. To solve the problems mentioned above, the PR theory and multiple linear regression (MLR) methods are introduced in the metric calculation to generate metrics closer to real values by conditionally referring sibling metrics to a common parent or candidate.  
After a thorough revision of the diverse approaches within the metric calculation for WMNs, statistical treatment for the employed models was found to be one of the main opportunities of this research. Even though in works such as [10; 14; 15] new linear models are presented for the calculus of variations, none of these have included the statistical software RStudio for its treatment. With the latter being the pivot of this work, we subsequently took the new linear model back to ns-3 where we performed the WMN performance tests.  
The RStudio allows for the management of multivariable models, including statistical tests such as an ANOVA, ANCOVA, STARGAZER, and STEPWIZE, which have not been considered in previous research.