## 4 Physical Features and Response Characteristics
### Defining the Features  
The physical features chosen to model the network response are pivotal to the success of the proposed performance model. A significant limiting factor applies to any feature which may be considered for use within the model. This states that any feature must be easily harvested from the network to minimise the amount of testing on each deployment. A further refinement is made stating that features must be available to simple packet probing contained within the networks own infrastructure, negating the need for additional debugging tools. This allows the possibility of a fully functional feature set to be garnered from a connected remote location, further reducing the cost of testing a deployment. With this constraint in mind, a set of features is defined as consisting of:  
* Primary
* 1. Size of network (number of nodes in the network). * 2. Network density (average over node densities). * 3. Network scale (average over individual node diameters). * 4. Channel quality (average link quality over whole network). * Secondary
* 1. Network density (standard deviation). * 2. Network scale (standard deviation). While this does not constitute an exhaustive set of features, it fulfils the main constraint and provides results which validate the suggested framework. Figure 3 illustrates these features with further discussion on each provided. The _size_, _density_ and _scale_ are linked, with each feature dependent on the other two. For example, if density and network scale are both high, the network size must be large. A high network density with low number of nodes would indicate a low scale. The dependency is defined in Table 1 outlying the Pearson correlation [28] between each variable and displayed in a correlation matrix in Figure 4. Both the table and the graphs imply a strong correlation between density-scale and scale-size. These are expected results from the experimentation phase. During simulations the main variables used were network size and physical area of the network. To asses a range of densities of a given network size the network area is varied dictating a change in scale. A change in the size of the network also  
Figure 3: Illustration of the manifestation of the physical features in the network. (**a**) Size is 22: Total number of nodes that constitute the network; (**b**) Density, 6: The number of nodes within communication range; (**c**) Diameter, 4: Minimum number of hops necessary to reach the root; (**d**) Illustrating a high standard deviation in terms of network density. This scenario can occur when a number of highly sensed environments exist with sparsely sensed environments within the same network; (**e**) Illustrating a high standard deviation with regard to network scale. This occurs commonly within buildings when nodes in geographically spaced rooms exist on the same network. dictated a significant change in scale as denoted by the \(p\)-values. The points in the graph represent the features of each of the 559 generated network variations used in the testing phase described in Section 7. The graph includes the networks from both training and test data sets. These facets also represent the main aspects of the network topology. Depending on the application, the size can greatly effect the amount of packets sent in the network. Density effects channel contention while scale effects hop count in the network with deviation in both greatly affecting latency, reliability and energy efficiency in the network. Taking the average density and scale over the whole network gives a good insight into the network topology but does not present the full picture. The scenarios shown in Figure 3d,e are common and cannot be expressed using node averages. The standard deviation then becomes important to determine these features. A taxonomy of the network composing of these features is easily obtained by each node sending its list of neighbours to a centralised point. _Channel quality_ is of importance to the Packet Reception Ratio (PRR) on each link.