## 3 Methodology and Proposed Innovation
Metrics like hop count, whose lowest values are favored, are categorized as _minimizable_, while the ones similar to throughput, with their greater values being more preferable, are called _maximizable_. After the path comparison procedure, the path ordering  
Figure 1: The flowchart of metric selection and composition. and ultimately the path selection take place. The decision of the most optimal path directly depends on the integrated unidimensional or multidimensional optimization objective, as well as the user-defined Wii-governed specifications. One of the fundamental mechanisms of the PA framework is the algebraic synthesis of miscellaneous networking elements into original resource descriptions. The combination of the values of different elementary metrics unlocks multidimensional path classification capabilities, and thus the intricate demands of sensitive NG applications can be met. Routing metrics can be composited in an additive, multiplicative, or lexicographic manner [40, 45, 46, 47]. The depth of metric composition can be controlled by the orchestrating authority, since composite metrics can be algebraically synthesized even further to address more specialized problems. Nevertheless, the composite metric and its elementary constituents must by properly designed to preserve the desirable PA properties. The PA framework provides an even firmer orchestration grip upon the SN elements. Special weighting factors can be incorporated into the calculations of the composite metric. Therefore, the impact of an elementary component on the synthesized structure can be made completely manageable. Such levels of detailed path description can lead to targeted resource allocations for modern user-centric applications. In the following sections, the PA-based variations of the incorporated performance-oriented primary metrics are initially introduced. Each one defines a distinct characteristic of performance for the candidate path. Their design aligns with the requirement of agile  
Figure 2: The flowchart of path description, comparison, and evaluation. solutions in NGN environments, exploiting already-available and easily computed values like the processing power (CPU) of a node, the available bandwidth (BW) of a link, latency, and jitter. The proposed metrics are proven monotonic and isotonic; hence, they can validly and optimally describe candidate networking elements. The additive composition of the performance-oriented metrics then takes place. The combination of their diverse values assigns a complete and original performance-driven description to the examined paths. The necessary mathematical proof is provided so that the synthesized metric maintains the same algebraic characteristics like its composited members, rendering its values valid and optimal as well. Finally, normalized weights via the Wii mechanism are imposed to all the constituents of the composite metric, in order to provide extensive management capabilities, based on human-defined behavior. The innovative features introduced by this research are governed by independence from technological limitations. This fact facilitates the entry of the portrayed specialized resource evaluation mechanism in both traditional cloud-based environments and modern E2E slicing scenarios. Thus, the proposed holistic performance-aware path enumeration strategy could be further developed by combining numerous service-specific and user-specific requirements in future work.