## 3 Methodology and Proposed Innovation  
The deployment of critical NG applications requires prompt and efficient performance-driven resource allocations. From commanding and controlling Unmanned Aerial Vehicles (UAVs) in drone-assisted networks to performing teleoperation actions for Autonomous and Connected Vehicles (ACVs) in IoV environments, orchestration authorities are greatly challenged to produce suitable resource embeddings [18; 19]. It can become clear that no single metric can fully describe performance-capable SN resources, especially in such versatile environments. Moreover, extreme heterogeneity is expected in NGNs; therefore, sensitive applications like telesurgery and emergency communications demand the employment of basic and always-available performance-revealing networking parameters. Such circumstances were the catalyst for inspiring the design of easily obtained measurements that declare different aspects of performance. It must be stated that by adopting the same PA-based methodology any set of metrics can be incorporated, provided that their formulation is compatible with the guidelines of the framework. However, to achieve a more comprehensive approach in such heterogeneous environments, the tool of metric composition is invoked, provided by PA. Hence, the different aspects of performance that the chosen indicators carry are algebraically combined into a unique versatile performance-based metric. As a result, and in contrast to the practices identified in the existing literature, the performance-oriented path embedding problem are multidimensionally tackled. Additionally, the concept of Wii enables the proposed path evaluation mechanism to successfully adapt to any variation scenario that may arise from user-specificparameterization, introducing this solution to the 6G and beyond era of administering human-influenced applications. The adopted methodology primarily follows the principles of the routing metric, which can accurately provide a valid eventuality to the preference of a network path. Nonetheless, the successfulness of such calculations is usually limited by the descriptive capabilities of the deployed mechanism. To materialize the needed designs, the directives of the PA framework are followed. As depicted in Figure 1, this implementation provides the ability to solve both mono-constraint and multi-constraint routing problems by the use of linear and nonlinear metrics, or combinations of both [42]. PA defines the properties a metric must hold to satisfy any optimization objective. Under this prism, new criteria can be introduced that allow the richer differentiation and more accurate classification of network paths, either unidimensionally or multidimensionally [43]. However, the verification of such intricate formulations must be unbiased. To this extent, the PA framework introduces the monotonicity and isotonicity properties. The former declares that a path extended by a new edge cannot be more preferable than the initial path, whereas the latter dictates that the established preference between two paths with the same root-node remains unchanged when both are suffixed by the same link. If both properties are followed, the validity and optimality of the chosen paths are, respectively, ensured, and eventually the credibility of the conceptualized algebraic model is solidly cemented [41, 44]. The creation of appropriate algebraic structures is followed by the computation of their values for all candidate paths. To proceed with the metric's value calculation, the PA framework uses the \(\oplus\) binary operator. The metric's design dictates whether an additive, multiplicative, minimal, or maximal operation will occur in the event of a path extension by a single or a series of edges [40]. Sequentially, the path comparison process occurs, as Figure 2 depicts. The employed preference notation \(\preceq\) correlates with either the _less than or equal to_ or _greater than or equal to_ relation, depending on the orientation of the incorporated elements.