## 3 Methodology and Proposed Innovation
### Packet Jitter  
In computer networking, Packet Jitter (PJ) is defined as Packet Delay Variation (PDV) [48]. PDV is an important QoS factor which plays an essential role in assessing the performance of a network. PDV's importance is greater regarding the deployment of sensitive applications, like interactive XR-based handling of industrial production lines, utilization of emergency communications in disaster-stricken areas, and teleoperation of drones in UAV-assisted networks. Since either the dispersion or clumping of the packets could similarly render a multimedia stream incomprehensible, the absolute value of PDV is exclusively considered in calculations of the framework, such that \(PDV\in\mathbb{R}^{+}\). In diversified and ambiguous environments like IoVs or Public Safety Networks (PSNs) in disaster-stricken areas, buffering capabilities are not guaranteed; hence, the effect of PDV cannot be inherently mitigated, and its impact on the user's QoE should be emphasized. For the purpose of this study, \(PJ_{l}\) is defined as the statistical normalized values of \(PDV_{l},\forall l\in E\), to avoid limitations due to different scales and measurement units.  
\[PJ_{l}=\frac{PDV_{l}}{\sum_{\forall l\in E}PDV}\left\{\begin{array}{c}\forall l \in E\\ PJ_{l}\,\ PDV_{l}\in\mathbb{R}^{+}\end{array}\right. \tag{1}\]  
where \(PDV\) represents the always-positive time deviation value from the expected transmission delay of link \(l\) and \(\sum_{l\in E}PDV\) the summation of all such values of \(l\in E\). In the case that \(\sum_{l\in E}PDV=0\), then automatically \(PJ\) becomes irrelevant for the examined physical underlay and is appointed the value of zero. Under this prism, the \(\varphi\) coefficient is structured as follows:  
\[\varphi\left\{\begin{array}{c}=\{\emptyset\}\\ =\omega(l)\\ =\omega(l),\forall l\in E\end{array}\right. iff\sum_{l\in E}PDV\
eq 0\wedge\exists l\in E: PDV_{l}^{SN}\leq PDV_{l}^{VNR}\\ iff\sum_{l\in E}PDV\
eq 0\wedge\exists l\in E: PDV_{l}^{VN}>PDV_{l}^{VN}\\ iff\sum_{l\in E}PDV=0\end{array}\right. \tag{2}\]  
\(PJ\)'s \(\varphi\) may either contain elements that provide undesirable PDV values regarding the VNR's demand or may be empty if each calculated path satisfies the mapping requirements. Specifically, \(\varphi\) will be an empty set, in case the underlying PDV value of every substrate link \(l\in E\) satisfies the PDV demand of each virtual edge \(l^{\prime}\in E^{\prime}\) of the incoming VNR, modeled as \(G^{\prime}=(V^{\prime},E^{\prime})\), such that \(PDV_{l}^{SN}\leq PDV_{l}^{VN}\). Contrariwise, if the physical link \(l\) of the SN, modeled as \(G=(V,E)\), yields an undesirable PDV value such that \(PDV_{l}^{SN}>PDV_{l}^{VN}\), then the virtual link \(l^{\prime}\) cannot be mapped upon \(l\), and thus the set \(\varphi\) is populated by \(l\). Nonetheless, in the event of zero jitter in the network, all possible paths will become elements of this special set. During the realization of the \(i\)th path on the  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Element** & **Usage** \\ \hline \(V\) & \(V=\{A,B,C,D,E,F,G,H\}\), \(|V|=8\) \\ \(P\) & \(P=\{AB,ABC,ABCD,\ldots,EFGH\}\), \(|P|=357\) \\ \(M\) & \(M=\{CPU,BW\}\) \\ \(\oplus\) & \(1\,\text{Path}\ i_{ABC}=A\oplus B\oplus C\) \\  & Extend path \(i_{ABC}\) by link \(CD\): \(i_{ABC}\oplus i_{CD}=i_{ABCD}\equiv ABCD\) \\ \(\omega\) & \(\omega(i_{EF})=100\), \(\omega(i_{GH})=0\) \\ \(\preceq\) & \(\omega(EF)\preceq\omega(GH)\equiv EF\) is more favorable compared to \(GH\) \\ \(\varphi\) & \(\varphi=\{GH,DHG,\ldots,ABCDHGF\}\rightarrow\text{all paths that contain the links GH and HG}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Utilization of adopted septet formulation in accordance with Figure 3.  
physical underlay, \(PJ\) is formed as the aggregate of the values of \(PDV\) to \(\sum_{l\in E}PDV\) ratio of all the links involved in that path.  
\[PJ_{i}=\sum_{l\in i}\frac{PDV_{l}}{\sum_{l\in E}PDV}\left\{\begin{matrix}\forall l \in i,\forall i\in P\\ PJ_{i}\,\ PDV_{l}\in\mathbb{R}^{+}\end{matrix}\right. \tag{3}\]