# Dynamic Virtual Network Slicing and Orchestration for Selective MEC Services over Wide-Area SDN
## 5 A Selective MEC Service Model Based on a Multitier Architecture
### End-to-End Latency Model
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(L_{E2E}\) & End-to-end latency between a UE and a MEC node \\ \(L_{\text{WL}}\) & Wireless transmission latency between a UE and its access point \\ \(L_{N_{i}}^{n}\) & Network latency between an access point and a MEC node \\ \(L_{C}^{n_{i},i}\) & Computing latency in MEC node \(n\) for a service request \(i\) \\ \(r_{s}\) & Access point associated with a service request \\ \(ge\) & Network edge gateway of \(r_{s}\) \\ \(gc\) & Network core gateway of \(ge\) \\ \(n_{r}\) & Access MEC node in zone\(-\)1 of \(r_{s}\) collocated with \(r_{s}\) \\ \(n_{e}\) & Edge MEC node in zone\(-\)2 of \(r_{s}\) collocated with \(g_{e}\) \\ \(n_{c}\) & Core MEC node in zone\(-\)3 of \(r_{s}\) collocated with \(g_{c}\) \\ \(N_{Z,k}\) & Set of MEC nodes in the zone\(-\)k of \(r_{s}\) \\ \(N_{C}^{i}\) & Set of candidate MEC nodes for a service request \(i\), \(N_{C}^{i}=N_{Z,1}\cup\ N_{Z,2}\cup\ N_{Z,3}\) \\ \(d(i,\ j)\) & Distance between node \(i\) and node \(j\) \\ \(s(i,\ j)\) & Propagation speed in a link medium between node \(i\) and node \(j\) \\ \(l(i,\ j)\) & Fiber link between node \(i\) and node \(j\) \\ \(P(s,\ d)\) & A set of links on the shortest path between node \(s\) and node \(d\) \\ \(U(s,d)\) & Normalized network utilization beween node \(s\) and node \(d\), \(0\leq U(s,d)\leq 1\). \\ \(y_{n_{r}}\) & Binary variable, represeting whether a request is not handled by MEC node \(n_{r}\) \\ \(y_{Z,\ k}^{n_{r}}\) & Binary variable, represeting whether a request is handled by MEC node \(n\) in zone-\(k\) \\ \(P_{n}\) & Total processing capacity of MEC node \(n\) \\ \(\mu_{n}\) & Average number of service requests to be handled by MEC node \(n\) at a time \\ \(\lambda_{n}^{i}\) & Average processing bits for service type \(i\) in MEC node \(n\) \\ \(\eta_{n}^{i}\) & Required processing cycles per bit for service type \(i\) in MEC node \(n\) \\ \(r_{n}^{i}\) & Available CPU resources in MEC node \(n\), \\ \(r_{n}^{n}\) & Available memory resources in MEC node \(n\) \\ \(r_{n}^{n}\) & Available storage resources in MEC node \(n\) \\ \(d_{i}^{i}\) & Latency demand for service request \(i\) \\ \(d_{i}^{c}\) & Initial CPU resource demand for service request \(i\) \\ \(d_{i}^{u}\) & Initial memory resource demand for service request \(i\) \\ \(d_{i}^{i}\) & Initial storage resource demand for service request \(i\) \\ \(R_{A}^{n}\) & Normalized resource availability in MEC node \(n\), \(0\leq R_{A}^{n}\leq 1\). \\ \(N\big{(}L_{E2E}^{n_{i},i}\big{)}\) & Normalized E2E (End-to-End) latency of MEC node \(n\) for service request \(i\), \(0\leq N\big{(}L_{E2E}^{n_{i},i}\big{)}\leq 1\) \\ \(\psi_{U}^{n}\) & Normalized number of UEs in the coverage area associated with MEC node \(n\) \\ \(\psi_{n}\) & Number of UEs in the coverage area associated with MEC node \(n\) \\ \(\omega_{Z,k}\) & Weight factor for \(\psi_{n}\) in zone-\(k\), \(0\leq\omega_{Z,k}\leq 1\) \\ \(c_{U}^{n,\ i}\) & Normalized centrality value of MEC node \(n\) for service request \(i\), \(0\leq c_{i}\leq 1\) \\ \(\bar{v}_{n}^{i}\) & Average data volume related with the requested service \(i\) in MEC node \(n\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of notations. UE, user equipment; CPU, central processing unit. by a zone\(-4\) (regional network core) MEC site. Thus, the network latency between a connected AP of a UE and a selected MEC node \(n\) is expressed as  
\[ \begin{split} L_{N}^{n}=y^{\prime}_{n_{r}}\cdot\frac{d(r_{s},\ n_{e})}{s(r_{s},\ n_{e})}+\sum_{n_{k}\in N _{Z,1}-\{n_{r}\}}y^{n_{k}}_{Z,\ 1}\cdot\frac{d(g_{e},\ n_{k})}{s(g_{e},\ n_{k})}+\sum_{n_{k} \in n_{Z,2}}y^{n_{k}}_{Z,\ 2}\cdot\sum_{l(i,\ j)\in P(g_{e},\ n_{k})}\frac{d(i,\ j)}{s(i,\ j)}\\ +\sum_{n_{k}\in n_{Z,3}}y^{n_{k}}_{Z,\ 3}\cdot\left\{\frac{d(g_{e},g _{e})}{s(g_{e},\ g_{e})}+\sum_{l(i,\ j)\in P(g_{e},\ n_{k})}\frac{d(i,\ j)}{s( i,\ j)}\right\}.\end{split}  \tag{2}\]  
There are four items in Equation (2). If \(n_{r}\) is selected for a service request, we denote \(L_{N}^{n}\) as zero.