## 6 Modified Priority-Based Greedy Heuristic
 \tag{117}\]

The total memory resource consumption is:

\[ \begin{split} MEM_{c}=\sum_{\gamma=0}^{|\Gamma|-1}\sum_{i=0}^{| \Phi|-1}\sum_{j=0}^{|R|+|G|-1}mem_{\gamma,n_{i}^{v}}\cdot x_{\gamma,n_{i}^{v},n _{u}^{s}}\end{split}  \tag{118}\]

The total CPU BRC is:

\[ \begin{split} BRC_{c}^{\text{CPU}}=\sum_{\lambda=0}^{\Lambda-1} \sum_{u=0}^{|R|+|G|-1}BRC_{\lambda}^{\text{CPU}}\cdot z_{\lambda,n_{u}^{s}} \end{split}  \tag{119}\]

The total memory BRC is:

\[ \begin{split} BRC_{c}^{\text{mem}}=\sum_{\lambda=0}^{\Lambda-1} \sum_{u=0}^{|R|+|G|-1}BRC_{\lambda}^{\text{mem}}\cdot z_{\lambda,n_{u}^{s}} \end{split}  \tag{120}\]

The total bandwidth consumption is:

\[ \begin{split} Band_{c}=\sum_{\gamma=0}^{|\Gamma|-1}\sum_{(n_{i}^{v },n_{j}^{v})\in E^{\text{E}}_{\gamma}}\sum_{(n_{u}^{s},n_{v}^{s})\in E^{\text{E} }}b_{\gamma,n_{i}^{v},n_{j}^{v}}\cdot y_{\gamma,n_{i}^{v},n_{j}^{v},n_{u}^{s},n _{u}^{s}}\end{split}  \tag{121}\]

The total cost of activating the MDC is:

\[ \begin{split} MDC_{c}=\sum_{u=0}^{|R|-1}\rho\cdot h_{n_{u}^{s}} \end{split}  \tag{122}\]As pointed out in Section 4.3, the mapping process should try to activate as few MDCs as possible, due to the additional cost involved. To introduce this strategy to the optimization model, a value \(\rho\) that represents the activation of an MDC is defined, which is assigned a greater value than other costs. ## References

* [PERSON] and [PERSON] (2018) [PERSON]; [PERSON] Next generation cloud computing: New trends and research directions. _Future Gener. Comput. Syst._**2018**, _79_, 849-861. [CrossRef]
* [PERSON] et al. (2016) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Edge Computing: Vision and Challenges. _IEEE Internet Things J._**2016**, \(3\), 637-646. [CrossRef]
* [PERSON] (2019) [PERSON] The emergence of edge computing. _Computer_**2019**, _50_, 30-39. [CrossRef]
* [PERSON] (2019) [PERSON] Internet of Things (IoT), mobile cloud, cloudlet, mobile IoT, IoT cloud, fog, mobile edge, and edge emerging computing paradigms: Disambiguation and research directions. _J. Netw. Comput. Appl._**2019**, _128_,105-140. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Network Function Virtualization: State-of-the-Art and Research Challenges. _IEEE Commun. Surv. Tutor._**2015**, _18_, 236-262. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON]; [PERSON]; [PERSON] Network function virtualization: Challenges and opportunities for innovations. _IEEE Commun. Mag._**2015**, _53_, 90-97. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A comprehensive survey of Network Function Virtualization. _Comput. Netw._**2018**, _212-262. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON] Towards a virtual network function research agenda: A systematic literature review of VNF design considerations. _J. Netw. Comput. Appl._**2019**, _146_, 102417. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Flexibility in softwarized networks: Classifications and research challenges. _IEEE Commun. Surv. Tutor._**2019**, _21_, 2600-2636. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Cost-Efficient Service Function Chain Orchestration for Low-Latency Applications in NFV Networks. _IEEE Syst. J._**2018**, _13_, 3877-3888. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] Virtual network function embedding in real cloud environments. _Comput. Netw._**2015**, \(3\), 506-517. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Complementing IoT Servthe through Software Defined Networking and Edge Computing: A Comprehensive Survey. _IEEE Commun. Surv. Tutor._**2020**, _22_, 1761-1804. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON] Virtual network function placement and resource optimization in NFV and edge computing enabled networks.