Optimized Kuhn–Munkres with Dynamic Strategy Selection for Virtual Network Function Hot Backup Migration

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This research proposed an integer linear programming-based approximation algorithm approach for virtual network function hot backup migration. It has good research merits. The authors have some key comments that need to be addressed, so a major revision is recommended. Please refer to my comments as follows.
Comment 1. Paper’s title:
(a) “Hybrid algorithm” does not precisely describe the techniques of algorithms.
(b) Use the full name for VNF because it is not a well-known acronym.
Comment 2. Abstract:
(a) Define acronyms VNF and NP.
(b) Provide descriptions of research results (numerically) and research implications.
Comment 3. Add more terms in the keywords to better reflect the scope of the paper.
Comment 4. Carefully check the entire article to ensure that spacing is added between words and in-text citations [x]. Examples are:
- network[1].
- advancement[2].
- support[3].
Comment 5. Section 1 Introduction:
(a) Define the acronym VNF.
(ab) Update Figure 1: Within service lists, there are three possible coloured blocks, of which only two were defined. In addition, the descriptions for those arrows and linkages between edge servers should be enhanced.
(c) Enhance the discussion of research contributions with evaluation metrics.
Comment 6. Section 2 Related Works:
(a) Include more existing works that were published in 2024 and 2025 to reflect the latest developments of the research topic.
(b) Enhance the content by summarizing the results and limitations of the existing works.
Comment 7. Section 3 System Model and Problem Formulation:
(a) Regarding the formulations and constraints, clarify if some parts followed existing works. If not, justify your formulation and explain why the formulation represents generic scenarios in real-world practice.
Comment 8. Section 4 Method:
(a) Enhance the description of the linkage between algorithms 1 and 2.
(b) Would the algorithms achieve the best solution?
Comment 9. Section 5 Experiment:
(a) Do not redefine the acronym VNF.
(b) How did the scenarios reflect the applicability of the proposed algorithms in real-world environments?
(c) A comparison between the proposed work and existing works is required.

Author Response

We would like to sincerely thank you for your valuable feedback and insightful comments. We greatly appreciate the time and effort you have dedicated to reviewing our manuscript. Your suggestions have been extremely helpful in improving the quality of our work, and we have carefully addressed all the points raised. Below, we provide a detailed explanation of the revisions made in response to your comments.

Comment 1. Paper’s title:
(a) “Hybrid algorithm” does not precisely describe the techniques of algorithms.
(b) Use the full name for VNF because it is not a well-known acronym.

Response 1:
(a) The paper title has been revised to "Optimized Kuhn-Munkres with Dynamic Strategy Selection for Virtual Network Function Hot Backup Migration", highlighting the algorithm's details.

(b)The full name Virtual Network Function has been adopted.

 

Comment 2. Abstract:
(a) Define acronyms VNF and NP.
(b) Provide descriptions of research results (numerically) and research implications.
Response 2:
(a) The definitions of Virtual Network Function (VNF) and Non-deterministic Polynomial-time(NP) have been provided at their first appearances in the paper.

(b) We have revised the abstract to include numerical descriptions of the research results and clarified their implications.

Comment 3. Add more terms in the keywords to better reflect the scope of the paper.
Response 3: We have added more relevant keywords to better reflect the scope of the paper.

Comment 4. Carefully check the entire article to ensure that spacing is added between words and in-text citations [x]. Examples are:
- network[1].
- advancement[2].
- support[3].
Response 4: We have carefully checked the entire article and ensured that spacing is correctly added before all in-text citations.

 

Comment 5. Section 1 Introduction:
(a) Define the acronym VNF.
(b) Update Figure 1: Within service lists, there are three possible coloured blocks, of which only two were defined. In addition, the descriptions for those arrows and linkages between edge servers should be enhanced.
(c) Enhance the discussion of research contributions with evaluation metrics.

Response 5:

(a) We have defined the acronym VNF at its first occurrence and used the abbreviation thereafter.
(b) Figure 1 has been updated to include definitions for all colored blocks and enhanced descriptions of the arrows and linkages between edge servers.
(c) The discussion of research contributions has been enhanced by emphasizing cost savings as an evaluation metric in the Introduction.

 

Comment 6. Section 2 Related Works:
(a) Include more existing works that were published in 2024 and 2025 to reflect the latest developments of the research topic.
(b) Enhance the content by summarizing the results and limitations of the existing works.

Response 6:
(a) We have included additional relevant works from 2024 and 2025 to reflect the latest developments in the research topic.
(b) The final paragraph of the Related Works section has been enhanced to summarize the results and limitations of the existing works and highlight the differences between them and our study.

 

Comment 7. Section 3 System Model and Problem Formulation:
(a) Regarding the formulations and constraints, clarify if some parts followed existing works. If not, justify your formulation and explain why the formulation represents generic scenarios in real-world practice.

Response 7:

The formulations and constraints used in this paper are based on those commonly found in VNF migration-related literature, representing generic scenarios. This approach is intended to demonstrate the general applicability of our proposed algorithm.

 

Comment 8. Section 4 Method:
(a) Enhance the description of the linkage between algorithms 1 and 2.
(b) Would the algorithms achieve the best solution?

Response 8:
(a) We have added the following paragraph to enhance the description of the linkage between Algorithms 1 and 2: "The Algorithm 1 provides an efficient mechanism for backup relocation under constrained network conditions. However, its isolated application may lead to suboptimal decisions when environmental parameters (e.g., node density, resource availability) vary significantly. To address this limitation, we establish a hierarchical decision framework where Algorithm 1 serves as the fundamental migration engine, and Algorithm 2 operates as a meta-controller that dynamically activates either Algorithm 1 or traditional redeployment based on real-time cost-benefit analysis."
(b) Algorithm 1 performs better than traditional migration algorithms in some cases, while Algorithm 2 outperforms either Algorithm 1 or traditional migration algorithms when used alone.

Comment 9. Section 5 Experiment:
(a) Do not redefine the acronym VNF.
(b) How did the scenarios reflect the applicability of the proposed algorithms in real-world environments?
(c) A comparison between the proposed work and existing works is required.
Response 9:
(a) We have ensured that the acronym VNF is only defined at its first occurrence.
(b) The experiment scenarios incorporate commonly used constraints in VNF migration and include multiple adjustable parameters. By varying these parameters, we simulate different environments. Additionally, user requests and edge network structures are randomly generated to reflect real-world applicability.
(c) A comparison between the proposed method and existing approaches has been conducted by adjusting parameters to simulate various environments. The cost reduction ratio is calculated and presented in Figure 6.

Once again, we would like to express our sincere gratitude for your thoughtful comments and suggestions. We believe that the revisions have significantly improved the clarity and quality of the paper. Should you have any further questions or require additional clarifications, please do not hesitate to reach out. We truly appreciate your contribution to enhancing this work.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the authors propose a hybrid migration algorithm for virtual network function (VNF) backup deployment. The authors explain the motivation for their study in the introduction section, the various applications of the problem in practice, and the importance of their work. They have described the paper's contribution at the end of the introduction, which concurs with the paper's content. The list of references is novel, as most referenced papers (23/36) originate from the last five years (2020-2025), confirming that the topic is novel and actual. 

Generally speaking, the paper is very well-written, with a nice structure such that it is understandable and easy to follow. There is a list of points that I consider important to be addressed in the paper:

1. Comment concerning the abstract:

• The abstract is well-structured, but I usually prefer to have some numbers showing the efficiency of the proposed method in the abstract. For example, having a number specifying the overall performance of the model or the amount of the performance gained with the proposed approach compared to the existing approaches is very useful, as it informs a reader right away of the accomplishment in the current study. The contribution that has been made could be evaluated right away, even before reading the full paper, and this could increase the readers' interest in the subject. I would like to suggest the authors adjust this accordingly and put the efficiency of the reduced VNF costs in the abstract if they share my opinion.

2. Comment about Section 5 (Experiment):

• The authors have designed three baseline schemes to compare with their proposed approach. I wonder if there are some papers from the state-of-the-art that propose these (or similar) baselines, or if there are some papers that deal with similar schemes as designed. Is it possible to include some references to those papers (if such exist)? For example, I believe that it would be possible at least to include a reference to the conventional VNF migration method (baseline scheme 2).

3. Comment about the Section 6 (Conclusion):

• The paper is concluded and the authors mention their future goals, but they do not mention the limitations of their proposed design. The limitation section should be included in the paper, and the authors should comment on the main shortcomings of their proposed approach or the weak points of their methodology if those exist in the paper. Also, the future work could be extended. I would kindly ask the authors to address this accordingly.

4. The references in the paper follow the order they appear in the text, and all figures are referenced correctly. There are some general comments about the formatting of the paper:

• There are some abbreviations whose full names are not given as required. For example, although VNF is a standardized term that is commonly used as an abbreviation in the papers, I believe that the full name of VNF abbreviation should be given in the abstract.
• In general, the full name of each abbreviation should be given when first mentioned, so please address this accordingly. For example, I have noticed that VNF is used before providing its full name in the main paper text. Also, I might be wrong, but this could be the case with and FMEC, DDQP, MTTN, MTTR, so please check all the abbreviations you have.
• There are a few abbreviations whose full names are given more than once (VNF, SFC, FMEC...).
• Also, the full name of the abbreviation is mostly given as „Full name (XY)“, where XY is the abbreviation itself. However, there are few places where the full name of the abbreviation is given as „XY (Full name)“, so please provide the full names of abbreviations according to journal formatting requirements and be consistent throughout the paper.

Comments for author File: Comments.pdf

Author Response

We would like to sincerely thank you for your valuable feedback and insightful comments. We greatly appreciate the time and effort you have dedicated to reviewing our manuscript. Your suggestions have been extremely helpful in improving the quality of our work, and we have carefully addressed all the points raised. Below, we provide a detailed explanation of the revisions made in response to your comments.


1. Comment concerning the abstract:

The abstract is well-structured, but I usually prefer to have some numbers showing the efficiency of the proposed method in the abstract. For example, having a number specifying the overall performance of the model or the amount of the performance gained with the proposed approach compared to the existing approaches is very useful, as it informs a reader right away of the accomplishment in the current study. The contribution that has been made could be evaluated right away, even before reading the full paper, and this could increase the readers' interest in the subject. I would like to suggest the authors adjust this accordingly and put the efficiency of the reduced VNF costs in the abstract if they share my opinion.

Response to Comment 1:

We have revised the abstract to include numerical results demonstrating the efficiency of the proposed method, specifically highlighting the reduction in VNF costs. 

2. Comment about Section 5 (Experiment):

The authors have designed three baseline schemes to compare with their proposed approach. I wonder if there are some papers from the state-of-the-art that propose these (or similar) baselines, or if there are some papers that deal with similar schemes as designed. Is it possible to include some references to those papers (if such exist)? For example, I believe that it would be possible at least to include a reference to the conventional VNF migration method (baseline scheme 2).

Response to Comment 2:
We have added references to existing papers that propose similar conventional VNF migration methods (baseline scheme 2). Since the baseline algorithms in this paper are adapted with modifications to fit our specific constraints, they are not exact replications of existing methods. Additionally, our proposed hybrid algorithm (Algorithm 2) integrates both the backup migration algorithm (Algorithm 1) and existing approaches, meaning improvements in existing methods also contribute to the performance enhancement of our proposed approach.

3. Comment about the Section 6 (Conclusion):

The paper is concluded and the authors mention their future goals, but they do not mention the limitations of their proposed design. The limitation section should be included in the paper, and the authors should comment on the main shortcomings of their proposed approach or the weak points of their methodology if those exist in the paper. Also, the future work could be extended. I would kindly ask the authors to address this accordingly.

Response to Comment 3:
We have revised the conclusion to explicitly highlight the main limitations of our proposed approach before discussing future work. Additionally, we have expanded the future work section to provide a more comprehensive outlook on potential research directions.

4. The references in the paper follow the order they appear in the text, and all figures are referenced correctly. There are some general comments about the formatting of the paper:

• There are some abbreviations whose full names are not given as required. For example, although VNF is a standardized term that is commonly used as an abbreviation in the papers, I believe that the full name of VNF abbreviation should be given in the abstract.
• In general, the full name of each abbreviation should be given when first mentioned, so please address this accordingly. For example, I have noticed that VNF is used before providing its full name in the main paper text. Also, I might be wrong, but this could be the case with and FMEC, DDQP, MTTN, MTTR, so please check all the abbreviations you have.
• There are a few abbreviations whose full names are given more than once (VNF, SFC, FMEC...).
• Also, the full name of the abbreviation is mostly given as „Full name (XY)“, where XY is the abbreviation itself. However, there are few places where the full name of the abbreviation is given as „XY (Full name)“, so please provide the full names of abbreviations according to journal formatting requirements and be consistent throughout the paper.

Response to Comment 4:
We have carefully reviewed all abbreviations in the paper and ensured that each is defined in the format “Full Name (Abbreviation)” upon its first occurrence. Subsequent mentions use only the abbreviation. Additionally, we have removed redundant definitions to maintain consistency throughout the paper.

Once again, we would like to express our sincere gratitude for your thoughtful comments and suggestions. We believe that the revisions have significantly improved the clarity and quality of the paper. Should you have any further questions or require additional clarifications, please do not hesitate to reach out. We truly appreciate your contribution to enhancing this work.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper studies algorithms to back up VNFs in mobile edge networks. Algorithms are proposed. Some experimental evaluations are reported. The reviewer has the following comments.

1. Most figures are rough and do not contain useful information. For example, what is the use of Fig. 1? How does it show delay sensitivity?

 

2. What does VNF stand for? The full term is not given until in the middle part of the paper.

 

3. The idea is to use VNF backups instead of mitigating VNFs between servers. The novelty seems limited. You may want to dig this idea a bit more to demonstrate further interesting novelty.

 

4. The development of the proposed design is rough. In some occasions, f_i\in{r_m}; in other occasions, f_i\in{F}. Why do you back up VNFs on two separate servers? Why not other numbers of backup servers? Equations (1) and (2) seem to conflict with each other. Equation (6) could incur misunderstanding.

 

5. How does your algorithm determine the backup servers? This is actually important as the backup server affects the performance of the proposed VNF system. Also, does your algorithm consider the dynamic network conditions? It seems not as you consider link delay is a constant. If so, you need to justify the rational reasons for this assumption.

 

6. There are many studies that improve delays while reducing the cost. For example, delay-optimal distributed edge computing in wireless edge networks, efficient resource utilisation for multi-flow wireless multicasting transmissions. Why cannot they be applied in VNF-based edge networks? It would be better if you could analyse and so to highlight the importance of the strategy of VNF backups. Also, the necessity of proposing your algorithms? In fact, it would be interesting if you could compare your VNF backup scheme with these schemes in VNFs.

 

7. The evaluation section is rough. The performance metrics described in the paragraphs are different from those on the figures. It is not professional to just name your algorithm as “my algorithm”. How do you simulate mobile entities? The cost of your proposal should be analysed.

 

Author Response

We would like to sincerely thank you for your valuable feedback and insightful comments. We greatly appreciate the time and effort you have dedicated to reviewing our manuscript. Your suggestions have been extremely helpful in improving the quality of our work, and we have carefully addressed all the points raised. Below, we provide a detailed explanation of the revisions made in response to your comments.


Comments 1:

Most figures are rough and do not contain useful information. For example, what is the use of Fig. 1? How does it show delay sensitivity?

Response to Comment 1:
We have revised the figures to improve clarity and enhance their informative value. For example, in Figure 1, we have highlighted the changes in delay before and after VNF migration to emphasize the necessity of backup migration or redeployment.

 

Comments 2:

What does VNF stand for? The full term is not given until in the middle part of the paper.

Response to Comment 2:
We have revised the paper to ensure that the full term for VNF is provided upon its first occurrence, with the abbreviation used consistently thereafter.

Comments 3:

The idea is to use VNF backups instead of mitigating VNFs between servers. The novelty seems limited. You may want to dig this idea a bit more to demonstrate further interesting novelty.

Response to Comment 3:
The novelty of our approach lies in dynamically selecting between VNF migration and redeployment by leveraging both primary VNF instances and hot backups, effectively reducing migration costs by approximately 15%. Additionally, we have revised the conclusion to further discuss the limitations of our work and potential future research directions.

Comments 4:

The development of the proposed design is rough. In some occasions, f_i\in{r_m}; in other occasions, f_i\in{F}. Why do you back up VNFs on two separate servers? Why not other numbers of backup servers? Equations (1) and (2) seem to conflict with each other. Equation (6) could incur misunderstanding.

Response to Comment 4:
We have revised the notation to improve clarity and avoid misunderstandings. Specifically, we updated f_i to f_{m,i} and changed it to f_{m,i} ∈ F_m, with r_m = (F_m, T^{err}_m, C_m), to indicate that it belongs to a specific user request rather than the global set. Additionally, we modified the variables in Equations 1 and 2 from P_{f_i,v_n,r_m} to P_{f_{m,i},v_n} to eliminate potential conflicts. Equation 6 has also been updated accordingly.

Comments 5:

How does your algorithm determine the backup servers? This is actually important as the backup server affects the performance of the proposed VNF system. Also, does your algorithm consider the dynamic network conditions? It seems not as you consider link delay is a constant. If so, you need to justify the rational reasons for this assumption.

Response to Comment 5:
The selection of backup servers is determined by Equation 11 in Algorithm 1, which takes into account factors such as computational resources, latency, and other relevant conditions. To improve clarity, we added line 10 to explicitly reflect these conditions. If other resource limitations need to be considered, they can also be incorporated into this section of the algorithm.

Regarding dynamic network conditions, our approach considers the Follow-Me Mobile Edge Cloud scenario, where network function instances follow user requests as they move within the edge network. We acknowledge that the link delay is assumed to be constant in our model, and relevant citations have been added to justify this assumption. However, if link delay variations need to be considered, they can be incorporated in the first line of Algorithm 1 during network model initialization, which would slightly increase the computational overhead without affecting the overall performance of the algorithm.

Comments 6:

There are many studies that improve delays while reducing the cost. For example, delay-optimal distributed edge computing in wireless edge networks, efficient resource utilisation for multi-flow wireless multicasting transmissions. Why cannot they be applied in VNF-based edge networks? It would be better if you could analyse and so to highlight the importance of the strategy of VNF backups. Also, the necessity of proposing your algorithms? In fact, it would be interesting if you could compare your VNF backup scheme with these schemes in VNFs.

Response to Comment 6:
We have added a comparative analysis in the last paragraph of the Related Works section, starting with "However," where we discuss the differences between our proposed VNF backup scheme and existing approaches. This comparison highlights the necessity of our approach and demonstrates why the strategy of using VNF backups is crucial. Additionally, we explain why these existing delay-improvement strategies cannot be directly applied to VNF-based edge networks, further emphasizing the relevance and innovation of our proposed algorithm.

Comments 7:

The evaluation section is rough. The performance metrics described in the paragraphs are different from those on the figures. It is not professional to just name your algorithm as “my algorithm”. How do you simulate mobile entities? The cost of your proposal should be analysed.

Response to Comment 7:
We have revised the figure legends to replace the term "my algorithm" with the more professional "Optimized BVNF migration algorithm." In the experimental setup section, we have clarified that mobile entities are simulated by randomly generating user requests, which reflects the movement of users within the network. Additionally, Figure 6 illustrates the cost reduction ratio, which varies with different parameter settings, to better demonstrate the performance of our proposed approach.

 

Once again, we would like to express our sincere gratitude for your thoughtful comments and suggestions. We believe that the revisions have significantly improved the clarity and quality of the paper. Should you have any further questions or require additional clarifications, please do not hesitate to reach out. We truly appreciate your contribution to enhancing this work.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have enhanced the quality of the article. I have some minor follow-up comments.
Follow-up comment 1. Figure 1: Why were different colors used for arrows?
Follow-up comment 2. Regarding research contributions, please include numerical results.
Follow-up comment 3. Figure 2: It is not sufficiently clear about points A to D.
Follow-up comment 4. Experiments: Figures did not report results of all scenarios (with different step size of parameters).

Author Response

We sincerely appreciate your valuable comments and suggestions, which have helped us improve the clarity and quality of our manuscript. We have carefully addressed each of your comments and made the necessary revisions accordingly. Below, we provide detailed responses to each of your points.

Comments 1:

Figure 1: Why were different colors used for arrows?
Response 1:
Thanks for your comments. Different colors were used in Figure 1 to distinguish various types of interactions. Specifically, the red arrows represent migration or redeployment actions, the blue brackets indicate latency, and the black bidirectional arrows illustrate data exchanges between mobile users and virtual network function instances. This color differentiation enhances clarity and helps visually convey the distinct roles of these elements in the system.

 

Comments 2:

Regarding research contributions, please include numerical results.
Response 2:
Thank you very much for your comments. We have included numerical results to highlight our research contributions. Specifically, our proposed approach reduces the migration cost of VNF hot backups by approximately 15% while ensuring the same level of latency requirements as existing methods. These numerical results have been explicitly stated in the abstract, the research contributions section, and the experimental results section to emphasize the impact of our work.

 

Comments 3:

Figure 2: It is not sufficiently clear about points A to D.
Response 3:
Thanks for your comments. We have updated Figure 2 by adding arrows to indicate user movement, making it clearer that the virtual network function instance moves from point A to point B. Additionally, we have revised the figure description in the paper to explicitly explain the rationale behind the backup migration from point C to point D. These enhancements improve clarity and help readers better understand the example.

 

Comments 4:

Experiments: Figures did not report results of all scenarios (with different step size of parameters).
Response 4:
Thanks for your helpful comments. We identified an issue where one figure was misnamed and not placed within the correct scenario subsection, which may have led to misunderstandings. We have now revised the experimental section to ensure that each figure is correctly named and placed in the appropriate scenario subsection. Additionally, we have provided clarifications in the paper to explicitly describe the results corresponding to each scenario.

Once again, we are grateful for your insightful feedback, which has significantly contributed to enhancing our work. We hope that our revisions and explanations satisfactorily address all of your concerns. Please do not hesitate to let us know if any further improvements are needed.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for revising the paper. However, the reviewer still has the following comments.

1. Some figures still need improvement. For example, fig. 1, the fonts are too small to read. Fonts in the simulation result figures should be enlarged.
2. Mathematical symbols still need to be improved. For example, what is T_{m}^{err}? What is C_m? Please check all design description and math symbols/expressions to ensure such issues fully addressed.
3. There are many studies focusing on avoiding hotspots, e.g., resource utilisation, efficient routing, and more. The paper should review these studies and explain why your solution using backup servers should be used in your communication scenario. For example, hotspot avoidance for p2p streaming distribution application: a game theoretic approach, efficient resource utilisation for multi-flow wireless multicasting transmissions, etc.
4. Please accommodate your answers to my previous and current comments in the paper. 

Author Response

We sincerely appreciate your valuable comments and suggestions, which have helped us improve the clarity and quality of our manuscript. We have carefully addressed each of your comments and made the necessary revisions accordingly. Below, we provide detailed responses to each of your points.

 

Comments 1:

Some figures still need improvement. For example, fig. 1, the fonts are too small to read. Fonts in the simulation result figures should be enlarged.

Response 1:
Thanks for your comments. We have enlarged the fonts in all figures, including Figure 1 and the simulation result figures, to improve readability.

 

Comments 2:

Mathematical symbols still need to be improved. For example, what is T_{m}^{err}? What is C_m? Please check all design description and math symbols/expressions to ensure such issues fully addressed.
Response 2:
Thanks for your helpful comments. We have standardized the notation by unifying T^{err} as T_{m}^{err}​ and C as C_m​. Additionally, we have provided clear explanations for these symbols in the relevant sections of the paper, including the notation table, to ensure consistency and clarity.

 

Comments 3:

There are many studies focusing on avoiding hotspots, e.g., resource utilisation, efficient routing, and more. The paper should review these studies and explain why your solution using backup servers should be used in your communication scenario. For example, hotspot avoidance for p2p streaming distribution application: a game theoretic approach, efficient resource utilisation for multi-flow wireless multicasting transmissions, etc.
Response 3:
Thank you very much for your comments. We have included the three papers you mentioned in the Related Works section. In the paper, we discuss the aspects of these studies that we found particularly valuable and how they differ from our work.

 

Comments 4:

Please accommodate your answers to my previous and current comments in the paper.

Response 4:

Thank you for your support. We have re-examined the paper based on both your current and previous suggestions, as well as the corresponding references you recommended.

Once again, we are grateful for your insightful feedback, which has significantly contributed to enhancing our work. We hope that our revisions and explanations satisfactorily address all of your concerns. Please do not hesitate to let us know if any further improvements are needed.

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for revising the paper. I still have some minor suggestions.

Section 4 could have a more informative title instead of “Method”.

The evaluation figures should be improved. Curves in the figures should not be covered by labels etc. You may consider plotting a larger figure in order to clearly accommodate all curves etc. Also, you should provide units for your captions on the y-axes. What is the unit for your average delay? Also, what do you mean by “Total Average of Recovery Delay”? Average is average, why total? Also, what is “Total Request Mitigation Cost”? How do you measure this in your experiments?

Author Response

reviewer3：

Comments 1:

Thank you for revising the paper. I still have some minor suggestions.

Section 4 could have a more informative title instead of “Method”.

The evaluation figures should be improved. Curves in the figures should not be covered by labels etc. You may consider plotting a larger figure in order to clearly accommodate all curves etc. Also, you should provide units for your captions on the y-axes. What is the unit for your average delay? Also, what do you mean by “Total Average of Recovery Delay”? Average is average, why total? Also, what is “Total Request Mitigation Cost”? How do you measure this in your experiments?

Response 1:

Thank you for your valuable feedback. We have carefully addressed your suggestions as follows:

• We have revised the title of Section 4 to “Optimized Algorithm for the BVNF Migration Problem” to make it more informative.
• The evaluation figures have been improved to ensure that labels do not obscure the curves. Most labels are now positioned above the curves for better readability.
• The y-axis labels have been updated to explicitly include units for clarity.
• The term “Total Average of Recovery Delay” was indeed a mistake, and we have corrected it to “Average of Recovery Delay.” We appreciate your attention to this detail.
• Regarding “Total Request Mitigation Cost,” this metric is derived from Equation (12). We have revised the experimental section to provide a clearer explanation of its measurement and significance.

We sincerely appreciate your insightful comments, which have helped us refine our work. Thank you again for your time and effort in reviewing our paper.