Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors
Round 1
Reviewer 1 Report
In the article “Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors” the authors propose a schedulability test for EDF based scheduling algorithm called SSF-EDF and three different processor allocation strategies for asymmetric multiprocessor systems.
The research is incremental, but relevant to the real-time systems domain.
Regarding the relevance to the special issue, this reviewer could not find any direct connection between the proposed research and “Cyber-Physical Systems for Intelligent Transportation Systems”. The proposed research is mainly theoretical as no implementation support is provided. Moreover, the results are only simulated. As the real-time operating systems in general and the ones compliant with different standards in Intelligent Transportation Systems do not implement EDF as a scheduling policy at any level (neither single processor nor multi-processor), it is hard to believe that the proposed allocation schemes could be directly applied in this field very soon. I would recommend the authors to apply to a more suitable mdpi journal special issue or to better clarify the connection with the Intelligent Transportation System domain.
Here are some comments for the authors, regarding the proposed article:
(line 8) Please do not use acronyms in the abstract. Use the full name of the Earliest Deadline First algorithm. And you should also provide the meaning of every acronym when they are first used.
(line 66) Please check again the value range of λ (lambda). As s(i+1) is greater than s(s), then it seems unlikely that lambda could be 0, otherwise please give an example for this limit.
(line 68) Please give the full name of the SSF-EDF algorithm. And because this algorithm is not presented in this paper for the first time, a reference and a brief description should also be included.
(line 65 and line 85) On line 65 the authors say “The processing speed of the processors increases from small to large, that is, the processing speed of pi is equal to or slower than that of pi+1”, but on line 85 they say that P1 is faster than P2. Is it not a contradiction?
The relationship between the task parameters and the processing speed is not presented clearly in the article. The execution time should scale with the processing speed, but T and D should not as Figure 1 shows. Still, this reviewer believes that extra explanations should be added.
(line 111) If “the total execution time of exactly v processors in [Ai,j, Ai,j + Di) is denoted by Jv”, then J0 doesn’t mean the total execution time of 0 processors (which is of course 0)? The explanation on line 112 is confusing. The following formula needs also a little clarification: if Jv already sums the execution time for v processors, why should we sum them again for determining the work done (W) for the same time interval?
This reviewer suggests that the authors add W and Q to table 1.
(line 148) For BSF and FSF, the full names should be provided and briefly described and referenced.
In Figures 3 to 7, SSF has the poorest performance. In conclusion, how is the proposed improvement relevant in this context?
Author Response
Original Manuscript Number:applsci-2200957
Original Article Title: Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors
Dear Editor, Dear Reviewers:
Thanks very much for the time and effort that you have put into reviewing the previous version of the manuscript entitled “Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors”(ID: applsci-2200957). We really appreciate all your comments and suggestions which have enabled us to improve our work! We have studied these comments carefully and tried our best to revise and improve the manuscript.
Our revision mainly focuses on the following aspects: 1)At the beginning of the paper, we clarified the research significance of this work to the field of intelligent transportation. 2)We have described three scheduling algorithms in detail. 3)We have explained each formula and symbol in more detail. 4)We added more experiments to demonstrate the advantages of our proposed method. 5)The English writing has been improved. Revised portions are highlighted in the paper. Please find my itemized responses below and my revisions in the re-submitted files.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We really appreciate for Editor and Reviewers’ warm work earnestly and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Peng Wu.
Reviewer #1:
Comment # 1: Regarding the relevance to the special issue, this reviewer could not find any direct connection between the proposed research and “Cyber-Physical Systems for Intelligent Transportation Systems”. The proposed research is mainly theoretical as no implementation support is provided. Moreover, the results are only simulated. As the real-time operating systems in general and the ones compliant with different standards in Intelligent Transportation Systems do not implement EDF as a scheduling policy at any level (neither single processor nor multi-processor), it is hard to believe that the proposed allocation schemes could be directly applied in this field very soon. I would recommend the authors to apply to a more suitable mdpi journal special issue or to better clarify the connection with the Intelligent Transportation System domain.
Author response: Thank you for your precious opinion. Now the field of unmanned vehicle research is very hot, and many large companies have also invested a lot of energy in the research of unmanned vehicles. The Linux kernel is used in many companies' unmanned vehicle operating systems, such as Tesla's operating system. The process scheduling of the Linux kernel uses the completely fair scheduling algorithm (CFS). EDF cannot be directly applied to the field of intelligent transportation, but it still has a good reference for the scheduling algorithm of the unmanned vehicle operating system. Thank you for this suggestion. In response to your comments, we have also added corresponding descriptions to lines 48-54 of the article.
Comment # 2: Please do not use acronyms in the abstract. Use the full name of the Earliest Deadline First algorithm. And you should also provide the meaning of every acronym when they are first used.
Author response: Thanks for pointing out the error. In response to your comments, we have changed EDF to the full name earliest deadline first on line 8.
Comment # 3: Please check again the value range of λ (lambda). As s(i+1) is greater than s(s), then it seems unlikely that lambda could be 0, otherwise please give an example for this limit.
Author response: Thank you very much for your valuable opinion. The value of λ (lambda) cannot be 0 indeed. In response to your comments, we have modified the value range of λ(lambda) on line 93.
Comment # 4: Please give the full name of the SSF-EDF algorithm. And because this algorithm is not presented in this paper for the first time, a reference and a brief description should also be included.
Author response: Thanks for your great comments. The full name of SSF-EDF is the slowest speed fit earliest deadline first, which is proposed for the first time in this paper. The algorithm is that the smaller the task deadline, the higher the assigned priority. Its processor allocation strategy is that high priority tasks are given priority to the slowest processor. And the algorithm supports preemption. In response to your comments, we have modified line 66.
Comment # 5: On line 65 the authors say “The processing speed of the processors increases from small to large, that is, the processing speed of pi is equal to or slower than that of pi+1”, but on line 85 they say that P1 is faster than P2. Is it not a contradiction?
Author response: Thank you very much for pointing out the error. In response to your comments, we have modified line 92 and changed p1 to the slowest processor.
Comment # 6: The relationship between the task parameters and the processing speed is not presented clearly in the article. The execution time should scale with the processing speed, but T and D should not as Figure 1 shows. Still, this reviewer believes that extra explanations should be added.
Author response: Thanks for your advice. In response to your suggestion, we have revised Figure 1 and explained the relationship between task execution time and processor speed in lines 85-91 and 145-149 of the paper.
Comment # 7: If “the total execution time of exactly v processors in [Ai,j, Ai,j + Di) is denoted by Jv”, then J0 doesn’t mean the total execution time of 0 processors (which is of course 0)? The explanation on line 112 is confusing. The following formula needs also a little clarification: if Jv already sums the execution time for v processors, why should we sum them again for determining the work done (W) for the same time interval?
Author response: Thanks for your advice. J_v represents the time when exactly v processors are executing. If only one processor happens to be executing in a certain period of time, then its execution time is J_1. In another period of time, there are two processors executing, so its execution time is J_2. And J_0 means the time when the processors are all in the idle state, and the value of J_0 is not necessarily 0 at this time. But under the assumption in the article, tau_i, j missed the deadline, then there must be processors executing during the time interval. Therefore, J_0 must be 0 at this time.
The explanation for the following formula is: J_v just means the length of time that v processors are executing. During a time interval, the number of running processors is changing. During this time interval, we would have J_0, J_1, J_2, etc. So over time intervals we need to sum to determine the total execution time. In response to your comments, we have described and explained the definition of J_v in more detail in lines 137-144 for the convenience of readers.
Comment # 8: This reviewer suggests that the authors add W and Q to table 1.
Author response: Thank you so much for your valuable advice. In response to your comments, we have revised Table 1 by adding W and Q to Table 1.
Comment # 9: For BSF and FSF, the full names should be provided and briefly described and referenced.
Author response: You have raised an important question and thank you for providing this insight. The full name of BSF-EDF is the best speed fit earliest deadline first. The task allocation strategy of the algorithm is that the smaller the task deadline, the higher the assigned priority. High priority tasks are assigned to the processor with the most suitable speed, and preemption is supported. The full name of FSF-EDF is the fastest speed fit earliest deadline first. The task allocation strategy of the algorithm is that the smaller the task deadline, the higher the assigned priority. High priority tasks are assigned to the fastest processor first, and preemption is supported. In response to your comments, we have revised lines 61-68 to describe BSF-EDF and FSF-EDF in detail.
Comment # 10: In Figures 3 to 7, SSF has the poorest performance. In conclusion, how is the proposed improvement relevant in this context?
Author response: Thank you for this great advice. In response to your comments, we have supplemented some experiments in the experiment section, as shown in Figure 8 and Figure 9. SSF-EDF outperforms the other two methods in terms of the number of task migrations and effective processor utilization.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents the schedulability test of SSF-EDF, a processor allocation strategy for asymmetric multiprocessor systems. In addition, the paper compares three different processor allocation strategies: BSF-EDF, SSF-EDF, and FSF-EDF. The technical content of the paper seems mostly sound, but I have several major concerns about the paper.
First of all, the topic of the paper seems not suitable for the special issue "Cyber-Physical Systems for Intelligent Transportation Systems." The paper only discusses task scheduling on asymmetric multiprocessor systems without considering intelligent transportation systems. Therefore, I have doubts that this paper should be accepted for the special issue.
Second, the paper does not motivate the importance of SSF-EDF well. It mainly focuses on the schedulability test of SSF-EDF, but the evaluation results show that BSF-EDF always outperforms the other processor allocation strategies, including SSF-EDF. The results significantly weaken the need for the schedulability test of SSF-EDF. If SSF-EDF always performs worst, what is the point of analyzing SSF-EDF in depth?
Third, the derivation of the schedulability test is difficult to follow, worsening the readability of the paper. The paper uses some notations such as J_v without clearly defining them. Also, the paper has many logical jumps, especially in Section 3.1. I think the paper should provide more detailed explanations for readers.
Lastly, the paper compares the three processor allocation strategies, but it does not explain the algorithms of the two processor allocation strategies, BSF-EDF and FSF-EDF. I think it would be good to have a brief description of each algorithm in the paper.
Other comments and questions:
- I would suggest using a different index variable for the processor-related notations such as s_i and S_i to avoid confusion because i is used to index tasks.
- Page 4: The paper mentions that the slowest processor speed is set to 1, but in Example 1, the paper uses a processor speed of less than 1. Also, in Example 1, P1 seems the slowest processor but the paper refers to it as "the fastest processor".
- Page 5: I don't understand why "Because of the nature of SSF-EDF, tau_i,j always runs on one of the processors during the interval. (...)". As far as I understood, tau_i,j should be the lowest priority task with the latest deadline, so it would be executed on the slowest processor only when no other tasks are running according to SSF-EDF.
- Page 5: I don't understand why "Notice, we can always find a moment t_0 that satisfies this formula". Please add more explanations about this claim.
- Page 6: this job -> these jobs?
- Page 7: I don't understand why "So the execution time of tau_p,q in [A_p,q, t_0) is no less than that of the sum of s_1 * J_v".
Please correct me if I am mistaken.
Author Response
Original Manuscript Number:applsci-2200957
Original Article Title: Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors
Dear Editor, Dear Reviewers:
Thanks very much for the time and effort that you have put into reviewing the previous version of the manuscript entitled “Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors”(ID: applsci-2200957). We really appreciate all your comments and suggestions which have enabled us to improve our work! We have studied these comments carefully and tried our best to revise and improve the manuscript.
Our revision mainly focuses on the following aspects: 1)At the beginning of the paper, we clarified the research significance of this work to the field of intelligent transportation. 2)We added more experiments to demonstrate the advantages of our proposed method. 3)We have explained each formula and symbol in more detail and add the main symbols in Table 1. 4)We have described three scheduling algorithms in detail. 5)The English writing has been improved. Revised portions are highlighted in the paper. Please find my itemized responses below and my revisions in the re-submitted files.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We really appreciate for Editor and Reviewers’ warm work earnestly and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Peng Wu.
Reviewer #2:
Comment # 1: First of all, the topic of the paper seems not suitable for the special issue "Cyber-Physical Systems for Intelligent Transportation Systems." The paper only discusses task scheduling on asymmetric multiprocessor systems without considering intelligent transportation systems. Therefore, I have doubts that this paper should be accepted for the special issue.
Author response: Thank you for your precious opinion. Now the field of unmanned vehicle research is very hot, and many large companies have also invested a lot of energy in the research of unmanned vehicles. The Linux kernel is used in many companies' unmanned vehicle operating systems, such as Tesla's operating system. The process scheduling of the Linux kernel uses the completely fair scheduling algorithm (CFS). EDF cannot be directly applied to the field of intelligent transportation, but it still has a good reference for the scheduling algorithm of the unmanned vehicle operating system. Thank you for this suggestion. In response to your comments, we have also added corresponding descriptions to lines 48-54 of the article.
Comment # 2: Second, the paper does not motivate the importance of SSF-EDF well. It mainly focuses on the schedulability test of SSF-EDF, but the evaluation results show that BSF-EDF always outperforms the other processor allocation strategies, including SSF-EDF. The results significantly weaken the need for the schedulability test of SSF-EDF. If SSF-EDF always performs worst, what is the point of analyzing SSF-EDF in depth?
Author response: Thank you for this great advice. In response to your comments, we have supplemented some experiments in the experiment section, as shown in Figure 8 and Figure 9. SSF-EDF outperforms the other two methods in terms of the number of task migrations and effective processor utilization.
Comment # 3: Third, the derivation of the schedulability test is difficult to follow, worsening the readability of the paper. The paper uses some notations such as J_v without clearly defining them. Also, the paper has many logical jumps, especially in Section 3.1. I think the paper should provide more detailed explanations for readers.
Author response: Thanks for your advice. In response to your comments, we have not only added some main symbols to Table 1, but also explained J_v and other symbols in more detail in lines 137-144 to facilitate readers' understanding.
Comment # 4: Lastly, the paper compares the three processor allocation strategies, but it does not explain the algorithms of the two processor allocation strategies, BSF-EDF and FSF-EDF. I think it would be good to have a brief description of each algorithm in the paper.
Author response: You have raised an important question and thank you for providing this insight. The full name of BSF-EDF is the best speed fit earliest deadline first. The task allocation strategy of the algorithm is that the smaller the task deadline, the higher the assigned priority. High priority tasks are assigned to the processor with the most suitable speed, and preemption is supported. The full name of FSF-EDF is the fastest speed fit earliest deadline first. The task allocation strategy of the algorithm is that the smaller the task deadline, the higher the assigned priority. High priority tasks are assigned to the fastest processor first, and preemption is supported. In response to your comments, we have revised lines 61-68 to describe BSF-EDF and FSF-EDF in detail.
Comment # 5: I would suggest using a different index variable for the processor-related notations such as s_i and S_i to avoid confusion because i is used to index tasks.
Author response: Thank you for your great advice. In response to your suggestion, we have changed the index i of S_i to k in Table 1, which is S_k.
Comment # 6: The paper mentions that the slowest processor speed is set to 1, but in Example 1, the paper uses a processor speed of less than 1. Also, in Example 1, P1 seems the slowest processor but the paper refers to it as "the fastest processor".
Author response: Thank you very much for pointing out the error. In response to your comments, we have redesigned Example 1 and modified Figure 1. And we have changed p1 to the slowest processor on line 92.
Comment # 7: I don't understand why "Because of the nature of SSF-EDF, tau_i,j always runs on one of the processors during the interval. (...)". As far as I understood, tau_i,j should be the lowest priority task with the latest deadline, so it would be executed on the slowest processor only when no other tasks are running according to SSF-EDF.
Author response: Thank you very much for your comments. tau_i,j is indeed only executed on the slowest processor if no other tasks are running. This section has been revised to describe it in more detail for the reader's convenience.
Comment # 8: I don't understand why "Notice, we can always find a moment t_0 that satisfies this formula". Please add more explanations about this claim.
Author response: Thanks for your suggestion. Please let us explain it to you. We can derive formula (14) from (12) and (13). And we can find many time points t satisfying the condition t less than or equal to A_i,j. t_0 is the earliest one among all the time points t that satisfy the condition. At t_0, formula (14) still holds. So we can always find a time t_0 that satisfies these formulas. In response to your comments, we have described this section in more detail to facilitate readers' understanding.
Comment # 9: this job -> these jobs?
Author response: Thanks for pointing out the error. We have changed "this job" to "these jobs" in response to your comments
Comment # 10: I don't understand why "So the execution time of tau_p,q in [A_p,q, t_0) is no less than that of the sum of s_1 * J_v".
Author response: Thank you for your valuable opinion. Please let us explain it to you. Due to tau_p,q is not completed before t_0. So the worst execution time of tau_p,q is not less than the execution time in [A_p,q, t_0). The interpretation of the sum of s_1 * J_v is as follows: first, J_v represents the time when v processors are executing. If only one processor is executing at a certain moment, its execution time is J_1. At another moment, there are two processors executing, so its execution time is J_2. So during the time interval, the number of running processors is changing. So during the time interval, the number of running processors is changing. During this time interval, we would have J_0, J_1, J_2, etc. So we need to sum them to determine a total execution time. However, due to the different speeds of the allocated processors, the effects executed at the same time will also be different. For example, in a time interval of length t, the actual execution time of a processor with speed = 1 is t, and the actual execution time of a processor with speed = 2 is 2t. So in the process of summing we need to take into account the speed of the allocation processor. Finally, we need to compare the worst execution time with the actual execution time. So we use s_1 as the processor allocation speed in the summing process. In response to your comments, this article has provided a more detailed description of this part to facilitate readers' understanding.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors focus their study on the performance analysis of asymmetric multiprocessors within computing platforms. Specifically, the authors compare the effects of three EDF scheduling algorithms under different processor allocation strategies on performance asymmetric multiprocessors and they propose an efficient schedulability analysis for an allocation strategy that assigns high priority tasks to the slowest processors. The manuscript is overall well written and easy to follow and the authors have well thought out their main contributions. The provided theoretical analysis is concrete, complete, and correct and the authors have provided all the intermediate steps in order to enable the average reader to easily follow it. Furthermore, the authors have provided a very detailed set of numerical results in order to show the pure performance and the operation of the proposed framework. The authors are highly encouraged to consider the following suggestions provided by the reviewer in order to improve the scientific depth of their manuscript, as well as they need to address the following minor comments in order to improve the quality of presentation of their manuscript. Initially, in Section 1, the authors need to discuss several existing research works that deal with the concept of approximate computing, such as Energy Efficient Edge Computing Enabled by Satisfaction Games and Approximate Computing, doi: 10.1109/TGCN.2021.3122911, in order to improve the scheduling of the computing tasks within the microprocessors. In Section 2, the authors need to include a table summarizing the main notation that has been used in the paper and also provide the units of the corresponding metrics which currently are missing from the provided analysis. Furthermore, in section three, the authors need to discuss the computational complexity of the proposed scheduling approaches and discuss if they can be implemented in a real time or even close to real time manner. Based on the previous comment, in Section 4, the authors need to provide some indicative numerical results showing the real execution time of the proposed scheduling approaches and discuss the real-time applicability. Furthermore, the authors need to compare those three approaches to other approaches that have been introduced in the state-of-the-art and justify their main operational characteristics and benefits compared to other approaches. Finally, the overall manuscript needs to be checked for typos, syntax, and grammar errors in order to improve the quality of its presentation.
Author Response
Original Manuscript Number:applsci-2200957
Original Article Title: Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors
Dear Editor, Dear Reviewers:
Thanks very much for the time and effort that you have put into reviewing the previous version of the manuscript entitled “Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors”(ID: applsci-2200957). We really appreciate all your comments and suggestions which have enabled us to improve our work! We have studied these comments carefully and tried our best to revise and improve the manuscript.
Our revision mainly focuses on the following aspects:1)We have added edge computing to the discussion at the beginning of the paper and cited relevant literature. 2)We have added the main symbols to Table 1 and described them. 3)We have included a discussion of time complexity in the text. 4)We added more experiments to demonstrate the advantages of our proposed method. 5)The English writing has been improved. Revised portions are highlighted in the paper. Please find my itemized responses below and my revisions in the re-submitted files.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We really appreciate for Editor and Reviewers’ warm work earnestly and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Peng Wu.
Reviewer #3:
Comment # 1: Initially, in Section 1, the authors need to discuss several existing research works that deal with the concept of approximate computing, such as Energy Efficient Edge Computing Enabled by Satisfaction Games and Approximate Computing, doi: 10.1109/TGCN.2021.3122911, in order to improve the scheduling of the computing tasks within the microprocessors.
Author response: Thank you very much for your opinion. In response to your opinion, we have added the research work in this aspect to the discussion in the first section of the article.
Comment # 2: In Section 2, the authors need to include a table summarizing the main notation that has been used in the paper and also provide the units of the corresponding metrics which currently are missing from the provided analysis.
Author response: Thank you for your important advice. In response to your comments, we have modified Table 1 and added all major symbols and descriptions. The processor rate involved in the algorithm in this paper is evaluated based on the clock frequency, the unit is Hz, and the task execution speed only depends on the processor speed. Thus, a processor with speed = 2 can perform all tasks exactly twice as fast as a processor with speed = 1.
Comment # 3: Furthermore, in section three, the authors need to discuss the computational complexity of the proposed scheduling approaches and discuss if they can be implemented in a real time or even close to real time manner.
Author response: Thank you for your comments. For your comments, we have provided the time complexity of the scheduling algorithm in this paper. The time complexity of this algorithm is O(mn), which can be used in real-time system.
Comment # 4: Based on the previous comment, in Section 4, the authors need to provide some indicative numerical results showing the real execution time of the proposed scheduling approaches and discuss the real-time applicability.
Author response: Thank you for your precious opinion. Our experiments have an assumption that the context switching time of task migration is not considered. Because this switching time is difficult to use a unified standard to evaluate. This makes it really difficult to calculate the real execution time of the proposed scheduling approaches. Our article mainly considers the throughput rate of real-time tasks, because the experimental results in the article can prove the effectiveness of the algorithm.
Comment # 5: Furthermore, the authors need to compare those three approaches to other approaches that have been introduced in the state-of-the-art and justify their main operational characteristics and benefits compared to other approaches.
Author response: Thank you for your opinion. We have read a lot of literature, but recently there are few studies on this aspect, it is difficult to find a suitable algorithm for comparison. In future work, we will consider some scheduling algorithms based on machine learning, and then compare them with traditional algorithms.
Comment # 6: Finally, the overall manuscript needs to be checked for typos, syntax, and grammar errors in order to improve the quality of its presentation.
Author response: Thank you for your valuable opinion. In response to your comments, we have carefully checked and revised the typos and grammatical errors in the article to improve the quality of the article.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have addressed most of my concerns.
Still, I have a last observation:
The authors say:
" Now the field of unmanned vehicle research is very hot, and many large companies have also invested a lot of energy in the research of unmanned vehicles. The Linux kernel is used in many companies’ unmanned vehicle operating systems, such as Tesla’s operating system. The process scheduling of the Linux kernel uses the completely fair scheduling algorithm (CFS). EDF cannot be directly applied to the field of intelligent transportation, but it still has a good reference for the scheduling algorithm of the unmanned vehicle operating system"
But in Linux kernel, there is an EDF based scheduling policy since 3.14 (https://en.wikipedia.org/wiki/SCHED_DEADLINE), thus the EDF can be applied to Linux based systems. It cannot be applied to most of the embedded operating systems for low-end devices, though.
Author Response
Dear Editor, Dear Reviewers:
Thanks very much for the time and effort that you have put into reviewing the previous version of the manuscript entitled “Three Processor Allocation Approaches towards EDF Scheduling for Performance Asymmetric Multiprocessors”(ID: applsci-2200957). We really appreciate all your comments and suggestions which have enabled us to improve our work! We have studied these comments carefully and tried our best to revise and improve the manuscript.
We have modified the description of the scheduling policy of the Linux kernel in the text. Revised sections are highlighted in the file.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We really appreciate for Editor and Reviewers’ warm work earnestly and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Peng Wu.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors have addressed in detail the reviewers' comments. A very detailed revision of the paper has been performed and detailed answers to the reviewers' comments have been provided. This reviewer has no further concerns about this paper.
Author Response
Dear Editor, Dear Reviewers:
Thank you very much for taking the time and effort to review the previous version of the manuscript entitled "Three Processor Assignment Methods for Performance Asymmetric Multiprocessor EDF Scheduling" (ID: applsci-2200957). Your comments and suggestions are very valuable to us. We really appreciate all your comments and suggestions which have enabled us to improve our work!
We really appreciate for Editor and Reviewers’ warm work earnestly.
Once again, thank you very much for your comments and suggestions.
Best regards,
Peng Wu.
Author Response File: 
Author Response.docx
