Review Reports - Parallel Simulation Using Reactive Streams: Graph-Based Approach for Dynamic Modeling and Optimization

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments on the manuscript ‘Parallel simulation using reactive streams: A graph-based approach for dynamic modeling and optimization’ (Ref: computation-3545388)

In this work, the authors have presented a method to construct simulation graphs from predefined transition functions. The authors claim that the computational graph, implemented using AKKA library offers a scalable framework for parallel computation. The reviewer has the following comments.

1. Though the authors have presented some examples to illustrate the method discussed in this work, the presentation of mathematical formulations of the problem, analytical solutions and results are not clear. The authors have mixed the presentation of the extensive definitions with the actual description of the examples. It is suggested that the authors should extensively revise the manuscript by separating the example section from the definition section.

2. Most of the definitions as presented in the paper are very standard in literature and can be found in textbooks. For example, the definition of variable, set, domain, dependent and independent variable, Boolean variables, cardinality, conditional dependence etc. are very standard. It is suggested that these details should be either removed and appropriate references should be provided, or these can be provided as supplementary data or can be moved to appendices. On the other hand, the authors should present the case studies more systematically in order to explain the method better.

3. There are too many mathematical expressions and most of these are not provided with equation numbers. This makes reading and interpreting the flow of information difficult for the reader. It is suggested that the authors should provide only the relevant equations and refer these with equation numbers.

4. The first example should describe the physical problem properly. It is a very simple problem of filling of tank with a constant area of cross-section. The variable is height of filled water h(t), which is a function of time. Fig. 1(b) shows the height, however, it is written as volume. Though one can find the volume from height by multiplying with constant area, it should be presented through ‘height h’. The constants are volume of tank. It should be either represented as V0 or A0*h0 (A0 is cross-sectional area and h0 is the total height beyond which water shall overflow). The inlet flow should be represented as Q0, instead of v/t. Usually, small ‘v’ is reserved for velocity in mathematical literature. First define the mathematical model and the analytical solution (it is very simple and straight-forward). In the next step, explain the procedure of construction of graph and parallelization scheme and present the results. Discuss the advantages of the new scheme vis-à-vis the scheme popularly used in literature. This shall make the presentation more readable. Show through this example if one can get significant computational advantage by adopting the new procedure.

5. The second example is rigid motion of an object in space. As mentioned earlier, present the classical mathematical formulation, analytical solution to the problem and solution using the new method and compare the advantages and disadvantages of each method including computational gains (if any). Present a comparative assessment through a Table.

6. It is suggested that, some slightly complex problems like simultaneous filling and draining of water from a tank (with different filling and draining rates) should be considered and the results should be presented as a case study instead of rigid motion of an object with constant velocity, which is too simple.
7. One of the major issues with this paper is that though it is claimed that the method is very superior and it is easily scalable, there are no examples which show that the current method is superior to the existing methods in literature. It is suggested that at least one complex problem and its results should be presented where the authors show the advantages of the current method over the methods existing in literature. The gain in computational time should be quantified with evidence presented for the same.

8. Figs. 2, 5, 6 and 7 show the same result of variation of volume of water with time in different formats. These repetitions should be avoided. Show the variation of height as a function of time in Fig. 1 itself. Moreover, it is not a god practice to present Figs. 3 and 4 which belongs to the second case study before the results of first case study is fully discussed. Please separate the case studies (formulation, graph construction and results) into different sections.

9. Fig. 5 and 9: The volume at t=20 is written as 90. It should be hundred as inlet flow is constant. Please check and rectify accordingly.

10. Fig. 10: Both (a) and (b) should be clubbed as (b) shows the transition functions.

11. Fig. 11 is not necessary as it is being explained in Fig. 12 through a set of transition functions. Joining of transition functions are presented in Fig. 13. It may be better if all the operations such as joining and clubbing of transition functions are presented together in a single figure instead of many figures such as Figs. 11 to 15. Please check.

12. Section 3 contains many information, which is already available in literature. It is suggested that this section should be shortened and only relevant graphs and associated discussions should be presented. This shall make the section more readable.

13. Fig. 16: The figure caption should be modified. The actual physical problem should be defined instead of just writing ‘slinky game’. The mathematical model should be presented for the physical problem before discussing the construction of transitions functions and the relevant graphs. The height of stairs should be define as these are the inputs for the solution.

14. Fig. 19: What are x and y axes? Please define the green and red curves with ‘legends’. Put appropriate caption for the figure instead of just writing ‘results of simulation’.

15. Fig. 24: What are w_1, w_2 and w_3. Please define. Provide proper caption and titles for x and y axes. Compare the current results with the results obtained using methods of literature and show if there are any error or improvements (either in computational time or any other feature).

16. Section 5: This section currently is written in a very generalized manner. It is suggested that each point in the discussion section to be related to the results presented in the earlier section so that both the results and discussions can be correlated. This section should be rewritten and abridged appropriately.

17. Conclusions: This section is not properly written currently. Only some relevant conclusions from the work should be presented in brief and in bulleted format. Please modify this section accordingly.

18. The abstract is too large and it contains many general descriptions. Please shorten the abstract and rewrite by including the novelty of the work. Some relevant results and conclusions should be presented briefly in the ‘abstract’.

19. References: The format of the references is not appropriate. At many places, surname is written first followed by name, whereas it is in reverse order at other places. At many places, both name and surnames are written in full, whereas the name is abbreviated at some references. Please check and correct. It is also found that the latest works of other authors in this area are not cited. Please conduct a thorough literature survey and include the relevant recently published work in this area. Moreover, please avoid references to web pages and other such non-professional sources. The name of the author is missing in Ref. [11]. Similarly, there are many other mistakes. Please check.

20. The source code listing in B1 is not needed in a technical paper. Please remove the same in the revised version.

21. Fig. 25 and associated expressions are not needed in Appendix. This is similar to first problem. It may not be needed here.

22. There are many grammatical mistakes and spelling errors. Please check the manuscript thoroughly and rectify. Check the spelling of ‘technics’ in Page-39 and other places.

23. Don’t use abbreviations such as AKKA in abstract. Please define all abbreviations before using these in the text.

24. The manuscript should be shortened considerably with more focus on presentation of the method and the case studies. The presentation of mundane definitions and other standard descriptions should be avoided.

Comments on the Quality of English Language

There are many grammatical mistakes and spelling errors. Please check the manuscript thoroughly and rectify. Check the spelling of ‘technics’ in Page-39 and other places.

Author Response

Dear Reviewer,

Thank you very much for your thorough and constructive review of our manuscript ‘Parallel simulation using reactive streams: A graph-based approach for dynamic modeling and optimization’ (Ref: computation-3545388). We truly appreciate the time and effort you dedicated to carefully analyzing our work and providing detailed, thoughtful feedback. Your comments have been extremely valuable in helping us refine and strengthen the paper.

We have carefully addressed each of your suggestions and concerns. In doing so, we revised the manuscript to improve clarity, focus, and readability; restructured key sections; refined the visual materials; and added or updated technical content where needed. We have also acknowledged and incorporated your recommendations for improving the presentation, terminology, and future research directions.

Below, you will find our detailed responses to each comment, including explanations of the changes made and, where applicable, the rationale for our decisions. We hope the revised version of the manuscript meets your expectations and we sincerely thank you again for helping us improve the quality and clarity of our work.

With kind regards,
Oleksii Sirotkin, on behalf of all authors

Though the authors have presented some examples to illustrate the method discussed in this work, the presentation of mathematical formulations of the problem, analytical solutions and results are not clear. The authors have mixed the presentation of the extensive definitions with the actual description of the examples. It is suggested that the authors should extensively revise the manuscript by separating the example section from the definition section.

Response: We sincerely appreciate the reviewer’s insightful feedback. In response to your suggestion, we have thoroughly revised the manuscript to improve clarity and logical structure. Specifically, we have separated the example—the mixing problem—from the section containing core definitions and formalism. The example is now presented in a standalone chapter to clearly illustrate the application of the proposed method without interrupting the conceptual development. Additionally, less relevant examples have been removed to maintain focus and readability. We hope these changes significantly enhance the manuscript’s organization and accessibility, and we thank you again for helping us improve the overall quality of our work.

Most of the definitions as presented in the paper are very standard in literature and can be found in textbooks. For example, the definition of variable, set, domain, dependent and independent variable, Boolean variables, cardinality, conditional dependence etc. are very standard. It is suggested that these details should be either removed and appropriate references should be provided, or these can be provided as supplementary data or can be moved to appendices. On the other hand, the authors should present the case studies more systematically in order to explain the method better.

Response: We thank the reviewer for this helpful observation. We fully agree that many of the foundational definitions (e.g., variables, sets, domains, dependence types) are well-established in the literature. However, based on our experience, we have found that these concepts can vary significantly in meaning and usage across different domains and contexts. To ensure precision and avoid potential ambiguity, we initially included these definitions in the main text to establish a clear and shared conceptual framework for all readers. That said, we appreciate your concern regarding the length and focus of the manuscript. In response, we have relocated several of these standard definitions to the appendices to streamline the main body of the paper, while preserving clarity for readers who may not be familiar with our specific modeling context. Additionally, we have revised the case study section to present the examples in a more structured and illustrative manner, as suggested. We hope these changes address your comments and contribute to a clearer and more concise presentation of our method.

There are too many mathematical expressions and most of these are not provided with equation numbers. This makes reading and interpreting the flow of information difficult for the reader. It is suggested that the authors should provide only the relevant equations and refer these with equation numbers.

Response: We appreciate the reviewer’s valuable observation. To improve the readability and flow of the manuscript, we have carefully reviewed all mathematical expressions and removed those that were less essential to the understanding of the core concepts. Our aim was to simplify the presentation without compromising the clarity or rigor of the methodology. Additionally, we have assigned equation numbers to all remaining formulas that are referenced later in the text to facilitate easier navigation and comprehension. We hope these revisions enhance the clarity and structure of the manuscript and thank the reviewer for this constructive suggestion.

The first example should describe the physical problem properly. It is a very simple problem of filling of tank with a constant area of cross-section. The variable is height of filled water h(t), which is a function of time. Fig. 1(b) shows the height, however, it is written as volume. Though one can find the volume from height by multiplying with constant area, it should be presented through ‘height h’. The constants are volume of tank. It should be either represented as V0 or A0*h0 (A0 is cross-sectional area and h0 is the total height beyond which water shall overflow). The inlet flow should be represented as Q0, instead of v/t. Usually, small ‘v’ is reserved for velocity in mathematical literature. First define the mathematical model and the analytical solution (it is very simple and straight-forward). In the next step, explain the procedure of construction of graph and parallelization scheme and present the results. Discuss the advantages of the new scheme vis-à-vis the scheme popularly used in literature. This shall make the presentation more readable. Show through this example if one can get significant computational advantage by adopting the new procedure.

Response: We thank the reviewer for this detailed and constructive feedback. In response, we have revised the examples to more accurately reflect the physical nature of the tank-filling problem. We have corrected the variable notation. We have added a clear definition of the mathematical model and its straightforward analytical solution. The entire example has been moved to a separate, dedicated chapter, and restructured to follow a logical progression: from physical problem → mathematical formulation → graph construction and parallelization → results and interpretation. We hope these revisions significantly improve the clarity, correctness, and overall impact of the example. Thank you again for your helpful suggestions.

The second example is rigid motion of an object in space. As mentioned earlier, present the classical mathematical formulation, analytical solution to the problem and solution using the new method and compare the advantages and disadvantages of each method including computational gains (if any). Present a comparative assessment through a Table.

Response: We appreciate the reviewer’s thoughtful recommendation. After careful consideration, we decided to remove the second example (rigid body motion) from the manuscript. Our rationale was to streamline the presentation and maintain a clear focus on the primary example, which we have now developed in greater detail. We felt that the second example, while relevant, did not add significant value in the context of the core methodological contributions of the paper. However, we fully acknowledge the importance of demonstrating comparative performance and advantages of the proposed method. To that end, we have enhanced the primary example to include a clearer comparison between the proposed approach and traditional methods. Where appropriate, we have also highlighted the computational benefits and trade-offs in a more structured manner. We hope this focused revision meets the intent of your suggestion and strengthens the overall clarity and impact of the manuscript.

It is suggested that, some slightly complex problems like simultaneous filling and draining of water from a tank (with different filling and draining rates) should be considered and the results should be presented as a case study instead of rigid motion of an object with constant velocity, which is too simple.

Response: Thank you for this valuable suggestion. In line with your recommendation, we have removed simpler, less informative examples—including the rigid motion case—and instead focused the manuscript around a more complex and representative case study. Specifically, we have chosen to develop the tank-filling scenario into a more realistic problem setting, which can easily be extended to include simultaneous filling and draining at different rates. This revised case study better reflects practical challenges and allows us to more effectively demonstrate the capabilities and advantages of the proposed method. We hope this refinement improves the depth and relevance of our work and aligns with the reviewer’s expectations.

One of the major issues with this paper is that though it is claimed that the method is very superior and it is easily scalable, there are no examples which show that the current method is superior to the existing methods in literature. It is suggested that at least one complex problem and its results should be presented where the authors show the advantages of the current method over the methods existing in literature. The gain in computational time should be quantified with evidence presented for the same.

Response: We thank the reviewer for this important and insightful comment. We fully agree that demonstrating comparative performance is essential to substantiating the claimed advantages of the proposed approach. However, the nature of our method is such that its true benefits—particularly in terms of scalability and distributed computation—become evident primarily in large-scale modeling problems involving dozens or even hundreds of computational nodes. Conducting a rigorous, quantitative comparison with existing methods in such a high-performance computing context is a substantial undertaking that we believe deserves dedicated treatment. Therefore, we plan to address this topic comprehensively in a follow-up publication focused specifically on benchmarking and performance evaluation. In this current manuscript, our primary aim was to introduce the method, establish its theoretical foundation, and clarify its modeling principles. Nevertheless, we have revised the example section to better highlight how the method could scale and we provide a qualitative discussion of its expected computational advantages. We hope this explanation clarifies the scope of this paper and sets the stage for our future work on detailed performance comparisons.

Figs. 2, 5, 6 and 7 show the same result of variation of volume of water with time in different formats. These repetitions should be avoided. Show the variation of height as a function of time in Fig. 1 itself. Moreover, it is not a god practice to present Figs. 3 and 4 which belongs to the second case study before the results of first case study is fully discussed. Please separate the case studies (formulation, graph construction and results) into different sections.

Response: We thank the reviewer for this valuable observation. In response, we carefully reviewed all visual materials in the manuscript and agree that several figures were redundant or prematurely placed. To improve clarity and readability figure 2 have been moved to the supplementary materials, as they were not essential to the main narrative. Rest of them have been removed to avoid unnecessary repetition, and the relevant content has been integrated into a more concise and focused presentation. Additionally, we have restructured the manuscript to clearly separate the formulation, graph construction, and results of each case study into distinct sections to ensure a logical and consistent flow of information. We hope these revisions significantly enhance the manuscript's clarity and presentation, and we greatly appreciate the reviewer’s thoughtful guidance.

Fig. 5 and 9: The volume at t=20 is written as 90. It should be hundred as inlet flow is constant. Please check and rectify accordingly.

Response: Thank you for pointing out this discrepancy. Upon review, we recognized that Figures 5 and 9 were not essential to the overall narrative and contributed to redundancy in the visual presentation. To improve clarity and focus, and to streamline the manuscript, we have removed these figures from the main text. The core insights they conveyed are now reflected more effectively through the updated example and revised illustrations. We appreciate the reviewer’s attention to detail, which helped us refine the manuscript.

Fig. 10: Both (a) and (b) should be clubbed as (b) shows the transition functions.

Response: We thank the reviewer for this suggestion. However, we believe that Figure 10, as currently presented, effectively illustrates a key conceptual distinction between the classical mathematical modeling approach (Fig. 10a) and the new transition-function-based approach proposed in this work (Fig. 10b). Keeping these subfigures separate helps emphasize the contrast in modeling paradigms and supports the reader’s understanding of the methodological shift introduced in the paper. For this reason, we have opted to retain the current structure of Figure 10 without modification. We hope this rationale is acceptable, and we truly appreciate your thoughtful feedback.

Fig. 11 is not necessary as it is being explained in Fig. 12 through a set of transition functions. Joining of transition functions are presented in Fig. 13. It may be better if all the operations such as joining and clubbing of transition functions are presented together in a single figure instead of many figures such as Figs. 11 to 15. Please check.

Response: Thank you for your helpful suggestion. In accordance with your recommendation, we have removed Figure 11 to reduce redundancy and improve the coherence of the visual presentation. We appreciate your feedback in helping us streamline and clarify the manuscript.

Section 3 contains many information, which is already available in literature. It is suggested that this section should be shortened and only relevant graphs and associated discussions should be presented. This shall make the section more readable.

Response: We appreciate the reviewer’s thoughtful recommendation. In response, we have revised Section 3 to improve focus and readability. Specifically, we have shortened the section by relocating definitions and explanations of widely known concepts to the supplementary materials. The main section now concentrates on the most relevant graphs and accompanying discussion that directly support the proposed methodology. We hope this revision makes the section more concise and accessible, as suggested.

Fig. 16: The figure caption should be modified. The actual physical problem should be defined instead of just writing ‘slinky game’. The mathematical model should be presented for the physical problem before discussing the construction of transitions functions and the relevant graphs. The height of stairs should be define as these are the inputs for the solution.

Response: Thank you for this detailed and helpful comment. Upon further consideration, we concluded that this example did not significantly contribute to the core objectives of the paper. As a result, we have removed the example along with Figure 16 to streamline the manuscript and maintain focus on the most relevant and illustrative case studies. We appreciate your suggestion, which helped us improve the clarity and relevance of the presentation.

Fig. 19: What are x and y axes? Please define the green and red curves with ‘legends’. Put appropriate caption for the figure instead of just writing ‘results of simulation’.

Response: Thank you for pointing this out. In accordance with your recommendation, we have updated Figure 19 by adding a legend to clearly distinguish the green and red curves. We have also labeled the x- and y-axes and revised the caption to more accurately describe the figure content and context. We believe these changes enhance the clarity and usefulness of the figure, and we appreciate your helpful feedback.

Fig. 24: What are w_1, w_2 and w_3. Please define. Provide proper caption and titles for x and y axes. Compare the current results with the results obtained using methods of literature and show if there are any error or improvements (either in computational time or any other feature).

Response: Thank you for this valuable feedback. In accordance with your recommendation, we have updated Figure 24 to include clear definitions for the variables w_1, w_2 and w_3. Additionally, we have labeled the x- and y-axes and revised the figure caption to provide a more informative and self-contained description. Regarding comparative analysis, while the primary focus of this manuscript is to introduce the proposed method and demonstrate its feasibility, we agree that a performance comparison is important. We have added a brief qualitative discussion on how the results compare conceptually to traditional approaches, including potential advantages in computational structure and flexibility. A full quantitative performance evaluation (e.g., in terms of computational time or accuracy) will be the focus of a future study, as it requires extensive benchmarking across various scenarios and platforms. We appreciate the reviewer’s suggestions, which have helped us improve the clarity and completeness of the presentation.

Section 5: This section currently is written in a very generalized manner. It is suggested that each point in the discussion section to be related to the results presented in the earlier section so that both the results and discussions can be correlated. This section should be rewritten and abridged appropriately.

Response: Thank you for this helpful suggestion. In response, we have thoroughly revised and condensed the Discussion section to improve focus and clarity. Where possible, we have directly linked each discussion point to the corresponding results and examples presented earlier in the manuscript. This restructuring aims to better correlate our theoretical insights with the demonstrated outcomes, as you recommended. We hope these revisions enhance the coherence and relevance of the discussion.

Conclusions: This section is not properly written currently. Only some relevant conclusions from the work should be presented in brief and in bulleted format. Please modify this section accordingly.

Response: Thank you for your valuable feedback. In response, we have rewritten the Conclusions section to align with your recommendation. It now presents only the most relevant findings from the study in a concise, bulleted format. We believe this structure improves clarity and helps highlight the key contributions of the work more effectively.

The abstract is too large and it contains many general descriptions. Please shorten the abstract and rewrite by including the novelty of the work. Some relevant results and conclusions should be presented briefly in the ‘abstract’.

Response: Thank you for your helpful comment. In response, we have revised and shortened the abstract to improve focus and clarity. The updated version highlights the novelty of the proposed method and briefly presents key results and conclusions, as suggested. We hope this new version more effectively communicates the essence and significance of our work.

References: The format of the references is not appropriate. At many places, surname is written first followed by name, whereas it is in reverse order at other places. At many places, both name and surnames are written in full, whereas the name is abbreviated at some references. Please check and correct. It is also found that the latest works of other authors in this area are not cited. Please conduct a thorough literature survey and include the relevant recently published work in this area. Moreover, please avoid references to web pages and other such non-professional sources. The name of the author is missing in Ref. [11]. Similarly, there are many other mistakes. Please check.

Response: Thank you for pointing out these important issues. We have carefully reviewed and reformatted all references to ensure consistency with the journal’s guidelines. This includes correcting author name formats, unifying citation styles, and removing non-professional sources such as general web pages where appropriate. We have also corrected omissions such as the missing author in Ref. [11]. Additionally, we have expanded our literature review to include several recent and relevant publications in the field to better position our work within the current research landscape. We appreciate your detailed comments, which helped us improve the quality and scholarly rigor of the manuscript.

The source code listing in B1 is not needed in a technical paper. Please remove the same in the revised version.

Response: Thank you for your suggestion. In accordance with your recommendation, we have removed Listing B1 from the manuscript. To ensure continued access to the implementation details for interested readers, we have replaced the in-text reference with a link to the publicly available source code hosted on GitHub. We believe this change improves the readability of the paper while still providing access to supplementary materials for those who wish to explore the implementation.

Fig. 25 and associated expressions are not needed in Appendix. This is similar to first problem. It may not be needed here.

Response: Thank you for your observation. In accordance with your recommendation, we have removed Figure 25 and the associated expressions from the Appendix, as they were indeed similar to the first example and not essential to the main narrative. We appreciate your feedback, which helped us streamline the content and improve the overall focus of the manuscript.

There are many grammatical mistakes and spelling errors. Please check the manuscript thoroughly and rectify. Check the spelling of ‘technics’ in Page-39 and other places.

Response: Thank you for pointing this out. We have thoroughly reviewed the manuscript for grammatical and spelling errors and have corrected all identified issues, including the incorrect use of the word "technics" on Page 39 and other similar instances. We appreciate your attention to detail in helping us improve the clarity and professionalism of the manuscript.

Don’t use abbreviations such as AKKA in abstract. Please define all abbreviations before using these in the text.

Response: Thank you for your observation. In accordance with your recommendation, we have removed the abbreviation "AKKA" from the abstract, as its mention was not essential to the meaning of the sentence. All other abbreviations used in the manuscript are now defined upon their first appearance in the main text to ensure clarity for all readers.

The manuscript should be shortened considerably with more focus on presentation of the method and the case studies. The presentation of mundane definitions and other standard descriptions should be avoided.

Response: Thank you for this important recommendation. In response, we have significantly shortened the manuscript by removing non-essential examples and minimizing less critical content. Additionally, definitions of well-known terms and standard concepts have been moved to the supplementary materials to maintain clarity without overloading the main text. These changes help to place greater emphasis on the core methodology and case studies, as suggested.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper introduces a novel approach using reactive streams as a general-purpose synchronization protocol. By structuring simulations as transition graphs composed of substates and transition functions, the method enables modular, scalable, and efficient execution. Implemented using AKKA reactive streams, the approach optimizes load balancing, ensures state consistency, and improves parallel execution. Theoretical analysis and practical implementation confirm its advantages over traditional methods, paving the way for future research in graph optimization, fault tolerance, and automation.

But it’s worth noting a few important remarks on this

Comment 1. While the paper claims that the proposed reactive streams approach improves scalability, there is no concrete benchmarking or comparison against established methods like Time Warp. A direct performance evaluation with empirical results is necessary to substantiate these claims.

Comment 2. The paper does not discuss the computational overhead introduced by reactive streams. Reactive architectures often come with increased memory consumption and latency due to event-driven processing. A detailed analysis of this trade-off is needed.

Comment 3. The construction of transition graphs and their integration into reactive streams is described conceptually, but no complexity analysis is provided. How does the proposed approach scale with an increasing number of states and transitions?

Comment 4. The paper briefly mentions fault tolerance as a future research direction but does not explore how errors, dropped messages, or inconsistencies in state transitions would be handled in real-world parallel simulations. A discussion on failure recovery is essential.

Comment 5. The proposed method is presented as a general-purpose solution, but no domain-specific case studies (e.g., computational biology, physics simulations) are provided to validate its applicability. How well does the approach adapt to different simulation domains?

Comment 6. The paper critiques traditional synchronization methods but does not compare its approach with alternative modern paradigms (e.g., speculative execution or distributed event-based frameworks). A comparative study would strengthen the argument for adopting reactive streams.

Comments on the Quality of English Language

Comment 1.

Overall Clarity & Readability – The paper is generally well-written, but some sentences are overly complex and difficult to follow. Simplifying certain explanations and breaking long sentences into shorter, clearer ones would improve readability.

Comment 2.

Technical Terminology – The use of technical terms is appropriate, but in some cases, definitions or brief explanations would help readers unfamiliar with reactive streams and transition graphs.

Comment 3.

Grammar & Syntax – There are a few grammatical inconsistencies and awkward sentence structures. Proofreading for minor errors in subject-verb agreement, punctuation, and word choice is recommended.

Comment 4.

Flow & Coherence – Some sections, especially the methodology and theoretical framework, could benefit from better transitions between ideas. Adding section summaries or signposting key points would enhance logical flow.

Comment 5.

Use of Figures & Examples – While the text is technically detailed, incorporating more diagrams or illustrative examples would improve comprehension, especially for explaining the transition graph and reactive streams integration.

Suggested Actions:

Perform a thorough proofread for grammar and syntax improvements.
Simplify certain complex sentences for better clarity.
Enhance transitions between sections for smoother reading.
Consider adding diagrams or examples to aid understanding.

Author Response

Dear Reviewer,

With kind regards,
Oleksii Sirotkin, on behalf of all authors

Comments and Suggestions for Authors

Response: Thank you for highlighting this important point. We fully agree that a direct performance comparison with established methods such as Time Warp is essential to empirically validate the scalability advantages of the proposed approach. However, the nature of our method is such that its benefits become most apparent in large-scale simulation scenarios involving dozens or even hundreds of computational nodes. Conducting a meaningful benchmarking study under such conditions is a substantial undertaking and falls outside the scope of the current manuscript. We plan to dedicate a future publication specifically to this topic, where we will present detailed performance evaluations and comparisons with existing approaches. In the present paper, our primary focus has been on introducing the new method and providing a thorough theoretical justification of its structure and scalability potential. We appreciate the reviewer’s suggestion and view it as a valuable direction for future work.

Response: We appreciate the reviewer’s insightful observation. We acknowledge that the reactive-streams approach may introduce certain overheads—such as increased memory usage and latency—due to its event-driven nature. However, a detailed quantitative analysis of these trade-offs, especially in large-scale simulation scenarios, is a substantial and complex task. To keep the current manuscript focused and concise, we have chosen to defer this investigation to a follow-up study. In that future work, we plan to conduct a comprehensive performance analysis, including overhead measurements and comparisons with alternative synchronization strategies. We believe this will offer a more complete picture of the practical implications and scalability of the proposed method. Thank you for pointing out this important aspect, which we agree deserves deeper attention.

Response: Thank you for this important question. We agree that a formal complexity analysis is a valuable aspect of evaluating the scalability of the proposed approach. However, we believe that such analysis would be most meaningful when supported by empirical data derived from testing the method on large-scale, real-world simulation problems. For this reason, we have planned a follow-up study that will focus on benchmarking the approach under more complex scenarios, where we will also analyze computational complexity in relation to the number of states and transitions. In the current manuscript, our primary aim is to present the conceptual framework and theoretical foundations of the method. We appreciate your suggestion and see it as a critical direction for our future research.

Response: Thank you for raising this important point. In the current manuscript, we briefly mention potential directions for implementing fault tolerance but intentionally did not go into detail, as we are still actively exploring various approaches. These include using built-in fault-handling capabilities of the AKKA framework as well as developing our own custom algorithms tailored to the structure of the proposed transition graph model. Given the complexity and critical importance of this topic—especially for real-world distributed systems—we plan to devote an entire future publication to a detailed examination of fault tolerance, including mechanisms for error detection, message loss handling, and recovery from inconsistent states. We appreciate the reviewer’s suggestion, which reinforces the importance of this future work.

Response: Thank you for this insightful comment. The proposed method was originally developed with applications in the energy sector in mind, particularly for modeling complex energy distribution systems. We are currently working on the implementation of a domain-specific, large-scale simulation in this area, which we plan to present in a separate, dedicated publication due to its scope and complexity. Given the extensive effort required for such domain-specific validation, we chose to focus this paper on introducing the method and illustrating its core principles through simpler, more general-purpose examples. We believe this provides a clear conceptual foundation for future applications across a range of simulation domains. We appreciate the reviewer’s suggestion and agree that showcasing broader applicability through domain-specific case studies is a valuable next step in demonstrating the versatility of the approach.

Response: We appreciate the reviewer’s thoughtful suggestion. We agree that a comparative study with alternative modern paradigms such as speculative execution and distributed event-based frameworks would provide valuable context and further substantiate the advantages of the proposed reactive-streams-based approach. Such an analysis is indeed part of our planned future work. We believe that comparing performance, scalability, and implementation complexity across these paradigms will offer important insights into their relative strengths and limitations. However, due to the breadth and technical depth required for such a study, we have chosen to focus this paper on the theoretical foundation and conceptual framework of our method. We thank the reviewer for highlighting this important direction, which we are committed to pursuing in subsequent research.

Comments on the Quality of English Language

Comment 1. Overall Clarity & Readability – The paper is generally well-written, but some sentences are overly complex and difficult to follow. Simplifying certain explanations and breaking long sentences into shorter, clearer ones would improve readability.

Response: Thank you for this helpful feedback. We have carefully reviewed the manuscript and made efforts to simplify the language where appropriate. Long and complex sentences have been restructured into shorter, clearer ones to improve overall readability and ensure the text is more accessible to a broader audience. We appreciate your suggestion, which has contributed to a clearer and more effective presentation of the work.

Comment 2. Technical Terminology – The use of technical terms is appropriate, but in some cases, definitions or brief explanations would help readers unfamiliar with reactive streams and transition graphs.

Response: Thank you for this valuable suggestion. To improve accessibility for readers who may not be familiar with reactive streams and transition graphs, we have revised the structure of the manuscript to provide clearer context and guidance throughout. Where appropriate, we have added brief explanations and included references to relevant literature to support further understanding. We hope these changes enhance the clarity and approachability of the paper for a broader audience.

Comment 3. Grammar & Syntax – There are a few grammatical inconsistencies and awkward sentence structures. Proofreading for minor errors in subject-verb agreement, punctuation, and word choice is recommended.

Response: Thank you for bringing this to our attention. We have thoroughly proofread the manuscript and corrected all identified issues related to grammar, punctuation, subject-verb agreement, and word choice. These revisions were made to ensure clarity and improve the overall readability of the paper. We appreciate your recommendation, which helped us enhance the quality of the manuscript.

Comment 4. Flow & Coherence – Some sections, especially the methodology and theoretical framework, could benefit from better transitions between ideas. Adding section summaries or signposting key points would enhance logical flow.

Response: Thank you for this helpful suggestion. To improve the logical flow and coherence of the manuscript, we have added brief introductions at the beginning of each major section to guide the reader and clarify the purpose of the content that follows. We also expanded the concluding remarks and restructured parts of the manuscript to ensure smoother transitions between ideas and improve overall readability. We hope these changes make the paper more cohesive and accessible.

Comment 5. Use of Figures & Examples – While the text is technically detailed, incorporating more diagrams or illustrative examples would improve comprehension, especially for explaining the transition graph and reactive streams integration.

Response: Thank you for this valuable recommendation. In line with your suggestion and similar feedback from other reviewers, we have revised the structure of the manuscript to improve clarity and readability. Specifically, we have added a dedicated section that provides a practical demonstration of the proposed approach, supported by additional diagrams and illustrative examples. We believe these enhancements make the concepts—particularly transition graph construction and reactive streams integration—more accessible and easier to understand.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all the comments of the reviewer and have revised the manuscript accordingly. The revised version of the manuscript may be accepted for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors responded to the comments and the manuscript can be published in its current form