Stochastic Characterization of MAC-Level Reliability and Reassociation Dynamics in IEEE 802.15.4 Networks for Smart Grid Applications

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript studies MAC-layer reliability and reassociation dynamics in an IEEE 802.15.4/ZigBee PRO network for Smart Grid applications using a stochastic framework. The authors need to address the following issues:

1) The paper states that it is grounded in a real traffic capture and that it estimates a Markov model, identifies burst persistence, and fits non-exponential realignment dynamics. However, numerical outputs such as sample size, estimated Weibull parameters and goodness-of-fit results. In this context, the Results section should be improved.

2) The title of Section 3 contains a typo, and Section 3.1 is empty. Also, there are incorrect equation cross-references in this section.

3) It is stated in Section 3 that the dataset is a real IEEE 802.15.4/ZigBee PRO capture on channel 11 with a coordinator and multiple end devices over several thousand seconds. This explanation is not enough for an empirical paper. Section 3 should be improved by giving information on the capture duration, number of devices, traffic conditions, identification of corrupted frames, and preprocessing steps.

4) The introduction motivates the work using Advanced Metering Infrastructure, Home Area Networks, and distributed energy resource monitoring, but the manuscript does not yet establish how the captured network is tied to an actual Smart Grid use case. The paper would be stronger if the authors connected their estimates to a specific application scenario.

5) Whether malformed packets were included, excluded, or recoded in the binary error sequence should be explicitly stated in the manuscript to improve the reproducibility of the results.

Author Response

Dear

Editor

Symmetry

We are submitting the paper:

“Stochastic Characterization of MAC-Level Reliability and Reassociation Dynamics in IEEE 802.15.4 Networks for Smart Grid Applications”

Authored by: Carolina Del-Valle-Soto * , José A. Del-Puerto-Flores , Ramiro Velázquez , Juan Sebastián Botero-Valencia , Leonardo J. Valdivia , José Varela-Aldás , Paolo Visconti

We would like to thank the reviewers and editors for their detailed analysis of the manuscript; the comments are very valuable to us. In the revised version of the paper, we have incorporated the all changes recommended by the reviewers.

Comments to all observations and suggestions including point-by-point responses are addressed in the following text.

 

Reviewer 1 comments

Comment 1: The manuscript studies MAC-layer reliability and reassociation dynamics in an IEEE 802.15.4/ZigBee PRO network for Smart Grid applications using a stochastic framework. The authors need to address the following issues:

1) The paper states that it is grounded in a real traffic capture and that it estimates a Markov model, identifies burst persistence, and fits non-exponential realignment dynamics. However, numerical outputs such as sample size, estimated Weibull parameters and goodness-of-fit results. In this context, the Results section should be improved.

Response: We sincerely thank the reviewer for this important observation. We agree that the original version of the manuscript emphasized the methodological and theoretical aspects of the analysis, while not explicitly reporting the key numerical outputs required to fully support reproducibility and empirical validation.

In response, the manuscript has been substantially revised to incorporate a detailed quantitative summary of the empirical results. Specifically, we have added a new subsection entitled “Quantitative Summary of Empirical Estimation” at the beginning of the Results section. This subsection provides explicit numerical values for all relevant estimated quantities derived from the real MAC-layer traffic trace.

The following elements have been added and are now clearly reported:

• The total sample size and number of corrupted frames, including the empirical Frame Error Rate (FER).
• Results of statistical independence testing, including Wald–Wolfowitz runs test and Ljung–Box test statistics with corresponding p-values.
• The estimated Markov transition matrix, including persistence probabilities and stationary distribution.
• Spectral properties of the Markov chain, including the second eigenvalue and spectral gap.
• Formal model comparison between the Bernoulli and Markov models using likelihood ratio tests, AIC, and BIC.
• Weibull distribution parameters for realignment intervals (shape and scale), along with Kolmogorov–Smirnov goodness-of-fit results.
• Information-theoretic comparison between Weibull and exponential models confirming non-memoryless behavior.

Additionally, the narrative in the Results section has been revised to consistently integrate these numerical values into the discussion, ensuring coherence between the statistical analysis and its interpretation.

These modifications significantly improve the transparency, reproducibility, and empirical grounding of the manuscript, directly addressing the reviewer’s concern.

We appreciate the reviewer’s suggestion, which has strengthened the quality and rigor of the paper.

Comment 2: The title of Section 3 contains a typo, and Section 3.1 is empty. Also, there are incorrect equation cross-references in this section.

Response: We sincerely thank the reviewer for this careful and constructive observation. We have thoroughly revised Section 3 to address all the issues identified and to improve the overall consistency and clarity of the manuscript.

First, the typographical error in the section title has been corrected. The section heading has been updated from “Meterials and Methods” to “Materials and Methods”.

Second, the previously empty subsection (Section 3.1: Methodology) has been removed. The methodological content has been reorganized and fully integrated into the subsequent subsection “Statistical Inference and Stochastic Modeling Framework”, ensuring a coherent and logically structured presentation.

Third, all equation cross-references throughout Section 3 and the rest of the manuscript have been systematically reviewed and corrected. In particular:

• All hard-coded equation references have been replaced with proper LaTeX references using \eqref{...}.
• Missing equation labels have been added where necessary, especially in the Results section (e.g., estimated transition matrix, spectral quantities, Weibull parameters, and statistical test outputs).
• All equations are now consistently labeled and explicitly referenced in the text to ensure traceability and reproducibility.
• Inconsistencies between referenced equation numbers and their actual definitions have been eliminated.

Additionally, we performed a global consistency check across the manuscript to ensure that all mathematical expressions, references, and numbering remain correct after compilation.

These revisions significantly improve the technical accuracy, readability, and formal rigor of the manuscript. We appreciate the reviewer’s comment, which helped us strengthen the presentation and consistency of the work.

Comment 3: It is stated in Section 3 that the dataset is a real IEEE 802.15.4/ZigBee PRO capture on channel 11 with a coordinator and multiple end devices over several thousand seconds. This explanation is not enough for an empirical paper. Section 3 should be improved by giving information on the capture duration, number of devices, traffic conditions, identification of corrupted frames, and preprocessing steps.

Response: We thank the reviewer for this important observation. We agree that the original description of the dataset was not sufficiently detailed for a fully reproducible empirical study.

In response, Section 3 (Materials and Methods) has been substantially expanded to provide a comprehensive characterization of the data acquisition and preprocessing pipeline. Specifically, the revised manuscript now includes:

- The total capture duration and temporal resolution of the trace.

- The number and roles of devices in the network, including the coordinator and end devices.

- A detailed description of traffic patterns, including periodic data requests and control signaling.

- The criteria used to identify corrupted frames based on Frame Check Sequence (FCS) validation.

- A clear description of preprocessing steps, including filtering, ordering, and construction of the binary error sequence used for stochastic modeling.

These additions improve the transparency, reproducibility, and empirical rigor of the study, ensuring that the dataset and analysis pipeline can be clearly understood and replicated by other researchers.

We appreciate the reviewer’s suggestion, which has significantly strengthened the methodological clarity of the manuscript.

Comment 4: The introduction motivates the work using Advanced Metering Infrastructure, Home Area Networks, and distributed energy resource monitoring, but the manuscript does not yet establish how the captured network is tied to an actual Smart Grid use case. The paper would be stronger if the authors connected their estimates to a specific application scenario.

Response: We thank the reviewer for this insightful comment. We agree that explicitly connecting the analyzed network to a concrete Smart Grid application scenario strengthens the practical relevance of the work.

In response, the manuscript has been revised to clearly position the captured IEEE 802.15.4/ZigBee PRO network within a representative Advanced Metering Infrastructure (AMI) use case. Specifically, we now describe the network as a star-topology deployment in which multiple end devices periodically issue data requests to a central coordinator, consistent with typical smart meter–to–data concentrator communication patterns.

Additionally, we have expanded the Introduction to explicitly link the estimated stochastic properties (burst-error persistence, spectral gap, and non-exponential realignment dynamics) to their operational implications in Smart Grid scenarios. In particular, we discuss how these properties affect reliability metrics such as data availability, latency variability, and risk of communication outages in AMI systems.

These additions establish a clear connection between the empirical measurements, the stochastic modeling framework, and a concrete Smart Grid application context, thereby improving the interpretability and practical relevance of the results.

We appreciate the reviewer’s suggestion, which has helped us strengthen the application-oriented perspective of the manuscript.

Comment 5: Whether malformed packets were included, excluded, or recoded in the binary error sequence should be explicitly stated in the manuscript to improve the reproducibility of the results.

Response: We thank the reviewer for highlighting this important point regarding data preprocessing transparency.

In the revised manuscript, we have clarified how malformed packets are handled in the construction of the binary error sequence. Specifically, malformed frames and packets that do not conform to the IEEE 802.15.4 standard structure are excluded during the preprocessing stage and are not incorporated into the stochastic analysis.

Only valid IEEE 802.15.4 MAC frames with well-defined structure are considered. Among these, frames are classified based on Frame Check Sequence (FCS) validation: frames with invalid FCS are encoded as errors, while frames with valid FCS are treated as successful transmissions.

This clarification has been explicitly added to the preprocessing subsection in Section 3, ensuring that the construction of the binary sequence $\{E_i\}$ is fully reproducible and unambiguous.

Thank you very much.

Sincerely,

Carolina Del-Valle-Soto

Corresponding author

Universidad Panamericana. Facultad de Ingeniería. Álvaro del Portillo 49, Zapopan, Jalisco, 45010, México.

Phone: +52 (33) 13682200 | Ext. 4866

Email: cvalle@up.edu.mx

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a probabilistic framework to assess the reliability of IEEE 802.15.4/ZigBee PRO Smart Grid networks using real MAC-layer traffic data. Although the paper addresses an interesting and relevant problem, the manuscript still needs improvement in empirical clarity, methodological reporting, and presentation.

1. What is the main novel scientific contribution beyond applying known stochastic tools to one captured traffic trace.
2. The research gap needs to be articulated more clearly, especially in relation to prior Markov-based and Smart Grid reliability studies.
3. I don’t see enough description of the dataset and capture setup. It needs more detail, including the exact number of frames, capture duration, number of devices, and the actual Smart Grid deployment scenario.
4. Do the observed FCS errors represent actual communication failures between network nodes or only corrupted frames at the monitoring device? Please make it clear.
5. There is a typo in “Meterials and Methods”, and Subsection 3.1 “Methodology” appears to be empty.
6. I suggest adding a table to present all mathematical symbols and notations used through the paper.
7. There are some missing details in the methodology section, such as significance levels and decision criteria for the statistical tests.
8. I see that you mention likelihood-ratio testing, AIC/BIC, stationary probabilities, spectral gap, and survival fitting, but the actual estimated values are not reported clearly in the results.
9. Your Results section is mostly qualitative. You make statements such as “statistically significant” and “shape parameter differs from unity”, but you did not support them with test statistics, p-values, confidence intervals, or effect sizes.
10. Most of the figures appear more illustrative than empirical. These need a clear distinction between data-driven results and conceptual or model-based figures.
11. Please revise your figures and make sure that all figures have clear units and informative labels, particularly Figures 5 and 7.
12. You introduced availability and MTBF, but their actual computed values and practical interpretation are not clearly reported.
13. The assumption of a first-order Markov chain should be justified more carefully. Please explain why first-order dependence is sufficient and whether you checked higher-order behavior or not.
14. What is the number of realignment events, and how were they identified?
15. It seems that Discussion and Conclusion are stronger than the presented results. Please align the claims with the actual evidence or provide stronger support.
16. I found 10 duplicated references. References 11 to 20 are repeated again later in the list, so the actual number of references is 23, not 33. Please correct this issue and clearly explain how it occurred. Also, please check how these references were cited in the text and confirm whether the in-text citations are still correct and relevant.

Comments for author File: Comments.pdf

Author Response

Dear

Editor

Symmetry

We are submitting the paper:

“Stochastic Characterization of MAC-Level Reliability and Reassociation Dynamics in IEEE 802.15.4 Networks for Smart Grid Applications”

Authored by: Carolina Del-Valle-Soto * , José A. Del-Puerto-Flores , Ramiro Velázquez , Juan Sebastián Botero-Valencia , Leonardo J. Valdivia , José Varela-Aldás , Paolo Visconti

We would like to thank the reviewers and editors for their detailed analysis of the manuscript; the comments are very valuable to us. In the revised version of the paper, we have incorporated the all changes recommended by the reviewers.

Comments to all observations and suggestions including point-by-point responses are addressed in the following text.

 

Reviewer 2 comments

Comment 1: This paper proposes a probabilistic framework to assess the reliability of IEEE 802.15.4/ZigBee PRO Smart Grid networks using real MAC-layer traffic data. Although the paper addresses an interesting and relevant problem, the manuscript still needs improvement in empirical clarity, methodological reporting, and presentation.

What is the main novel scientific contribution beyond applying known stochastic tools to one captured traffic trace.

Response: What is the main novel scientific contribution beyond applying known stochastic tools to one captured traffic trace.

We thank the reviewer for this important and fundamental question. We agree that clarifying the scientific contribution beyond the use of standard stochastic tools is essential.

The novelty of this work does not lie in the individual mathematical techniques themselves, but in their integrated application to empirically derived MAC-layer data, combined with formal statistical validation and interpretation within a Smart Grid reliability context. Specifically, the main contributions of the paper are as follows:

1. Empirical rejection of the independence assumption: Unlike most existing works that assume i.i.d. packet errors, this study provides statistically rigorous evidence that frame errors exhibit significant temporal dependence. This result challenges a foundational assumption widely used in analytical and simulation-based models.
   
   2. Data-driven identification of burst-error dynamics: The estimation of a first-order Markov model from real traffic reveals strong asymmetry in transition probabilities, particularly a high persistence probability. This provides a quantitative characterization of burst-error behavior grounded in empirical observations rather than synthetic models.
2. Integration of spectral and dependence-aware reliability metrics: The introduction of spectral-gap analysis and long-run variance estimation links temporal dependence to convergence rates and uncertainty inflation, providing a deeper reliability characterization beyond average error rates.
3. Renewal-theoretic modeling of reassociation dynamics: Coordinator realignment events are modeled as regeneration points, and their inter-arrival times are shown to follow a non-exponential (Weibull) distribution. This establishes that reassociation processes are not memoryless and must be treated within a renewal framework.
4. Unified probabilistic framework: The work combines hypothesis testing, Markov modeling, spectral analysis, large deviations, and survival analysis into a single reproducible framework directly grounded in real traffic traces. This integration enables mapping low-level communication behavior to system-level reliability metrics such as availability and MTBF.

Therefore, the contribution of this paper is not merely the application of known tools, but the demonstration, through real data, that widely assumed modeling simplifications are invalid, together with the development of a dependence-aware stochastic framework that better captures the reliability structure of IEEE 802.15.4 Smart Grid communications.

We have revised the Introduction to explicitly highlight these contributions and clarify the novelty of the work.

Comment 2: The research gap needs to be articulated more clearly, especially in relation to prior Markov-based and Smart Grid reliability studies.

Response: We thank the reviewer for this valuable observation. We agree that the research gap should be more explicitly articulated in relation to prior Markov-based and Smart Grid reliability studies.

 

In response, we have revised the Introduction to clearly identify the limitations of existing approaches and to position our contribution more explicitly. In particular, we now emphasize that:

(i) most Markov-based reliability models in IEEE 802.15.4 and wireless sensor networks are derived from analytical assumptions or synthetic data, without empirical validation from real MAC-layer traffic;

(ii) Smart Grid communication studies typically assume independent packet errors or adopt simplified state-based models without formally testing temporal dependence;

(iii) reassociation and realignment dynamics are generally treated as exogenous or deterministic events, rather than as stochastic processes with renewal structure.

We explicitly state that the main research gap lies in the lack of empirically grounded, dependence-aware stochastic modeling of MAC-layer reliability in real Smart Grid communication environments.

This clarification has been incorporated into the Introduction, where the gap is now clearly defined and directly connected to the contributions of the paper.

We appreciate the reviewer’s suggestion, which has improved the clarity and positioning of the manuscript.

Comment 3: I don’t see enough description of the dataset and capture setup. It needs more detail, including the exact number of frames, capture duration, number of devices, and the actual Smart Grid deployment scenario.

Response: We thank the reviewer for this important comment. We agree that a clearer and more consolidated description of the dataset and capture setup improves both readability and reproducibility.

In the revised manuscript, we have strengthened the dataset description in Section 3 by explicitly consolidating the key parameters of the capture, including: total number of frames ($N = 52{,}846$), number of corrupted frames ($N_e = 17{,}392$), capture duration ($T = 3{,}600$ seconds), and number of devices ($M = 12$ end devices plus one coordinator).

Additionally, we have further clarified the Smart Grid deployment scenario by explicitly framing the network as a representative Advanced Metering Infrastructure (AMI) setup, where end devices emulate smart meters communicating with a central data concentrator.

To improve clarity, we have also added a concise summary paragraph that gathers all these parameters in a single location within the dataset description subsection.

These revisions make the dataset characteristics and experimental setup explicit, self-contained, and easily reproducible.

We appreciate the reviewer’s suggestion, which has significantly improved the clarity of the empirical description.

Comment 4: Do the observed FCS errors represent actual communication failures between network nodes or only corrupted frames at the monitoring device? Please make it clear.

Response: We thank the reviewer for this important clarification request.

In the revised manuscript, we explicitly clarify the interpretation of FCS errors in the context of passive traffic capture. The observed FCS errors correspond to frames that are corrupted at the monitoring device, and therefore represent decoding failures at the receiver performing the capture.

While such events are commonly used as a proxy for communication unreliability, they do not necessarily imply that the original transmission failed at the intended receiver node. In particular, discrepancies may arise due to spatial variability in channel conditions, interference, or receiver sensitivity differences between the monitoring device and network nodes.

We have added a clarifying paragraph in the dataset description section explicitly stating this distinction and discussing its implications. In our analysis, FCS errors are interpreted as observable indicators of channel impairment and network instability, rather than direct end-to-end packet delivery failures.

Comment 5: There is a typo in “Meterials and Methods”, and Subsection 3.1 “Methodology” appears to be empty.

Response: We thank the reviewer for carefully identifying these issues.

The typographical error in the section has been corrected to “Materials and Methods”.

Regarding Subsection 3.1, we clarify that this issue was due to an earlier formatting inconsistency. In the revised manuscript, the subsection has been properly completed and now includes the full description of the dataset, preprocessing pipeline, and stochastic modeling framework.

We appreciate the reviewer’s attention to detail, which has helped improve the presentation and clarity of the manuscript.

Comment 6: I suggest adding a table to present all mathematical symbols and notations used through the paper.

Response: We thank the reviewer for this valuable suggestion.

In the revised manuscript, we have added a dedicated table summarizing the main mathematical symbols and notations used throughout the paper. This table provides concise definitions of the stochastic variables, parameters, and key quantities introduced in the modeling framework.

The inclusion of this table improves readability and facilitates navigation of the manuscript, particularly for readers less familiar with stochastic-process notation.

Comment 7: There are some missing details in the methodology section, such as significance levels and decision criteria for the statistical tests.

Response: Thank you for this valuable comment. We have revised the manuscript to explicitly include the significance level and decision criteria used in all statistical tests.

In the Statistical Inference and Stochastic Modeling Framework subsection, we now state that all hypothesis tests are conducted at a significance level of $\alpha = 0.05$, and we clearly define the rejection criteria based on $p$-values and corresponding test statistics for the Wald–Wolfowitz runs test, the Ljung–Box test, and the likelihood ratio test.

These additions improve the transparency and reproducibility of the statistical methodology and ensure that the inference procedure is fully specified.

Comment 8: I see that you mention likelihood-ratio testing, AIC/BIC, stationary probabilities, spectral gap, and survival fitting, but the actual estimated values are not reported clearly in the results.

Response: Thank you for this important observation. We have carefully revised the Results section to ensure that all estimated quantities are explicitly and clearly reported.

Specifically, we now provide the numerical values for all key elements of the proposed framework, including:

• The likelihood-ratio test statistic ($\Lambda = 428.3$, $p < 10^{-6}$),
• Model selection criteria (AIC and BIC for both Bernoulli and Markov models),
• The estimated stationary distribution ($\boldsymbol{\pi} = (0.671, 0.329)$),
• The spectral properties (second eigenvalue $\lambda_2 = 0.53$ and spectral gap $\delta = 0.47$),
• The fitted Weibull parameters for realignment intervals ($\widehat{\beta} = 1.47$, $\widehat{\eta} = 83.2$), along with goodness-of-fit statistics.

These values are now consolidated and clearly presented within the Quantitative Summary of Empirical Estimation subsection, improving readability and ensuring that all methodological components are supported by explicit numerical results.

Comment 9: Your Results section is mostly qualitative. You make statements such as “statistically significant” and “shape parameter differs from unity”, but you did not support them with test statistics, p-values, confidence intervals, or effect sizes.

Response: We thank the reviewer for this important observation.

In the revised manuscript, we have ensured that all qualitative statements are explicitly supported by quantitative statistical evidence. In particular, the Results section now reports the corresponding test statistics and p-values for all hypothesis tests, including the Wald–Wolfowitz runs test, the Ljung–Box test, the likelihood-ratio test, and the Kolmogorov–Smirnov test.

Additionally, key model parameters (e.g., transition probabilities, stationary distribution, spectral gap, and Weibull parameters) are reported explicitly, allowing direct assessment of effect size and practical significance.

To further improve clarity, we have added a dedicated paragraph emphasizing that all claims of statistical significance and model behavior are grounded in the reported numerical results. These revisions ensure that the Results section is fully quantitative and reproducible.

Comment 10: Most of the figures appear more illustrative than empirical. These need a clear distinction between data-driven results and conceptual or model-based figures.

Response: Thank you for this important observation. We agree that clearly distinguishing between empirical (data-driven) and model-based figures is essential for proper interpretation of the results.

In the revised manuscript, we have made the following improvements:

1. Explicit distinction in figure captions: All figures are now clearly labeled as either empirical (derived directly from the captured MAC-layer dataset) or model-based (constructed from the inferred stochastic model or analytical expressions). This distinction is explicitly stated in each figure caption.
2. Clarification in the Results section: We have added a dedicated paragraph at the beginning of the Results section explaining the difference between empirical and model-based visualizations, ensuring that readers can correctly interpret the origin of each figure.
3. Addition of a fully data-driven figure: To strengthen the empirical grounding of the paper, we have included a new figure showing the empirical distribution of the binary error process. This figure is directly computed from the dataset and provides a baseline characterization of the marginal error behavior before introducing dependence-aware analysis.
4. Improved consistency between text and figures: The manuscript text now explicitly states whether each result corresponds to observed data or to model-based interpretation (e.g., large-deviation rate functions and phase diagrams).

Comment 11: Please revise your figures and make sure that all figures have clear units and informative labels, particularly Figures 5 and 7.

Response: Thank you for this valuable comment. We agree that clear labeling and proper specification of units are essential for the correct interpretation of figures.

In the revised manuscript, we have carefully reviewed and improved all figures, with particular attention to Figures 5 and 7. The following changes have been implemented:

1. Explicit units in all axes: All figures now include clearly defined axis labels with appropriate units. For example, in the realignment dynamics figure, time is expressed in seconds and the hazard rate in s$^{-1}$.
2. Clarification of dimensionless quantities: For theoretical quantities such as probabilities and rate functions (e.g., the large-deviation rate function), we explicitly indicate that these are dimensionless to avoid ambiguity.
3. Improved axis descriptions: Axis labels have been rewritten to be more informative, explicitly stating the physical meaning of each variable (e.g., empirical error rate, time since realignment event).
4. Enhanced figure captions: Captions have been expanded to clearly describe the variables, their units, and their interpretation within the stochastic framework.

Comment 12: You introduced availability and MTBF, but their actual computed values and practical interpretation are not clearly reported.

Response: Thank you for this important observation. We agree that the introduction of availability and MTBF should be supported by explicit numerical results and practical interpretation.

In the revised manuscript, we have incorporated a dedicated paragraph in the Results section where both metrics are explicitly computed and interpreted. Specifically:

MTBF estimation:

1. Using the fitted Weibull model for realignment intervals, we compute the expected cycle length as $\mathbb{E}[C_k] \approx 75.6$ seconds, leading to an estimated MTBF of approximately 75.6 seconds.
2. Realignment rate: The corresponding realignment rate is reported as $\lambda_r \approx 0.0132$ s$^{-1}$.
3. Availability estimation: Based on the empirical trace, network availability is estimated as $A \approx 0.91$, indicating that the system remains operational approximately 91% of the time.
4. Practical interpretation: We have added a detailed interpretation explaining that reliability is governed by frequent but short-duration instability cycles, rather than isolated failures, providing direct insight into Smart Grid operational behavior.

Comment 13: The assumption of a first-order Markov chain should be justified more carefully. Please explain why first-order dependence is sufficient and whether you checked higher-order behavior or not.

Response: Thank you for this important comment regarding the justification of the first-order Markov assumption.

In the revised manuscript, we have added a dedicated paragraph clarifying both the empirical and theoretical justification for adopting a first-order model. Specifically:

1. Empirical verification: We evaluated second-order conditional probabilities. $\mathbb{P}(E_{n+1} \mid E_n, E_{n-1})$ and compared them with first-order transitions. The results showed only marginal differences, indicating that the dependence structure is primarily governed by the immediate past state.
2. Model selection criteria: We assessed higher-order models using likelihood-based methods. Although second-order models increase the number of parameters, they do not provide a meaningful improvement in likelihood and are penalized by AIC and BIC, supporting the first-order specification.
3. Consistency with dependence structure: The observed geometric decay of autocorrelation and the presence of a strictly positive spectral gap indicate short-range dependence, which is well captured by a first-order Markov process.
4. Parsimony and robustness: The first-order model provides a balance between capturing temporal dependence and avoiding overparameterization, ensuring stable and interpretable estimates.

Comment 14: What is the number of realignment events, and how were they identified?

Response: Thank you for this important comment. We have revised the manuscript to explicitly report both the number of realignment events and the procedure used for their identification. Realignment events are now detected directly from the MAC-layer trace using IEEE 802.15.4 command-frame classification, specifically by identifying Coordinator Realignment commands via their MAC command identifiers, and corroborating them with orphan notification and reassociation sequences. A total of Nr=47N_r = 47Nr​=47 realignment events were identified over the 3,600-second observation interval. To ensure robustness and avoid overcounting, temporally adjacent control frames within short time windows are grouped and treated as a single event. The resulting event timestamps are then used to construct inter-event intervals for the renewal and survival analyses. These additions clarify the empirical basis of the reassociation modeling and improve the reproducibility of the results.

Comment 15: It seems that Discussion and Conclusion are stronger than the presented results. Please align the claims with the actual evidence or provide stronger support.

Response: We thank the reviewer for this important observation. In response, we have carefully revised the Discussion and Conclusions sections to ensure that all claims are fully aligned with the empirical evidence presented in the Results. Specifically, we have moderated statements that could be interpreted as overly general or theoretical, replacing them with data-driven interpretations explicitly tied to the analyzed IEEE 802.15.4 dataset. We now consistently qualify our findings using expressions such as “the empirical results indicate” and “in the analyzed deployment,” and we explicitly reference estimated quantities (e.g., $\widehat{\mathrm{FER}} = 0.329$, $\widehat{p}_{11} = 0.82$, and $\delta = 0.47$) to support all interpretations. Additionally, broader claims regarding general applicability, resilience interpretation, and large-deviation implications have been reformulated as scenario-specific observations or potential extensions rather than universal conclusions. These revisions ensure that the manuscript maintains a clear and rigorous correspondence between results and interpretation, avoiding overgeneralization while preserving the contribution of the work.

Comment 16: I found 10 duplicated references. References 11 to 20 are repeated again later in the list, so the actual number of references is 23, not 33. Please correct this issue and clearly explain how it occurred. Also, please check how these references were cited in the text and confirm whether the in-text citations are still correct and relevant.

Response: We appreciate the reviewer’s suggestion to strengthen the Introduction. In response, we have expanded this section by adding two new paragraphs that improve the conceptual flow and provide a broader and more up-to-date contextualization of the problem. Specifically, we first introduced a paragraph addressing the impact of heterogeneous wireless architectures and multi-hop IEEE 802.15.4 deployments, highlighting the role of cross-layer interactions and network-level dependencies in reliability analysis. This was followed by a second paragraph emphasizing the importance of data-driven and measurement-based approaches for capturing real-world stochastic behavior beyond classical analytical assumptions. These additions were carefully placed after the general theoretical framework and before the Motivation subsection to ensure a coherent progression from general context to the specific research gap addressed in this work. Furthermore, we incorporated new, high-quality references from recognized scientific sources, including recent works from IEEE Communications Surveys & Tutorials, Computer Networks, IPSN, and Ad Hoc Networks). These references complement the existing literature without redundancy and reinforce the relevance of empirical and dependence-aware modeling in Smart Grid communication systems. Overall, the revised Introduction now provides a clearer narrative structure, stronger literature support, and a more precise positioning of the contribution within current research trends.

Thank you very much.

Sincerely,

Carolina Del-Valle-Soto

Corresponding author

Universidad Panamericana. Facultad de Ingeniería. Álvaro del Portillo 49, Zapopan, Jalisco, 45010, México.

Phone: +52 (33) 13682200 | Ext. 4866

Email: cvalle@up.edu.mx

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript studies link reliability in ZigBee/IEEE 802.15.4 smart grid communications using MAC-layer packet capture data, with a focus on frame-error correlation and re-association dynamics. The topic is relevant and of practical interest. However, the current version still needs further improvement in dataset description, result presentation, model justification, and discussion of practical implications. Major revision is therefore recommended before further consideration.

1. The description of the dataset and experimental scenario is still insufficient to fully support the claim of real-world validation. More details on sample size, capture duration, network topology, traffic load, interference conditions, and deployment setting would improve the credibility and reproducibility of the study.
2. The manuscript uses several statistical tests and model selection methods, but the quantitative results are not reported in enough detail. For key conclusions, it would be helpful to provide test statistics, p-values, AIC/BIC values, parameter estimates, and confidence intervals.
3. The smart grid application background is clearly stated, but the connection between the statistical findings and application-level performance is still limited. Further discussion on how the results affect meter-reading latency, alarm reliability, or maintenance strategy would strengthen the practical significance of the work.
4. The first-order Markov model is adopted as the main model, but its suitability is not fully justified. It would be helpful to explain more clearly why this model is sufficient and what advantages it has over the independent model in capturing burst errors or consecutive failures.
5. A more direct comparison with the conventional independent-error assumption would make the contribution clearer. In particular, showing how the two assumptions lead to different outcomes in reliability evaluation or system design would better highlight the value of the proposed framework.
6. The Methods section includes many probabilistic and statistical concepts, but some symbols and variables are defined in a scattered way. A notation table or a more organized presentation of key variables would improve readability.

Author Response

Dear

Editor

Symmetry

We are submitting the paper:

“Stochastic Characterization of MAC-Level Reliability and Reassociation Dynamics in IEEE 802.15.4 Networks for Smart Grid Applications”

Authored by: Carolina Del-Valle-Soto * , José A. Del-Puerto-Flores , Ramiro Velázquez , Juan Sebastián Botero-Valencia , Leonardo J. Valdivia , José Varela-Aldás , Paolo Visconti

We would like to thank the reviewers and editors for their detailed analysis of the manuscript; the comments are very valuable to us. In the revised version of the paper, we have incorporated the all changes recommended by the reviewers.

Comments to all observations and suggestions including point-by-point responses are addressed in the following text.

 

Reviewer 3 comments

Comment 1: This manuscript studies link reliability in ZigBee/IEEE 802.15.4 smart grid communications using MAC-layer packet capture data, with a focus on frame-error correlation and re-association dynamics. The topic is relevant and of practical interest. However, the current version still needs further improvement in dataset description, result presentation, model justification, and discussion of practical implications. Major revision is therefore recommended before further consideration.

The description of the dataset and experimental scenario is still insufficient to fully support the claim of real-world validation. More details on sample size, capture duration, network topology, traffic load, interference conditions, and deployment setting would improve the credibility and reproducibility of the study.

Response: We thank the reviewer for this valuable observation. In response, we have strengthened the description of the dataset and experimental scenario in Section 3 (Materials and Methods) to improve clarity, credibility, and reproducibility. Specifically, we have added a new paragraph detailing the deployment environment, explicitly stating that the data were collected in an indoor Smart Grid–like testbed under real operating conditions in the 2.4 GHz ISM band, where coexistence with other wireless technologies (e.g., WiFi and Bluetooth) introduces realistic, uncontrolled interference. In addition, we incorporated a dedicated paragraph discussing the measurement scope and limitations of the dataset, clarifying that while the sample size and duration support robust statistical inference, the results correspond to a specific deployment scenario and may vary under different interference levels, traffic conditions, or network configurations. These additions complement the existing quantitative description (sample size, capture duration, topology, and traffic characteristics) and provide a more complete and transparent characterization of the experimental setting, as requested.

Comment 2: The manuscript uses several statistical tests and model selection methods, but the quantitative results are not reported in enough detail. For key conclusions, it would be helpful to provide test statistics, p-values, AIC/BIC values, parameter estimates, and confidence intervals.

Response: We thank the reviewer for this important suggestion. In the revised manuscript, we have expanded the quantitative reporting of the statistical analysis by explicitly including confidence intervals for the main estimated parameters. In particular, Section 4 now reports 95% confidence intervals for the empirical frame error rate, the Markov transition probabilities, and the Weibull model parameters, based on asymptotic approximations. These additions complement the already reported test statistics, p-values, and AIC/BIC values, providing a more complete and statistically rigorous characterization of the results and reinforcing the robustness of the conclusions.

Comment 3: The smart grid application background is clearly stated, but the connection between the statistical findings and application-level performance is still limited. Further discussion on how the results affect meter-reading latency, alarm reliability, or maintenance strategy would strengthen the practical significance of the work.

Response: We thank the reviewer for this valuable comment. In the revised manuscript, we have strengthened the connection between the statistical findings and application-level performance by adding a dedicated discussion paragraph in Section 5. Specifically, we now explicitly relate burst-error persistence to increased meter-reading latency, discuss the impact of temporal correlation on alarm reliability in safety-critical scenarios, and interpret the non-exponential realignment dynamics in terms of maintenance and network management strategies. These additions clarify the practical implications of the proposed stochastic framework for Smart Grid operation.

Comment 4: The first-order Markov model is adopted as the main model, but its suitability is not fully justified. It would be helpful to explain more clearly why this model is sufficient and what advantages it has over the independent model in capturing burst errors or consecutive failures.

Response: We thank the reviewer for this insightful comment. In the revised manuscript, we have strengthened the justification of the first-order Markov model in Section 3 by explicitly explaining its ability to capture burst-error behavior. In particular, we now contrast the probability of consecutive failures under the independent Bernoulli model with that of the Markov model, highlighting how the persistence parameter enables modeling of error clustering observed in the empirical data. This addition clarifies both the sufficiency and the practical advantage of the proposed model for representing temporal dependence in MAC-layer errors.

Comment 5: A more direct comparison with the conventional independent-error assumption would make the contribution clearer. In particular, showing how the two assumptions lead to different outcomes in reliability evaluation or system design would better highlight the value of the proposed framework.

Response: We thank the reviewer for this valuable suggestion. In the revised manuscript, we have added a direct quantitative comparison between the independent Bernoulli model and the proposed Markov model in the Results section. Specifically, we now show how both assumptions lead to significantly different probabilities of consecutive transmission failures, demonstrating that the independent model substantially underestimates burst-error events. This addition clarifies the practical implications of the proposed framework for reliability evaluation and system design.

Comment 6: The Methods section includes many probabilistic and statistical concepts, but some symbols and variables are defined in a scattered way. A notation table or a more organized presentation of key variables would improve readability.

Response: We thank the reviewer for this helpful suggestion. In the revised manuscript, we have introduced a dedicated notation table (Table 2) that consolidates all key symbols, variables, and parameters used throughout the probabilistic and statistical modeling framework.

This table provides a structured and centralized reference for the main quantities involved in the analysis, including stochastic variables, model parameters, and reliability metrics. As a result, the presentation of notation is no longer scattered across the text, and overall readability and clarity have been significantly improved.

Thank you very much.

Sincerely,

Carolina Del-Valle-Soto

Corresponding author

Universidad Panamericana. Facultad de Ingeniería. Álvaro del Portillo 49, Zapopan, Jalisco, 45010, México.

Phone: +52 (33) 13682200 | Ext. 4866

Email: cvalle@up.edu.mx

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed my comments adequately.

However, the response to the last comment is not relevant. Although they resolved the reference issue, the requested explanation of “how it occurred and whether the in-text citations are still correct and relevant” is still missing. The response to this comment looks like a response to another reviewer’s comment and is not relevant to the issue raised. Below are my comment and the authors’ response.

Comment 16: I found 10 duplicated references. References 11 to 20 are repeated again later in the list, so the actual number of references is 23, not 33. Please correct this issue and clearly explain how it occurred. Also, please check how these references were cited in the text and confirm whether the in-text citations are still correct and relevant.

Response: We appreciate the reviewer’s suggestion to strengthen the Introduction. In response, we have expanded this section by adding two new paragraphs that improve the conceptual flow and provide a broader and more up-to-date contextualization of the problem. Specifically, we first introduced a paragraph addressing the impact of heterogeneous wireless architectures and multi-hop IEEE 802.15.4 deployments, highlighting the role of cross-layer interactions and network-level dependencies in reliability analysis. This was followed by a second paragraph emphasizing the importance of data-driven and measurement-based approaches for capturing real-world stochastic behavior beyond classical analytical assumptions. These additions were carefully placed after the general theoretical framework and before the Motivation subsection to ensure a coherent progression from general context to the specific research gap addressed in this work. Furthermore, we incorporated new, high-quality references from recognized scientific sources, including recent works from IEEE Communications Surveys & Tutorials, Computer Networks, IPSN, and Ad Hoc Networks). These references complement the existing literature without redundancy and reinforce the relevance of empirical and dependence-aware modeling in Smart Grid communication systems. Overall, the revised Introduction now provides a clearer narrative structure, stronger literature support, and a more precise positioning of the contribution within current research trends.

Comments for author File: Comments.pdf

Author Response

Dear

Editor

Symmetry

We are submitting the paper:

“Stochastic Characterization of MAC-Level Reliability and Reassociation Dynamics in IEEE 802.15.4 Networks for Smart Grid Applications”

Authored by: Carolina Del-Valle-Soto * , José A. Del-Puerto-Flores , Ramiro Velázquez , Juan Sebastián Botero-Valencia , Leonardo J. Valdivia , José Varela-Aldás , Paolo Visconti

We would like to thank the reviewers and editors for their detailed analysis of the manuscript; the comments are very valuable to us. In the revised version of the paper, we have incorporated the all changes recommended by the reviewers.

Comments to all observations and suggestions including point-by-point responses are addressed in the following text.

 

Reviewer 2 comments

Comment 1: The authors have addressed my comments adequately.

However, the response to the last comment is not relevant. Although they resolved the reference issue, the requested explanation of “how it occurred and whether the in-text citations are still correct and relevant” is still missing. The response to this comment looks like a response to another reviewer’s comment and is not relevant to the issue raised. Below are my comment and the authors’ response.

Comment 16: I found 10 duplicated references. References 11 to 20 are repeated again later in the list, so the actual number of references is 23, not 33. Please correct this issue and clearly explain how it occurred. Also, please check how these references were cited in the text and confirm whether the in-text citations are still correct and relevant.

Response: We appreciate the reviewer’s suggestion to strengthen the Introduction. In response, we have expanded this section by adding two new paragraphs that improve the conceptual flow and provide a broader and more up-to-date contextualization of the problem. Specifically, we first introduced a paragraph addressing the impact of heterogeneous wireless architectures and multi-hop IEEE 802.15.4 deployments, highlighting the role of cross-layer interactions and network-level dependencies in reliability analysis. This was followed by a second paragraph emphasizing the importance of data-driven and measurement-based approaches for capturing real-world stochastic behavior beyond classical analytical assumptions. These additions were carefully placed after the general theoretical framework and before the Motivation subsection to ensure a coherent progression from general context to the specific research gap addressed in this work. Furthermore, we incorporated new, high-quality references from recognized scientific sources, including recent works from IEEE Communications Surveys & Tutorials, Computer Networks, IPSN, and Ad Hoc Networks). These references complement the existing literature without redundancy and reinforce the relevance of empirical and dependence-aware modeling in Smart Grid communication systems. Overall, the revised Introduction now provides a clearer narrative structure, stronger literature support, and a more precise positioning of the contribution within current research trends.

Response: Thank you for your careful reading of our manuscript and for pointing out the lack of a proper explanation in our previous response. We sincerely apologize for the confusion caused, as the response provided indeed did not address the specific concern raised in Comment 16.

Regarding the duplicated references, the issue originated during the manuscript preparation process when we were exploring additional and diverse sources to strengthen the literature review. In some instances, we used an LLM-based software tool to suggest potentially relevant references. When subsequently verifying and incorporating these references manually, some entries were unintentionally duplicated. This occurred because the same reference was generated or retrieved in slightly different BibTeX formats, which made them appear as distinct entries during the editing stage, although they corresponded to the same source.

We fully acknowledge that this was an oversight on our part, and we apologize for it. To address this issue, we have carefully reviewed and cleaned the reference list, removing all duplicated entries. Additionally, we verified each in-text citation to ensure that it correctly points to the intended and unique reference. We confirm that all in-text citations are now consistent, accurate, and relevant to the discussion in which they are used.

Furthermore, we observed that the number of duplicated references was relatively small. Instead of simply reducing the total count, we took this opportunity to improve the manuscript by incorporating alternative references that address the same topics. As part of this revision, we also refined and expanded several paragraphs in the paper, which resulted in a slightly larger but more coherent and better-supported reference list.

In particular, we added three new references that we consider relevant and appropriate within the scope of this minor revision, and we hope this addition is acceptable to the reviewer. All references in the revised manuscript have been carefully verified to avoid any inconsistencies or duplication.

We appreciate the reviewer’s observation, which helped us improve the overall quality and accuracy of the manuscript, especially regarding the integrity of the references.

Thank you very much.

Sincerely,

Carolina Del-Valle-Soto

Corresponding author

Universidad Panamericana. Facultad de Ingeniería. Álvaro del Portillo 49, Zapopan, Jalisco, 45010, México.

Phone: +52 (33) 13682200 | Ext. 4866

Email: cvalle@up.edu.mx

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I have reviewed the authors' responses to the previous round of revisions and the updated manuscript.I am satisfied that the authors have adequately addressed all the points raised during the review process. The manuscript has been improved accordingly.I have no further comments or corrections at this stage.