Equilibrium Strategies for Overtaking-Free Queueing Networks under Partial Information

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a novel theoretical approach to customer strategic decision-making in overtaking-free queueing networks. The authors analyze equilibrium strategies when customers base their actions on partial information (total number of customers in the system), demonstrating that threshold strategies are optimal equilibrium strategies. Numerical examples are provided to support these theoretical findings and elucidate the characteristics of strategies in overtaking-free networks.

 

1.     Historical Context and Literature Review:

The introduction would benefit from a more comprehensive discussion of the historical background of queueing theory and a more thorough comparison with extant research. For instance, the critique of D'Auria & Kanta (2015) presented later in the paper could be introduced earlier to better contextualize the current research within the existing literature. Additionally, the inclusion of more recent references, particularly those related to decision-making based on partial information and applications of reinforcement learning to queueing models, would enhance the paper's contemporary relevance and broader applicability.

 

2.     Interpretation of Numerical Results:

While Figures 3 and 4 present intriguing numerical analysis results that support the theoretical findings, a more detailed explication of the specific interpretations suggested by each figure and table would be beneficial. In particular, a more in-depth discussion of the differences between Models A and B, as well as the economic advantages demonstrated by each model, would provide valuable insights.

 

3.     Limitations and Future Work:

The conclusion acknowledges the limitation of relying on exponential distributions. However, a more explicit discussion of the constraints imposed by the assumptions of no overtaking and partial information notification would better highlight the paper's limitations. This could lead to a more comprehensive outline of potential future research directions.

 

4.     Practical Applications:

While the theoretical framework is clearly presented and the equilibrium strategies are mathematically derived, the paper would benefit from a more extensive discussion of potential real-world applications. Providing specific examples of how this theory could be applied to practical systems, such as transportation networks or communication systems, and discussing the potential effectiveness of these strategies in real-world scenarios would enhance the research's practical significance.

Comments for author File: Comments.pdf

Author Response

We sincerely appreciate the referee's comments.
We have carefully considered all of them, and we are pleasantly grateful that they helped improve the quality of our paper.

Besides some corrected typos, all the added and modified text is highlighted in violet allowing you to quickly see the modifications with respect to our previous version. Of course, all text will be black in the published version.

Comments 1: Historical Context and Literature Review:
The introduction would benefit from a more comprehensive discussion of the historical background of queueing theory and a more thorough comparison with extant research.
For instance, the critique of D'Auria & Kanta (2015) presented later in the paper could be introduced earlier to better contextualize the current research within the existing literature.
Additionally, the inclusion of more recent references, particularly those related to decision-making based on partial information and applications of reinforcement learning to queueing models, would enhance the paper's contemporary relevance and broader applicability.

Response 1: We improved the introduction, adding more details and references to the historical background and better highlighting the motivations and the results of our research.

Comments 2: Interpretation of Numerical Results:
While Figures 3 and 4 present intriguing numerical analysis results that support the theoretical findings, a more detailed explication of the specific interpretations suggested by each figure and table would be beneficial.
In particular, a more in-depth discussion of the differences between Models A and B, as well as the economic advantages demonstrated by each model, would provide valuable insights.

Response 2: We improved Section 6 Numerical Computations including some details on the interpretation of the Figures 3 and 4 (now 5).
In particular in Figure 3(a) we modified μ=1.15.

Comments 3: Limitations and Future Work:
The conclusion acknowledges the limitation of relying on exponential distributions.
However, a more explicit discussion of the constraints imposed by the assumptions of no overtaking and partial information notification would better highlight the paper's limitations.
This could lead to a more comprehensive outline of potential future research directions.

Response 3: We added a new section titled Limitation and future work containing the suggested information.

Comments 4: Practical Applications:
While the theoretical framework is clearly presented and the equilibrium strategies are mathematically derived, the paper would benefit from a more extensive discussion of potential real-world applications.
Providing specific examples of how this theory could be applied to practical systems, such as transportation networks or communication systems, and discussing the potential effectiveness of these strategies in real-world scenarios would enhance the research's practical significance.

Response 4: In the introduction, we listed some possible applications of our research.
In particular, we gave two examples of applications related to the two models, A and B, introduced in Section 6.

Reviewer 2 Report

Comments and Suggestions for Authors

This work studies overtaking-free queueing networks aiming at providing equilibrium strategies with the partial information of the total number of customers already in the network. This work has certain significance in e.g., performance model or evaluation for computing systems, but there are some issues should be addressed.

1. In abstract, the compute method and its evaluated results as well as conclusion should be briefly introduced.

2. At the beginning, the paper should give an introduction on overtaking-free queueing networks and the focused problem. In addition, the discussion on the significance of the focused problem is missing.

3. It would be better to conduct simulated experiments for the performance evaluation. Besides, state-of-the-art works should be compared with.

4. The findings and limitations should be discussed.

5. Up-tu-data related works are missing.

Author Response

We sincerely appreciate the referee's comments.
We have carefully considered all of them, and we are pleasantly grateful that they helped improve the quality of our paper.

Besides some corrected typos, all the added and modified text is highlighted in violet allowing you to quickly see the modifications with respect to our previous version. Of course, all text will be black in the published version.

Comments 1: In abstract, the compute method and its evaluated results as well as conclusion should be briefly introduced.

Response 1: We modified the abstract including some comments on the used methodology and the results obtained.

Comments 2: At the beginning, the paper should give an introduction on overtaking-free queueing networks and the focused problem.
In addition, the discussion on the significance of the focused problem is missing.

Response 2: We agree with the referee's comment and accordingly modified the introduction.

Comments 3: It would be better to conduct simulated experiments for the performance evaluation.
Besides, state-of-the-art works should be compared with.

Response 3: We decided not to include simulations, since the paper is about a methodological approach that leads to explicit formulas, computable through a recursive algorithm.
We have included a new figure in Section 6 comparing the throughput of the two models described in that same section.

Comments 4: The findings and limitations should be discussed.

Response 4: We added a new section titled Limitation and future work addressing this information.

Comments 5: Up-tu-data related works are missing.

Response 5: We enriched the introduction by adding many recent works related to the economic analysis of queueing systems and queueing networks, as well.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have carefully reviewed the revised manuscript and confirm that significant improvements have been made.

Reviewer 2 Report

Comments and Suggestions for Authors

No more comment