Evaluation of the Accuracy of the Analytical Model of a Queuing System with a Finite-Compression Mechanism in Relation to Real Service Disciplines^†

Round 1

Reviewer 1 Report

The paper is devoted to comparison of “analytical model” proposed by authors and systems with “real service disciplines” (such as FIFO, cFIFO, vFIFO). The model of a multi-service queuing system supporting both elastic and adaptive traffic is considered.  The main feature of the study is a finite compression mechanism, which is a very interesting. In my background, I don’t meet such queueing models. As I understood, it is proposed by the authors in [1], but unfortunately it is not free to download. 

 I believe the authors have obtained original results, but its presentation in the paper is failed. I did not find the scientific value of this study. There are the following reasons:

1)     The main feature of the analytical model is already proposed in [1].

2)     There are no analytical studies of the model.  Formulas (3)-(6) depend on the probability distribution P[n], but  P[n] was not obtained. (Only balance equations (2) is written).

3)     The comparison of two different models (QS with a finite compression mechanism and QS with vFIFO) is mathematically senselessly. What is the aim of the study?

4)     Numerical results based on the simulation gives questionable conclusions. Relative error archives 45%, regularity is not captured, may be it needs more examples.

If authors can explain this comments and edit the paper, it can be accepted.

I also note a few more points that should be corrected:

1)     There are too many references to own works.

2)     SDFIFO is bad explained. How a discipline depends on a system state? What the difference between SDFIFO and a finite compression mechanism.

3)     The introduction needs editing. The queuing theory background is not enough.

4)     Line 49 The term “multidimensional queueing system” needs to be explained

5)     There are typos (e.g. “fallows”, “exemplify” “am”, “probabiliyu”)

6)     There is a confusion with Vr, Vv, Vq. In lines 88-98 the mean of this variables is different from figures and further study.

7)     What distribution law has duration of the service.  From the text, we know only its intensity. As for arrivals.

8)     Lines 155 and 201 needs citations.

9)     As I said, the paper needs more numerical examples, and more visible regularity demonstrations.

The paper has some typos, but english is good for understanding.

Author Response

We are grateful to the reviewer for his kind comments that significantly improved the quality of our work. Thanks to his suggestions as to how papers might be improved we had a chance to clarify specific details with regard to the content of the paper and correct the typos. We have extensively revised our manuscript according to the reviewers’ recommendations to improve the quality of the paper. Responses to all of the Reviewer's comments are included in the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper addresses the important topic of evaluating the accuracy of analytical models for queuing systems, with a particular emphasis on the finite-compression mechanism, which is a significant novelty of the paper. The potential applications of this approach lie in multimedia systems of next-generation telecom networks. Overall, the paper is well-written, follows appropriate methodology, and provides a rigorous evaluation of the derived results. However, I have some minor points for improvement. In Section 2, it would be beneficial to provide more details about elastic and adaptive traffic, along with additional references. Moreover, please provide more information about the experimental methodology employed in Section 4. Lastly, it would be helpful to explain the significance of measuring the blocking probability by providing further details and relevant citations.

the quality of English is good

Author Response

We are grateful to the reviewer for his kind comments that significantly improved the quality of our work. Thanks to his suggestions as to how papers might be improved we had a chance to clarify specific details with regard to the content of the paper and correct the typos. We have extensively revised our manuscript according to the reviewers’ recommendations to improve the quality of the paper. Responses to all of the Reviewer's comments are included in the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors did a very good job on the paper and took into account almost all comments.  A few more points need to be corrected before the publication.

1. Lines 57-60. In my comment (#3), I mean that the paper needs more information about related models of queuing systems (i.e. with a finite-compression mechanism) and methods of their study. Authors have already added new references in the text, I think  it would be good to add a few words to the introduction.

2. Line 69. “This discipline allows system analysis using the Markov process.”  is not quite correct.  Markov processes method  is used in queueing systems not only with SDFIFO discipline. The greatest influence is given by the laws of service and arrivals.

3. Line 139. It is good that authors give explanation of P[n], but it will not be superfluous to add a few words about the method of their calculation. Authors should not be afraid to repeat themselves with paper [1]. If you have obtained the analytical formula for P[n], please write it. It makes  better visibility and clarity of the results.

4.  “%” is missing in Formula (7).

5. As for the numerical results, I recommend to write some conclusions (without figures and numbers) devoted the results of the comparison for other values of the model parameters (e.g. low arrival rate, bigger numbers of traffic classes or even examples with only elastic traffic), if authors have conducted them. It can help to generalize the study results and gives them great practical value.

Author Response

We are grateful to the reviewer for his kind comments that significantly improved the quality of our work. Thanks to his suggestions as to how papers might be improved we had a chance to clarify specific details with regard to the content of the paper and correct the typos. We have extensively revised our manuscript according to the reviewers’ recommendations to improve the quality of the paper. The answers to all comments are included in the attached file.

Author Response File: Author Response.pdf