Fluid Net Models: From Behavioral Properties to Structural Objects

Round 1

Reviewer 1 Report

The paper deals with the characterization of some properties of timed continuous Petri net models. The topic is interesting, the paper is well organized and the presented results seem sound.

The major concern of the reviewer is that the new contribution of this paper is not clear. In fact, all the presented propositions, theorems and examples are from previous published works of the authors (refs. [13, 14, 15]). In my opinion, the authors need to be clear about the paper’s objective or new contributions with respect to their previous work.

Some other remarks to improve the paper are the following:

L59. In the next of the paper only MTS is mentioned in the different propositions/theorems. Could they be considered for MTSR nets also?  

L305. “paths loosing/gaining marks” not clear

L467: reference to figure 9 is needed for (a) and (b).

English and minor remarks:

• Behaviour/behavior: please be consistent
• Many typos need to be corrected: (e.g. L17: appear; L112: provides…)
• Figure 2: please specify the axis labels
• L307: 1(b) -> figure 1(b); figure 4(a) -> figure 4.
• Sometimes Fig. is used rather than figure, please be consistent.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

This paper builds on a substantial body of work lead by the last author (Manuel Silva). Please clarify and state clearly what the new contributions of this paper under review are. This could be done in a new paragraph starting with ‘The contributions of this paper are as follows: …’, which could be inserted before or after the currently last paragraph in the ‘Introduction and Motivation’. 

Likewise, state clearly which notions you re-use from previously published work; at best next to the definitions, propositions, theorems, which you repeat to make the paper self-contained.

The PN in Figure 1 needs to be much better explained in order to fit its purpose to serve as an introductory motivating example. Using meaningful names for all nodes might help; otherwise provide a table explaining the meaning of every place and transition, and the initial marking. For example, the wording speaks of input/output stores; where do I find the corresponding places in the PN? Which PN components correspond to the robot or conveyor? Besides, what is a  CNC machine or a two site belt (two-site belt?)?

To make the paper self-contained,  spend a few words explaining:

- infinite server semantics;

- how you obtain Figures 2, 7b/c, 8, 10, 11; 

- how to read Figure 5;

- ‘the number of firings of transitions per time unit defines the system throughput’ ?

There seems to be no related work, at least nothing is explicitly given in the paper. Either state clearly that there is no closely related work or add a corresponding paragraph.

The readability of Figure 9 would take advantage of giving all abbreviations in the caption.

Please add a list of all abbreviations at the end of the paper.

The English needs fixing; please seek professional help.

some minors (not exhaustive):

- or even worst -> or even worse

- k1 varies in the range [0 7]  -> [0, 7] ?

- λ2 varies in the range [0 4]  -> [0, 4] ?

- non monotonicity -> non-monotonicity

- referring to specific sections or figures requires capitalisation; e.g. ‘see Figure 5’, but ‘in the following figures’;

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

In the paper the authors propose a study on equilibrium throughput in manufacturing systems. The proposed work leverages the concepts about fluidization and analysis techniques used in Timed Continuous Petri nets (TCPN). In particular, it is known in TCPN that increasing the initial marking/firing rate ((increasing the initial marking/firing rate means considering more/faster machines)) does not always lead to an increase in the throughput.

The proposed paper shows that the structural objects named problematic configurations are responsible that varying the initial marking or firing rate of transitions the equilibrium throughput of the net exhibits paradoxical behaviors, such as non monotonicities and discontinuities.

In my opinion the paper is well written but the new contributions are not clear. In the Introduction the authors should put in evidence the list of new contributions.

Moreover, in the paper several needed propositions and theorems are taken from other works. Propositions 4.3 and 4.6 are not proved. I do not understand if they are new contributions or are taken from other works.

The number of references seems limited. In the first part of the Introduction, the authors should include papers that investigate throughput by Petri nets in general.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors address all the reviewer's remarks.