Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control

Round 1

Reviewer 1 Report

The authors propose a discrete-time lattice hydrodynamic traffic model to uncover the varying time-delay on traffic flow and reduce its impact on traffic flow. The authors present a though literature review on traffic models to understand traffic congestion. I think this is a well-written paper. The analysis of the impact of varying time-delay and delay-independent feedback control strategy on traffic flow seems novel. There are minor comments suggested for the authors to improve this paper.

- Please provide more information about the simulation environment.

- Please provide the details of the parameters used in the simulations. It would be better to explain how those parameters are determined.

- figure -> Figure

- Please define the simulation time step clearly.

- Please rearrange figures so they are placed close to where they are mentioned.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript entitled "Study on the Lyapunov stability of a discrete-time macroscopic traffic system with varying time-delay and feedback control" presents a very interesting approach.

General comments:

Equation numbering can be revised to see if all numbered equations are in fact cited along the manuscript; I believe many of them aren't.

Conclusion Section number is not correct.

L19-22: this sentence is hard to follow, can't the authors rewrite it in a simple way?

L150: there is an extra space here (there are also some typos along the text, so, I would suggest the authors to revise it carefully).

L181: can the authors include some reference to support the claim?

L214-215: these matrices definition can be done in one sentence, instead of occupying such big space.

Section 4, L296-298: Why do the authors choose those values for the parameters? Would the findings be different for other values?

How the research findings could be useful for drivers or traffic managers? How this approach could be integrated to become an active component for traffic management?

Conclusion: the main findings are described, but it is missing some notes on the limitation of the study and also on future research developments.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf