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Dear Dr. XXX,

We have received the reports from our advisers on your manuscript, "XXXXXXXXXXX", submitted to
Journal of XXXXXXXX

Based on the advice received, the Editor has decided that your manuscript can be accepted for publication after you have carried out the corrections as suggested by the reviewer(s).

Attached, please find the reviewers' comments for your perusal.

YOU ARE KINDLY REQUESTED TO ALSO CHECK THE WEBSITE FOR POSSIBLE REVIEWER ATTACHMENTS.


I am looking forward to receiving your revised manuscript
before 08 Mar 2015

With kind regards,
David Barton, Ph.D.
Associate Editor

Reviewer #1: Review Report for  XXXXXXX
Comments for the Author:


The paper presents an improvement of the aw-rascle model of vehicular traffic, which basically consists in implementing the mathematical structure the authors proposed for the derivation of models by an approximation of the pseudopressure obtained by a detailed analysis at the microscopic scale. The idea is good and leads to a model, which describes the behavior of the flow in steady uniform conditions, namely the velocity and flow diagrams. The qualitative analysis, which follows is correct. Accordingly, this paper deserves attention.

Unfortunately, it does not properly refers to the existing literature, where similar ideas have been proposed although technically different from that proposed in this paper.

The paper can be published after a careful revision focused on the aforementioned drawback. Bearing this in mind, the following indications are given as hallmarks for the required revisions.
È»ºóÏÂÃæÊÇÎåÆªÎÄÏ×£¬¶¼ÊÇ˵ÎÒÎÄÖеÄij¸öÏÖÏóÓÐÈËÓò»Í¬µÄ·½·¨·¢ÏÖ¹ý¡£

In conclusion, the paper can be published after an improved reference to the existing literature, while the present edition is somehow misleading.




Reviewer #2: Review Report for  XXXXXXX

This paper proposes a modified Aw-Rascle model based on the car following principle with a maximal constraint on the density-velocity relationship. The essence is to use a nonconvex function $F(u)$ instead of $u$ in the momentum equation in the standard Aw-Rascle model, such that some complicated traffic phenomena can be captured, for example the phase transition. The authors also show that the new model develops the standard Aw-Rascle model for the reason that it amends some nonphysical features of the original one. In addition, all the Riemann solutions for the model are constructed completely by using the analysis of the convex hull in the $(\rho,q )$ phase plane which can illustrate some interesting traffic phenomena in detail.

I believe that the model is new and interesting in the traffic flow theory and the result seems correct to me. But there needs some corrections of language, for example
(1)     On page 1, line -6, "the density and the velocity all" should be "both the density and the velocity".
(2)     On page 2, line 8, "there is still some" should be "there are still some".
(3)     On page 2, line -3, "which envelop curve you chose the solution of some riemann problems" should be "which envelope curve you choose the solution of some Riemann problems".
(4)     On page 5, line 8, "Take (2.2) into (2.3)" should be "Taking (2.2) into (2.3)".
(5)     On page 6, line 11, "It is naturally that" should be "It is natural that".
(6)     On page 7, line 5, "In order to analysis" should be "In order to analyze".
Besides these comments, I recommend the manuscript for publication in Journal of Engineering Mathematics.


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