In the traffic route guidance models:
1- What are the widely used method and mathematical formation of this problem?
2- What are the controlling parameters and the decision variables that should be solved to obtain simultaneous user equilibrium and social optimum?
3- Is there known exact prevailng generalized solution of this ITS application?
This is a good question with lots of possible answers.
A thorough study of the mathematics in solving one form of the route guidance problem is given in
http://www.utrc2.org/sites/default/files/pubs/collaborative-exploratory-research-anticipatory-route-guidance-problem-journal_0.pdf
See Section 2, starting on page 4, for a formulation of the problem. Mathematical properties of the anticipatory guidance problem (ARG) are given in Section 3, starting on page 13.
The mathematics of dynamical optimal routing is given in
https://hal.inria.fr/file/index/docid/740347/filename/trb2013_Ma_Lebacque_HAL.pdf
A complete, thorough study of the mathematics of the route guidance problem is given in
http://web.unlv.edu/centers/trc/paz/pdf/education_Alexander_Paz_dissertation.pdf
I have not exact idea what is route guidance problem but i think this may be correlated with transportation problem(operation research ) and also with depth search problem or network stheory problems
What kind of route guidance strategies are you interested in? As I know, some researchers focus on the routing strategy via GPS devices, and some others focus on providing traffic information through variable message signs. I did some works related to the signs, such as the attached papers. For more work, please see my webpage and I am happy to discuss more detail with you.
Article A traffic-condition-based route guidance strategy for a sing...
Article A self-regulation traffic-condition-based route guidance str...
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