I have written 2 papers related to your research problem.

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0166064

http://www.journalmodernpm.com/index.php/jmpm/article/view/184

Do let me know if you need any further information.

http://wiki.openstreetmap.org/wiki/Train_routing

http://www.siam.org/meetings/alenex03/Abstracts/LAnderegg3.pdf

Routing trains through a railway station based on a node packing model

Peter J. Zwaneveld, Leo G. Kroon, Stan P.M. van Hoesel, Routing trains through a railway station based on a node packing model, In European Journal of Operational Research, Volume 128, Issue 1, 2001, Pages 14-33, ISSN 0377-2217, https://doi.org/10.1016/S0377-2217(00)00087-4.

(http://www.sciencedirect.com/science/article/pii/S0377221700000874)

Keywords: Railway transportation; Timetabling; Routing trains; Node packing problem

Dear resercher,

You can see in my profile. There are some papers of routing of passengers train based of fuzzy linear programming method.

I have written 2 papers related to your research problem.

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0166064

http://www.journalmodernpm.com/index.php/jmpm/article/view/184

Do let me know if you need any further information.

http://www.siam.org/meetings/alenex03/Abstracts/LAnderegg3.pdf

https://algo2.iti.kit.edu/download/diss_geisberger.pdf

https://uic.org/cdrom/2008/11_wcrr2008/pdf/PS.2.21.pdf

Article Scheduling and Routing Algorithms for Rail Freight Transportation

https://pubsonline.informs.org/doi/abs/10.1287/trsc.30.3.181?journalCode=trsc

https://cs.stackexchange.com/questions/83759/routing-algorithm-for-train-network