Extending a train pathing model from one-way to two-way track

A train pathing model and algorithms for a real network was presented and tested in a previous paper. There it was assumed that each rail line has two or more tracks and each was dedicated to traffic in one direction as is usual in Europe. Here, this paper shows how to adapt and extend that model and algorithms so as to handle trains on single line two-way track, as is usual in North America. Though introducing two-way track makes the formulation appear more complex, it is shown that somewhat surprisingly, (a) it does not increase the number of constraints or variables, including 0-1 variables, and (b) the model with two-way track should generally be easier to solve.