If your origin/destination only has one train per day, then that's unfortunate. But the existence of a one train per day (or week) service on a more direct route, for a flow where there are many more services via alternative route, should not have a negative impact on customers.What do you class as regular, once a day is frequent to people living in Brigg
I think that in this instance it is safe to ignore the direct route which runs from Dalmeny to Linlithgow via Kirkliston. The National Routeing Guide Instructions tell us that "the shortest route is calculated by reference to the National Rail Timetable". In that timetable, none of the tables listed in the Index for Dalmeny (242) or for Linlithgow (228 and 230) show a distance for Dalmeny to Linlithgow via Kirkliston.Given that there is no regular scheduled service from Inverkeithing to Falkirk avoiding Edinburgh, the shortest route should be 92 miles: Leuchars - Ladybank - Perth - Gleneagles - Stirling - Glasgow QS.