This article focusses mainly on plans to run six Edinburgh-Glasgow trains an hour/
http://www.scotsman.com/news/transport/edinburgh-glasgow-trains-every-ten-minutes-1-4009584
(Upgrading Greenhill Junction, west of Falkirk seems to be key).
But relevant to this thread is this bit:
"
The Network Rail document also includes another shelved element of the original Egip scheme, to divert some trains via another line for part of the journey to reduce congestion in Edinburgh.
Some services would run from Winchburgh, near Linlithgow, then via Dalmeny, near the Forth Bridge, to enter the capital on the Fife line.
That would avoid trains having to cross tracks around congested Haymarket Station in the west end of the city
"