Personally speaking I would be happy if the same system was used as on the Jubilee and Northern Lines, as it would enhance network compatibility.
I would also hope that the ability to use the 1938 stock heritage train and the 'steam on the met' trains is retained in the new arrangement.
Of course the system will need to be compatible with the Chiltern, SWT and Overground trains which operate over routes also used by the subsurface Underground network.
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Someone somewhere else who works in the transport industry has said that the most logical thing would be for LU to use a system which is ERTMS compatible.
I wonder whether LU would be so happy. After all, they see themselves as an urban metro - not part of a mainline railway system. But whether they like it or not the historical connections with other railways and consequential joint services mean that LU cannot fully isolate itself from the 'big' railway.
ERTMS compatibility would, I assume, make future life easier on all routes which are shared with mainline trains (Metropolitan, District and Bakerloo Lines), as it would mean that any new trains that are introduced in the future, plus any train that needs to use that route as a diversion would automatically be compatible with the signalling.
Simon