"During the 2012 Games many of our passengers made small changes to their journeys which meant we were able to carry record numbers without the transport network feeling any busier.
"This section of the Northern Line is exceptionally busy during part of the morning and while the modernisation of the line will help to relieve crowding when complete next year this trial will look at whether we can improve the situation now.
"By making a small change to the time they travel our passengers' journeys could be faster and more comfortable."
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Crossrail contractors have been hit with a fine of more than a million pounds over the death of a worker and other incidents.
Anh Nhu Nguyen, 52, claimed he lived in the North Kensington block and that his wife and son had died in the fire.
Roads will be closed in central London on Saturday 29 July and in London and Surrey on Sunday 30 July.