Don't know if this is up to date/current
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Off-road cycleway gritting
Cycleway Priority 1 - these routes will be the first to receive treatment whenever weather conditions dictate, and will be pre-treated where possible, when frost, snow or ice is forecast. Areas treated include
Middle Meadow Walk
Leamington Walk in Bruntsfield Links
Innocent Railway Path, between St Leonards Lane and The Jewel at ASDA
sections of the Caledonian Cycle Track, North Edinburgh Cycle Network.
All other parts of the Council's off road cycleway network are considered by the Neighbourhood Teams and prioritised with all other competing winter treatment demands.
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http://www.edinburgh.gov.uk/info/20047/severe_weather/1139/priority_system_for_winter_gritting_routes