What is the ratio of flights that follow the track system in the north Atlantic and those that don't? Also what is the general trend in this ratio over time?
According to ICAO NAT doc 007 (North Atlantic Operations and Airspace Manual, edition 2014/2015) (PDF), approximately half of the North Atlantic (NAT) flight use the Oceanic Track System (OTS).
2.1.3: It should be appreciated, however, that use of OTS tracks is not mandatory. Currently about half of NAT flights utilise the OTS. Aircraft may fly on random routes which remain clear of the OTS or may fly on any route that joins or leaves an outer track of the OTS. There is also nothing to prevent an operator from planning a route which crosses the OTS. However, in this case, operators must be aware that whilst ATC will make every effort to clear random traffic across the OTS at published levels, re-routes or significant changes in flight level from those planned are very likely to be necessary during most of the OTS traffic periods.
Note that not all flights in the NAT do cross the Atlantic from East to West or vice versa. For example:
Flights from Northern Europe to Spain / Canaries / Portugal and v.v.
Flights from Portugal to the Azores and v.v.
Flights from Iceland
And then there are a number of fixed routes that allow aircraft that do no meet the minimum navigation performance requirements to cross the ocean. These tracks do not change with the daily winds like the OTS tracks.
All these are included in the 'about half'
But especially in the Northern part of the NAT airspace, covered by the Reykjavik FIR there are many random routes. According to the website of Iceavia:
In 2010, 92.3% of the traffic in the Reykjavik CTA was on random tracks and 7.7% was on the NAT tracks.
But that is mainly because the OTS tracks are usual south of the Reykjavik FIR.
That same page says:
In effect, where the preferred track lies within the geographical limits of the OTS, the operator is obliged to choose an OTS track or fly above or below the system. Where the preferred track lies clear of the OTS, the operator is free to fly it by nominating a random track. Trans-Atlantic tracks, therefore, fall into three categories: OTS, Random or Fixed.