I have recently been reading David McKittrick (et al)'s Making Sense of the Troubles. An interesting point, which I wasn't aware of before, is their contention that the late 70s and Roy Mason's tenure as Northern Ireland secretary was an important turning point. In fact, you could make an interesting comparison with Iraq in 2007-2008.
Mason's policy was to forget about further top-level negotiations, after the collapse of the Sunningdale agreement, and focus on security and economic issues in the hope that progress from the bottom up would bring the conflict parties back to the negotiating table on better terms. In fact, during his tenure, there was a dramatic drop in the rate of killings that was never reversed. This is the hub of McKittrick's argument - having surged in 1971 and peaked in 1972-3, levels of violence stayed very high until 1977 and then dropped to a new, much lower average level.
The British government in this period tried various expedients. The military used more special forces, and integrated their intelligence systems and those of the police and security services. Overall, there was a deliberate effort to project the whole war as a law-enforcement problem (very much a theme of US and Iraqi government propaganda during the "surge"), and to launch as many criminal prosecutions as possible. They tried hard to recruit informers and to make use of supergrasses.
McKittrick and his co-authors argue that there was a sort of cycle-of-recruitment effect at work - terrorism caused recruitment into the loyalist terrorist organisations, whose violence caused further IRA recruitment, which led to more military intervention and more loyalist violence. They further argue that this cycle was broken or at least slowed down in the late 1970s - whether the government was succeeding in providing security or not, it at least reduced the demand for unofficial, privatised violence. The government also tried hard to recruit potential paramilitaries into its own forces, and demonstrated that it was willing to use force against loyalists as well as republicans (they argue that the failure of the 1977 loyalist strike was important). This is all quite familiar.
However, the drop in violence was an over-determined event. There was a major change in the IRA leadership and strategy, which emphasised holding out for the long term and eventually led to an increased emphasis on the ballot box. (The parallel with the Sadr movement stands out.) There was a major protest movement demanding peace, which is another way of saying that the people were unwilling to tolerate so much violence any more.
Although this turning point meant much less violence, it didn't solve anything in and of itself. And it involved quite a lot of state violence in itself - especially during interrogations. This Musings on Iraq roundup is telling - rather than gunbattles and mass bombings, the war continues with a low-level assassination campaign. In Northern Ireland, the best any security solution could ever do in the absence of a political solution was to hold the levels of violence down around the post-77 average, with a very significant cost to society as a whole.