What determines the duration of the assault phase in Payday: The Heist?

From my experience, the further you go in the assaults waves, the longer they'll last. You can do the test on First world bank, for instance: wait for the assaults without accomplishing any of the objectives. The first assaults will be harder and harder (because introducing new ennemies such as buldozers and tazers), but when there will be no new cops types to rise the difficulty, the assaults duration will be extended.

The difficulty level is also to take into account: assaults in easy are WAY shorter than hard or overkill assaults.

Also I'm pretty sure that the final assaults (where you have to escape from the level before the timer ends) are endless.

As Anto said I would have to completely agree, the assault will last a bit longer if special swats are dead, so technically speaking an assault could end quicker avoiding them. Essentially assaults are time based and not body counts, this video here will prove that :)