Reduce supply. The less space there is for cars, the fewer ppl will drive. Essentially, limit traffic to a few areas, and make most of the city (not just manhattan) traffic-free. That will reduce the number of cars (simple geometry) and alleviate traffic.

This is what they did in Amsterdam in the 70s, and now they barely have any traffic whatsoever. I visited recently, it was crazy. A lot of the city looks just as dense and lively as any random neighborhood in Manhattan or BK yet there's no honking or cars just stuck there not moving. There is traffic, and there are cars, but I never saw a car stuck in traffic.