There we go again guys, we are re-inventing the wheel....
Average speed is distance divided by time. Providing the distance stays the same, you need to shorten the time it takes you to cover it. In other words, cycle faster and your average speed will increase. It is really that simple.
Everything else is secondary. That is the problem with cyclists sometimes. We have way to many excuses (tires, frames, weight, etc) when the answer simply is that our bikes are way better than we deserve.
Eddy Merckx said it best when asked how to become a better cyclist, he answered: "Ride a bike, ride a bike, ride a bike...."