I have a Local blog since 2011 that generates me about 2500 Pageviews Daily and Etechvilla.com from Feb. 2013 that generates about 500-800 daily Pageviews daily but my blog with fewer traffic has a better alexa ranking. This is why i beleive that alexa doesnt really rank sites due to traffic rate.
Below are the few steps you should apply to increase your alexa rank in Few days.
#1. Claim your blog at Alexa: This is really the first step to take. Claiming your site/blog at alexa will help boost your ranking. You can Signup a free account and you are done with this part.
#2. Install Alexa Widget: This step has to do with placing alexa widget on your blog. This also helps to boost your alexa ranking.
#3. Create a Custom Toolbar: Create and Install an Alexa toolbar on your PC. Ths helps in boosting your alexa ranking. Also, Ask your blog readers/friends to also install your toolbar on their PC as every of their visit to your blog will boost your rank.
#4. Review Your Blog/Website: Reviewing your blog/website boosts ranking also. You can review it your self and ask your blog readers/friends to review it also.