1.Advertise. This one is so obvious, we're going to look at it first.
2.Get Social.
3.Mix It Up.
4.Write Irresistible Headlines.
5.Pay Attention to On-Page SEO.
6.Target Long-Tail Keywords.
7.Start Guest Blogging.
8.Invite Others to Guest blog on Your Site
There are different traffic sources like organic traffic source, referral and direct traffic source. There are also campaigns like email marketing (if applicable) that can help you to increase your site traffic. It is just all matter of creating a marketing plan and strategy for your business.
I think you should share your articles across many social networks such as Facebook, Twitter, Google+...and if you have budgets, you should run some PPC campaigns. With these ways you will drive many traffic to your site.