There are several methods and techniques that come handy in the case you need to call an external resource periodically or if you are waiting for a server push, but I present here an easy and straightforward one using HTML5's Server-Sent Events (SSE).
A lot of people have written posts on integrating Yii and WordPress. This article combines goncin's approach with an article I read about integrating Symfony and WordPress and applies it all to Yii and WordPress.
The Advanced PHP Cache is a PHP extension which primarily serves as an opcode cache for PHP. The basic idea is to save PHP from re-evaluating the PHP code to intermediate bytecode on each request. Installing and enabling APC already yields a significant performance benefit. However, APC is not a black box that will magically change all for the better. More over it is important to understand that APC needs memory to operate.