Note
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People who aren't thoroughly familiar with the way web servers work and distribute the load may mistake persistent connects for what they're not. In particular, they do not give you an ability to open 'user sessions' on the same link, they do not give you an ability to build up a transaction efficiently, and they don't do a whole lot of other things. In fact, to be extremely clear about the subject, persistent connections don't give you any functionality that wasn't possible with their non-persistent brothers.

Its extremely simple and efficient. Persistent connections are good if the overhead to create a link to your SQL server is high. Whether or not this overhead is really high depends on many factors. Like, what kind of database it is, whether or not it sits on the same computer on which your web server sits, how loaded the machine the SQL server sits on is and so forth. The bottom line is that if that connection overhead is high, persistent connections help you considerably. They cause the child process to simply connect only once for its entire lifespan, instead of every time it processes a page that requires connecting to the SQL server. This means that for every child that opened a persistent connection will have its own open persistent connection to the server. For example, if you had 20 different child processes that ran a script that made a persistent connection to your SQL server, you'd have 20 different connections to the SQL server, one from each child.