How long should a temporary notification (toast) appear?

For our intranet application we have little notification messages (toasts) that indicate successful operations like "information saved," "logged out" etc. Most of them are not important enough to require a modal operation (like Stack Exchange's "click to close" windows) so they close automatically after 2500ms and I'm trying to make them disrupt the user as little as possible. They are however important to present as users need confirmation an action was successful as it may be part of a repetitive or complex workflow.

I want to make sure they're readable and understandable within the time frame so I was wondering if there was any research on how long it takes people to read information especially in a "pop up" style context. It's not actually a pop up window, more like SE's notification bar but it automatically goes away. If I could ballpark how long to expect reading to take it would help tune the duration of the message and the length of messages.