How long does my ad takes to reach my selected displays?

It depends. 

After you place an ad on displays, each display owner will receive an alert on the software and by e-mail to approve or reject the campaign. We can't control it, but we know they are really interested on approving as fast as they can for the obvious reason the faster they approve, the faster they monetize their displays.
 
In some cases they can reject, when the ad conflicts with they establishment. For example, let's suppose their establishment is a Bakery, and the ad is from another competitor, I mean, another Bakery :)

After the publisher approve the campaign,  and his displays are online (connected to the Internet), it takes around 1 to 5 minutes to start playing. It's really fast !