With regular STP, default timers, a designated port takes 2xforward_delay to go from discarding (blocking) to forwarding. When a port is coming up, it has by default a designated role and will thus take 30 seconds to go forwarding, unless you configure it for portfast.
When a port has an alternate or backup role, i.e. this port has been determined as redundant because it is receiving better bpdus, it is in also in discarding state. If this port fails to receive any better bpdus in max_age (20 seconds by default), it will move to designated role, and we are back to the previous case. But in that case, the complete transition from discarding to forwarding will take max_age + 2x forward_delay = 50 seconds.
RSTP and MST are designed to converge without using any timers (in an appropriate network with edge port identified and point-to-point links). Those protocols can thus provide sub-second reconvergence.
Regards,
Francois
