What would I do in this situation? This isn't a terribly detailed scenario, so I'll assume that you are tied with your arms behind your back in a locked room with nothing in it at all.
I would probably start with just trying to push one of my arms farther into the rope to hopefully cinch it at a different tightness than the standard "really tight", because most knots when cinched from the outside can still be moved a bit from the inside if they are tied improperly. Then I would proceed to pull my hand back to the smallest area of my arm (probably my wrist) and try to use one hand to try to crush the other one sideways (it would hurt like hell, but I would rather that then starve, or wait to be found by someone else) and attempt to pull it out, if that succeeds, it would be trivial to escape after that.
If I couldn't change the cinch on the rope, I would kick at the door about 3 inches above the door handle, it may take a couple of attempts to do it, but hopefully it would knock the door down. If that fails I would attempt to bash a hole through a wall to try to get out or find something sharp to work with.
If none of that works, I would kick the doorhandle off the door and pull out the metal piece in the middle, and proceed to bash the crap out of it to make little dents in it, stick it back into the handle, and try to "saw" the rope off. Any remotely effective dent could rip a fiber off the rope would be able to get me out in around 20-30 minutes.
If a handle doesn't exist, I would try to burn the rope as best I could with the light above if it is incandescent...
It a light doesn't exist, I would try to take a shoelace off of my shoe, and wrap it around as best I could the rope. I would wrap it around about 5 times minimum, and stand on each side of the lace, then move my hands really swiftly from left to right repeatedly, this will gain a lot of heat, and if the lace doesn't break (They are surprisingly durable), it could damage the rope enough to get free.
If I didn't have laces though, I would rub my face against a wall to remove the duct tape, and put it at about waist level, turn around and grab it with my hands, and rip off half of it, and drag it against the ground to collect anything solid, Then I would roll it up and wrap around it once with the remaining tape, and stomp on it to make it as solid and small as possible. Then I would try to push it into the crack of the door to try to push the nub that keeps the door closed in enough, always applying pressure to the door when not pushing (that hardened tape wouldn't be sturdy enough to do it in one go) to keep it's position, and repeat until it is close enough to force open...
There are other things, but that would require more detail.
