Just to get this straight in my head--the process when the gate doesn't work is this:
Customer uses call button and contacts main office.
Main office calls porter on cell phone.
Porter goes to gate.
Porter determines if gate should be raised (I'm assuming that the porter checks to make sure the customer has actually paid and isn't trying to get out of the garage for free.)
Porter calls main office to get gate lifted.
If that doesn't work, porter calls supervisor.
It's a pretty complicated procedure, with opportunities for wait time and delays at every step. And if getting to step 3, where human help finally arrives, takes 30 minutes, I can understand why the customers are getting impatient.
I'd be impatient too, if a company whose main job is to let me in and out of a parking space took 30 minutes or more to get me out of their garage. Thirty minutes to perform the chief reason the company is in business for, when it should take less than a minute to exit the garage?
I know it is not your fault, OP, that all this happens. You have no control over any of this. But I think Merry Mrs. Martin and greencat have a point--the customers really do have reason to be a bit upset at the system. Starting out realizing that they are have a reason to be upset is good. Realizing that they are upset with the system and not really upset with you is another thing that might help. You are just the person they can vent to.
So start with that in mind--these people have been trapped in the garage for 10-30 minutes. They have places to be and things to do. It's possible they are missing an appointment or running late to a party or lunch date or theater because of the malfunctioning gate. And I think it is normal for them to think that when you show up, the problem is going to be fixed. I'd expect the management to send someone who can immediately fix the problem. So finding out that you have to make another call and I would have to wait for yet another person to show up--and if you took 30 minutes to get to the gate, does that mean I'm going to have to wait another 30 minutes for the supervisor?
Be polite. Remember they aren't really upset with you, but the situation. Keep them informed of what is going on--let them know what you are going to do, what the next step is, how long they will need to wait for the supervisor, etc. Sympathize with them that the wait is long.
Then get to work in whatever way you can to change the system so that it doesn't take so long to fix gate problems.