
The key here is to have your situation looked at before the others. Call it selfish, if you must. But there are a limited number of seats and trying accommodate a full plane of customers from a cancelled flight onto later flights can be a challenge. Here is what you can do to improve your chances of of a desirable outcome:
Program airline phone numbers in your mobile phone. (Go ahead and do this now, I'll wait). This way while you are standing in line at the customer service/rebooking center, you can concurrently call the airline. By the time you hang up the phone, many of your fellow passengers may still be in line awaiting their fate.