Computer flex schedule/staffing

Our unit is currently using paper flex scheduling, but the requests for days off and our holiday scheduling has become a nightmare. Can anyone tell me about the using the computer software for scheduling? Is it fair for the holidays or getting your requested days off? Is it better then the old paper system? I am not sure I see the advantage of the paperless system?? I would be grateful for any input anyone has for scheduling for requested days off and holiday scheduling.
We have internet self sched. It is great! I can access my sched from anywhere. The program has a tab you use to send a req for time off.For holidays we have a system where you rank your desired days off, it is matched up to last years sched. Then the manager has fun trying to figure out the fairest way

Hi Flo, We are also doing paper scheduling and we are experiencing some problems with this format. It sounds like internet based self sheduling would work well for us but Im having a hard time finding a suitable program/system for it. Can you let me know what the name of the system is that you are using so I can take a look.ThanksJason