Maybe setting up a pilot with dummy data to simulate load will be a good idea. Organize a test group that can send queries to thsi group on sms, mails and faxes etc and actually measure the KPIs. Then maybe you will have some base line data to work with.
Do you have any previous data available? Any statistics in terms of volumes from the past. Start maintaining a record of the volume of work being processed, the amplitute fluctuation and frequency changes. If you do not have a SLA in place then this may be your best starting point. You may need to develop your own SLA.