There should be a target cycle time for processing. The shorter the cycle the more effective the process must be. If the cycle is longer than expected it implies there is a problem.
You probably have a goal of at least attempting to process everything you receive on the day you receive it (allowing for peak periods). If the first attempt is successful you may succeed in this.
People would like things processed quickly, within 1 day is normally the target with 48 hrs acceptable. Beyond 5 working days and people will probably chase to find out what is happening, causing more queries. We know that time frames can vary depending on the process under review. You may be happy with a shorter or longer cycle time, but probably the shorter the better.
For the processing cycle you are trying to determine the average time taken. You can assess this through sampling (tracking some of the volume), workflow records (if you use workflow software), use dates recorded by your computer system (eg: for Accounts Payable the invoice date is usually entered into the system and the entry date will be recorded by the system itself. Compare the two and allow 5-7 days for the supplier to raise the invoice and post it to you), a last option is simply to ask people for their estimate.