The problem with this type of questions is that we intuitively assume a constant flow of calls whereas they have a random arrival and length pattern (governed by known distributions). I often have to go back to the math and try a couple of examples first to see what the answer is and then try to figure out why
First, I was too quick to respond and mixed ASA and utilization, and I apologize for that confusion. As for ASA, if staffed correctly to meet the service level relative to their call volume, there shouldnt be a difference in ASA between small and large call canters.
However, there will be more queued calls in the large call center and the agents will work harder (utilization will go up). According to Erlang C formula, the probability of a call being queued increases with call volume (everything else being equal). This has to do with the fact that calls arrive at random according to a Poison distribution, which means that statistically speaking, there is a higher probability of experiencing a call rate that is higher than the average CPH (strange, I know), while calls are cleared at a fixed (non random) rate (AHT, which has a normal (sometimes log-normal) distribution).
I tested this with actual data
I hope this helps a bit.
Joe Barkai
DIAGNOSTIC STRATEGIES
www.DiagnosticStrategies.com