I am afraid that we are dealing with two separate phenomena and possibly ignoring some real-world realities.
First, it is true that in general, in two call centers stuffed according to their call volume and for the same SL, the ASA in the larger call center is usually better due to the better utilization as we have already established. This is not because most of them will be answered within the AWT which will result in a lower ASA but rather the higher (statistical) availability of agents leads to ASA that can be better than SL.
I will even agree to a rough rule of thumb that says that in small call centers ASA is usually greater than SL and in larger ones ASA < SL, although this highly depends on the specifics.
The other phenomenon is the relationships between staffing and ASA. Stating that ASA is better in large call centers is an oversimplification of the situation, as demonstrated in
http://www.diagnosticstrategies.com/erlang/fig3.jpg This statement applies only where is large call center is significantly larger than the small one. The range of data in this plot is from 33 to 250 agents, yet the ASA improvement trend is hardly noticeable.
To give you additional food for thought, I reran my calculations on a larger range of call center size range: 25-500 agents and placed it in
http://www.diagnosticstrategies.com/erlang/cc.xls
Notice that the average ASA (a bad term
) has improved from 53 seconds to 49 seconds, hardly noteworthy
You will also notice the zigzag nature of ASA caused by adding capacity in multiples of integer person units, and that in a smaller call center the ASA range is significantly greater. Still, as the graph sows, a small call center CAN accomplish ASA that is the same or better than the large one, and actual calculation in call centers may not agree with the general statement.
Finally, you will notice that ASA is indeed showing an improvement trend, but at a given point is seems to become worse! This coincide with the area were utilization reaches 0.99. Two points:
1. In my calculations I dont assume that 100% utilization is practical and force lower utilization if the calculations reach 100%. In actual planning we watch for the number and shoot for a much lower workload. If your math assumes that 100% utilization is possible, your results will be different.
2. The ASA trend line is a second order polynomial, which seems to work, but I havent spent any time validating it.