A discussion of service level metrics

When such a complex phenomenon as service level is reduced to a few numbers, then it is
unavoidable that certain aspects are ignored.
As an example, take the waiting times of just 4 calls: 0, 10, 30, 100 seconds. Then
the ASA is 35 seconds. However, the sequence 35, 35, 35, 35 has the same ASA. This
shows that the ASA, by its proper definition, does not depend on the variability: is the
ASA caused by many calls having a short waiting time or by a few calls having a very long
waiting time? Both are possible!
This is a good reason to look for other service level metrics. Consider next the TSF,
which is indeed, to a certain extent, sensitive to variability. However, in case of a bad
SL (a low TSF) you can better have high variability, and in the case of a high SL a low
variability! This can be seen from the following examples, each with AWT 20 seconds: 15,
15, 15, 15 (ASA 15, TSF 100), 0, 30, 0, 30 (ASA 15, TSF 50); 25, 25, 25, 25 (ASA 25,
TSF 0), 15, 35, 15, 35 (ASA 25, TSF 50).
Another disadvantage of the TSF is that does not take into account the waiting time in
excess of the AWT: the sequences 0, 10, 30, and 100 seconds and 0, 10, 24, and 30 seconds
give the same TSF of 50, although there is a clear difference between the situations! The
difference shows up if we vary the AWT. This however would lead to a SL metric consisting
of multiple numbers, which has the disadvantage that it is harder to interpret and to
compare.
Thus we find that neither the ASA nor the TSF represents the SL well. Focusing on one
of these can lead to consequences that go against common sense: it motivates managers to
take decisions that decrease the common perception of SL.
A call center has two types of calls: calls with a negociated SL in terms of a TSF that has
to be met, and ”best effort” traffic where the revenue depends on the SL. Under high traffic
conditions the TSF of the first type of calls cannot be met, even when priority is given to
these calls. Therefore, the rational decision, given the contract, is to give priority to best
effort calls in case of high load and to give priority to fixed TSF calls when traffic is low to
catch up with the SL. This is in complete contradiction with the intentions behind the SL
contract. (Source: Milner & Olsen, Management Science, 2006.)
It is common practice in call centers to answer the longest waiting call first. If the SL
is only measured through the TSF, then this is not a good solution: calls waiting longer
than the AWT should not be answered at all, instead the call that waits the longest among
those that wait less than the AWT should be helped. Thus the TSF stimulates wrong
behavior.
For the ASA the order in which calls are answered does matter at all. A possible solution
would be to report both the ASA and the TSF. Still priority is given to calls waiting a
little less than the AWT, but long-waiting calls eventually get served. An alternative SL
metric consisting of a single number that motivates us to help long waiting calls first is
as follows. It takes the AWT into account, and it penalizes waiting longer than the AWT
by measuring the time that waiting exceeds the AWT. We call it the average excess time
(AET). For the 0, 10, 30, 100 sequence the waiting times in excess of 20 seconds are 0, 0,
10, and 80, giving 90/4 = 22.5 seconds as AET. For 0, 10, 24, 30 it gives 3.5, and for 35,
35, 35, 35 the AET is equal to 15. When using the AET is it clear that those calls that
wait longer than the AWT get priority.