The meeting with K was productive. We have a last hurdle to clear. The bank data record the arrival and calling time, but no information on when customers abandon (before being called).
So far there is no good solution. The MS paper assumes abandon customers leaves just a minute before being called. The assumption simplifies analysis, but is unrealistic. We cannot get away with the similar assumption.
We figured out how to pinpoint the abandonment time. First, we use regression to find the abandon probability Pa upon arrival. This is an accurate estimation. Then We use this Pa to generate abandonment. Specifically, we ask each customer to toss the coin with Pa to leave. After the first round tossing, those who stayed advance to the next epoch, 1/4V. We can count the number of staying customers, say n1. Then we can run the regression again to find the abandonment probability Pa1. We repeat the above process, till time runs out.
In this process, the probability Pa is self-regenerating, and path dependent. To have a full picture of the process, we need to run the above game for 1000 times. In each game, we assess the validity of the regression. Then we can use histogram to summarize the overall validity of the regression.
This is a best solution so far.