New history-based delay predictors for service systems

We are interested in predicting the wait time of customers upon their arrival in some service system such as a call center or emergency service. We propose two new predictors that are very simple to implement and can be used in multiskill settings. They are based on the wait times of previous customers of the same class. The first one estimates the delay of a new customer by extrapolating the wait history (so far) of customers currently in queue, plus the last one that started service, and taking a weighted average. The second one takes a weighted average of the delays of the past customers of the same class that have found the same queue length when they arrived. In our simulation experiments, these new predictors are very competitive with the optimal ones for a simple queue, and for multiskill centers they perform better than other predictors of comparable simplicity.