Estimating and interpreting the waiting time for customers arriving to a non-stationary queueing system

When a customer arrives to a service system, how long should they expect to wait, and how long might their wait actually be? Computer simulation is an ideal tool for answering such questions for very general and complex queueing systems, but they are not always answered by the automatic statistical summary generated by commercial simulation languages. Using an illustration based on passenger check-in at an airport, we demonstrate how standard summary measures go wrong and provide methods that correctly answer these questions.