Add to ORKGArrival processes to queues often exhibit time dependence, but time-dependent queues are notoriously difficult to analyze. Usually one adopts some kind of steady-state approximation for time-dependent performance. We consider a range of queue-ing models that see wide use in practice, particularly in the modeling of service industry applications, and develop approximations for the error involved in using a steady-state approximation for time-dependent quantities. We focus on the distri-bution of the waiting time before reaching service, although the approach we use could be extended to many other performance measures. The results reinforce and extend what is known about such errors. For example, customer abandonment leads to dramatic reducti...