This talk presents an accumulated priority model for multi-server queues in which waiting customers accumulate priority credit at a linear rate that depends upon their priority classification. The advantage of an accumulated priority model over a classical priority queue is that the longer a customer waits, the greater their priority – thereby ensuring a better outcome for customers of lower priority. Numerical examples illustrating the delay impact of the accumulation rates will be presented. We hope to be able to provide broad conclusions based on the numerical experiments about the nature of priority accumulation in a multi-server environment.