We model the set of tenure-track faculty members at a university as a queue, where "customers" in queue are faculty members in active careers. Arrivals to the queue are usually young, untenured assistant professors, and departures from the queue are primarily those who do not pass a promotion or tenure hurdle and those who retire. There are other less-often-used ways to enter and leave the queue. Our focus is on system effects of the elimination of mandatory retirement age. In particular, we are concerned with estimating the number of assistant professor slots that annually are no longer available because of the elimination of mandatory retirement. We start with steady-state assumptions that require use of Little's Law of Queueing, and we progress to a transient model using system dynamics. We apply these simple models using available data from our home university, the Massachusetts Institute of Technology.