Minimal Evacuation Times and Stability

We consider a system where packets (jobs) arrive for processing using one of the policies in a given class. We study the connection between the minimal evacuation time and the stability region of the system and show that evacuation time optimal policies can be used for stabilizing the system (and for characterizing its stability region) under broad assumptions. Conversely, we show that while a stabilizing policy can be suboptimal in terms of evacuation time, one can always design a randomized version of any stabilizing policy that achieves an optimal evacuation time in the asymptotic regime when the number of evacuated packets scales to infinity.