Waiting Time in a General Active Queue Management Scheme

We derive the waiting time in a queueing scheme, which an arriving job can be denied service with probability relative to queue size. Such scheme is generalization of tail-drop queue, when buffer (waiting room) full, and found computer networking, call centers other everyday life applications systems. To make model very general, we use arrival process enables shaping arbitrary interarrival distribution autocorrelation, as well general rejection probabilities. For such model, prove theorems on transient case, i.e. function time, stationary case. Theoretical results are illustrated via numerical examples, dependence behaviour system various parameters depicted. Among things, it demonstrated that assumed mechanism may induce rather unexpected times if combined strong autocorrelation process.