Buffer with Dropping Function and Correlated Packet Lengths

We analyze a model of the packet buffer in which a new packet can be discarded with a probability connected to the buffer occupancy through an arbitrary dropping function. Crucially, it is assumed that packet lengths can be correlated in any way and that the interarrival time has a general distribution. From an engineering perspective, such a model constitutes a generalization of many active buffer management algorithms proposed for Internet routers. From a theoretical perspective, it generalizes a class of finite-buffer models with the tail-drop discarding policy. The contributions include formulae for the distribution of buffer occupancy and the average buffer occupancy, at arbitrary times and also in steady state. The formulae are illustrated with numerical calculations performed for various dropping functions. The formulae are also validated via discrete-event simulations.