Average queueing delays in ATM buffers under cell dropping

We derive a closed-form expression for the average delay that surviving cells experience in ATM buffers when cells are dropped to avoid overflow or to control buffer occupancy. The expression, which depends on the cell arrival rate, the cell dropping rate, and the average time dropped cells spend in the buffer prior to dropping, follows from a variant of Little's law that we show to hold for lossy queues using a virtual buffer model that explicitly accounts for the effects of cell dropping. To illustrate the expression's utility we use it to prove that policies that drop cells closest to the head of the buffer incur the smallest average surviving cell delays. No explicit knowledge of the arrival process is required obtain these results. Only stationarity and ergodicity of the queueing processes are assumed.