Responsive buffers—properties in the fluid flow limit

Responsive buffers are conceived in which the buffer drain rate varies with the buffer backlog. Such buffers offer potential as components of communication, transportation, and manufacturing networks because, unlike in the usual buffer model with fixed drain rate (in which overflow and loss are inevitable with standard input models), responsive buffers may or may not exhibit overflow. A simple condition characterizing losslessness in responsive buffers is given. The stationary buffer backlog distribution of lossless responsive buffers subject to a maximally bursty on–off input process is shown to be related to the beta distribution, and under the same conditions, overflow in lossy responsive buffers is shown generally to be exponentially distributed. An important special case of responsive buffers is considered, a linear filter dubbed the leaky bladder. The linearity of the leaky bladder enables us to determine its mean delay and relative smoothing.