The objectives of this research are to develop an information estimation scheme and to introduce queueing to adaptive signal processing so that a time-sharing type estimator can be devised. Convex set theory is used to determine how much innovative information is contained at each data point. The significance of the proposed research stems from its immediate application in many communication problems such as digital speech interpolation and statistical multiplexing; its efficient use of observation data that can yield computationally efficient, cost effective, and numerically stable algorithms; and its interaction among VLSI technologies, queueing theory, and adaptive signal processing.