Small Flow Completion Time (FCT) of short-lived flows, and fair bandwidth allocation of long-lived flows have been two major, usually concurrent, goals in the design of resource allocation algorithms. In this paper we present a framework that naturally unifies these two objectives under a single umbrella; namely by proposing resource allocation algorithm Markov Active Yield (MAY). Based on a probabilistic strategy: "drop proportional to the amount of past drops", MAY achieves very small FCT among short-lived flows as well as max-min fair bandwidth allocation among long-lived flows, using only the information of short history of already dropped packets. It turns out that extremely small amount of on-chip SRAM (roughly 1 bit per flow in Pareto-like flow size distributions) is enough for storing this drop history. Analytical models are presented and analyzed and accuracy of results is verified experimentally using packet level ns2 simulations.