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Despite its well-known advantages, per-flow fair queueing has not been deployed in the Internet mainly because of the common belief that such scheduling is not scalable. The objective of the present paper is to demonstrate using trace simulations and analytical evaluations that this belief is misguided. We show that although the number of flows in progress increases with link speed, the number that needs scheduling at any moment is largely independent of this rate. The number of such active flows is a random process typically measured in hundreds even though there may be tens of thousands of flows in progress. The simulations are performed using traces from commercial and research networks with quite different traffic characteristics. Analysis is based on models for balanced fair statistical bandwidth sharing and applies properties of queue busy periods to explain the observed behaviour.