*ABR rate allocation schemes can achieve high link utilizations by maintaining non-zero (small) queues in the steady state, and draining queues when the sources do not have data to send. The queue length (and queuing delays) can be controlled if part of the available bandwidth is used for draining queues in the event of queue build up. A simple threshold function can allocate such bandwidth to drain queues. Better control of the queues, and hence delay, can be achieved using more sophisticated queue control functions. We study the design and analysis of several such queue control functions: the step, linear, hyperbolic and inverse hyperbolic functions. Analytical explanation and simulation results consistent with analysis are presented. From the study, we conclude that the inverse hyperbolic is the best queue control function. To reduce complexity, the linear function can be used since it performs satisfactorily in most cases. *

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