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The focus of this paper is the analysis of threshold-based admission control policies for distributed video-on-demand (VoD) systems. Traditionally, admission control methods control access to a resource based on the resource capacity. We have extended that concept to include the significance of an arriving request to the VoD system by enforcing additional threshold restrictions in the admission control process on request classes deemed less significant. We present an analytical model for computing blocking performance of the VoD system under threshold-based admission control. Extending the same methodology to a distributed VoD architecture we show through simulation that the threshold performance conforms to the analytical model. We also show that threshold-based analysis can work in conjunction with other request handling policies and are useful for manipulating the VoD performance since we are able to distinguish between different request classes based on their merit. Enforcing threshold restrictions with the option of downgrading blocked requests in a multirate service environment results in improved performance at the same time providing different levels of quality of service (QoS). In fact, we show that the downgrade option combined with threshold restrictions is a powerful tool for manipulating an incoming request mix over which we have no control into a workload that the VoD system can handle.