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Packet fair queueing (PFQ) algorithms are packetised versions of generalised processor sharing (GPS), which is an idealised fluid scheduling model with desirable properties in terms of delay bound and fairness. To support a large number of sessions with diverse bandwidth requirements, the grouping architecture, which is scalable, has been proposed to approximate PFQ algorithms. The authors analyse the relationship between the guaranteed service rates and utilisation for cell-based schedulers with the grouping architecture. Based on this analysis, call admission control (CAC) schemes are proposed to provide the guaranteed service rate for each session, and their performance is evaluated and compared in terms of computational complexity.