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The buffered crossbar packet switch employs the crossbar-based switching fabric architecture with internal buffers and the combined input and output queueing scheme. It is promising to support quality of service (QoS) in buffered crossbar switch without complex implementation. In this paper, we study the problem of supporting traffic classes whose QoS requirements are stated statistically in buffered crossbar switches. Specifically, we investigate the resource allocation issue. We extend the network calculus-based model and techniques developed in Q. Duan and J. N. Daigle (Oct. 2002) to determine the amount of bandwidth and number of credits that must be allocated in a buffered crossbar switch to guarantee each traffic class a packet delay that is upper bounded with a small violation probability. We find that the required amount of resources for probabilistic delay upper bound guarantee is less than what is required for deterministic delay upper bound guarantee. This implies that bandwidth and credits can be saved in buffered crossbar switch if resource allocation is based on probabilistic delay objective.