In this study, a crosspoint-queued (CQ) switch that features a buffer size larger than one and employs the workconserving random scheduling algorithm under uniform Bernoulli i.i.d. traffic is investigated through both theoretical analysis and simulation. The effect of the crosspoint buffer state on switch performance is modelled and quantified. A novel method for calculating the throughput and delay of a CQ switch with a given switch size, input load, and buffer size is proposed. Compared with existing models, the proposed calculation model offers a simpler and more accurate result, and can serve as a theoretical guide in designing high-speed switch fabrics.