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Its not a bandwidth issue as bandwidth is not fully utilized on the link, more case of quantity of packet filling the hardware queue and dropping I believe.
What causes packets to fill a queue? A. Insufficient bandwidth; that's why they are being queued.
That said, there's a lack of transient bandwidth and a lack of long term bandwidth. The latter generally needs to be addressed by adding bandwidth, but the former might be addressed by providing sufficient queuing.
Do you have QoS enabled? If so, and you're not really using QoS, disable it.
If you're are using the QoS, buffering can be "tuned". What I've found seems to help on the 3750s (much similar to 2960s), is moving buffer resources from interface reserved to the shared pool. This allows low usage ports to provide their unused buffers to high usage ports.
