If we have a catalyst switch with slot capacity x Gbps, then if we insert a 12 port line card with total BW of 4x Gbps, then we will have only 3 non-blocking ports in the line card and other 9 ports will be blocked (depending on line card port group)
as an example if we have 4507R-E and we insert line card WS-X4712-SFP+E
and the chassis slot capacity is 48 Gbps so we will only have 4 non-blocking ports in this line card
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I believe that should be understood as there's a 12 Gbps "channel" to the fabric, that's shared by three 10g ports. So the issue is any combination of the three 10g ports, that tries to push more than 12 Gbps, will queue, and a port's packets could be "blocked" even though its port utilization is well under 10 Gbps.
For example, if port 1 and 2 were both accepting 6 Gbps, and port 3, 1 Gbps, all ports utilization is under their 10, but the combination of 13 Gbps, will create congestion on the channel to/from the fabric. Packets on port 3, again even though it's only using 1 Gbps, could be "blocked" waiting behind packets from ports 1 and 2.
Right, "random" blocking time, but they should be pretty brief on a 10g port. Nothing near minutes, as it's unlikely there's sufficient buffer capacity for that. Much more likely, over subscription will cause there to be drops.
Don't know why you didn't see the other ports work. The reason for the 2.5:1 over subscription, that's 30Gbps(3x10):12Gbps(channel) or 2.5:1.