Total output drops are still increasing on a Cisco 2960 switch trunk interface that is connected to ASA interface.
What causes these drops?
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Drops are normally caused by buffers filling up. If data comes in destined for a port faster than it can be sent out of that port then some of it is going to have to be dropped.
In general most bulk transfer protocols will increase the data rate until they start seeing packet drops then back off slightly. So it is absoloutely normal that some packets are dropped somewhere in your network.
Where the drops happen will depend on the topology of your network. If the ASA is doing routing between local subnets then the line from the switch to the ASA is likely one of the most congested on your network, so it is where you would expect to see drops.
If the ASA is only doing routing to/from the outside world then it would be more unusual to see drops on the line feeding the ASA unless your internet connection is as fast as your LAN.
Total packets dropped is a fairly meaningless metric, what you really need to know is the proportion.
Usually, that would be due to an oversubscription. For example, if it is a 24-port switch, with 24 1 Gbps access interfaces, and a 1 Gbps uplink interface, then you could have 24 Gbps coming into the switch from the access interfaces and contending for 1 Gbps on the uplink interface. That is a 24:1 oversubscription, and you are going to lose 23 out of 24 frames to output drops because the uplink can only handle 1 Gbps.