Which management protocol should we use to analyze network traffic in and out of a router interface?

Well if you have NTA in your environment then you use NetFlow/sFlow/J-Flow 

https://documentation.solarwinds.com/en/success_center/nta/content/nta-setting-up-network-devices-to-export-netflow-data-manually-sw75.htm

vinay.by is correct. Flow data would be the best to *analyze* traffic passing through a router interface. SNMP will alert you that you have high bandwidth utilization but not what that traffic is. NetFlow Traffic Analyzer (NTA) or Hybrid Cloud Observability Advanced license will give you those features.