Cisco Router 4321 has a high ping

[sysadmin@cwcmh.org]

I need some assistance with my router. My network monitoring service has started alerting me that the router has high pings. How could i troubleshoot this? I can ssh into the router and can enter priveleged exec mode.

[pieterh]

>>> I can ssh into the router and can enter privileged exec mode. <<<
this may not Help !
you need tot determine the delays in components between your monitoring system and your router

start with a traceroute from your monitoring system to your router,
-> check what path is used and inspect all individual hop response times
NB! if your monitoring system is a VM, than your VM host (or its network adapter) may be overloaded
-> also do a ping to the next-hop of your monitoring system and inspect the response time

[MHM Cisco World]

steps to reduce this DDoS effect 
1-only apply ACL and deny ICMP any any and apply ACL to any Interface connect to unsecure network 
2- you can disable ICMP unreachable this make CPU not response to any ICMP to any IP that not reachable by ICMP