If you'd like to experiment with modifying sysctls, you can set a security context as follows, per pod:

apiVersion: v1
kind: Pod
metadata:
 name: sysctl-example
spec:
 securityContext:
   sysctls:
   - name: kernel.shm_rmid_forced
     value: "0"
   - name: net.core.somaxconn
     value: "10000"
   - name: kernel.msgmax
     value: "65536"
   - name: ipv4.ip_local_port_range
      value: ‘1024 65535'

You can also tune variables such as the ARP cache, as Kubernetes consumes a lot of IPs at scale, which can exhaust space in the ARP cache. Changing these settings is common in large scale HPC clusters and can help with address exhaustion with Kubernetes as well. You can set these values, as follows:

net.ipv4.neigh.default.gc_thresh1 = 90000
net.ipv4.neigh.default.gc_thresh2 = 100000
net.ipv4.neigh.default.gc_thresh3 = 120000