Site becomes inaccessible due to PHP-FPM listen queue, CPU touches 100%

Question

I've been racking my brains apart trying to solve this issue that comes up randomly every few hours on my production server hosting a single Wordpress blog (with decent traffic: 2000 users realtime on average days, 5000+ on good days, pageviews per minute varies from 300 to 700+).

I use Newrelic to monitor performance and I've noticed a peculiar thing:

Every few hours (randomly), the PHP-FPM pool status goes something like below (real status taken yesterday)

pool:                 www
process manager:      static
start time:           02/Jan/2017:05:03:16 -0500
start since:          27290
accepted conn:        1107594
listen queue:         777
max listen queue:     794
listen queue len:     40000
idle processes:       0
active processes:     100
total processes:      100
max active processes: 101
max children reached: 0
slow requests:        0

Restarting PHP-FPM and nginx solves the issue but it happens again in a couple of hours. Any help is appreciated. Please guide me.

---

Server setup:

DigitalOcean 48GB Memory
16 Core Processor
480GB SSD Disk

PHP-FPM pool setting:

pm = static
pm.max_children = 100
pm.max_requests = 5000

nginx config:

worker_processes  32;
worker_rlimit_nofile 100000;
events {
    worker_connections  40000;
    use epoll;
    multi_accept on;
}

I'm also using xcache, varnish with W3TC on Wordpress. (also have Cloudflare)

sysctl.conf:

# Increase size of file handles and inode cache
fs.file-max = 2097152

# Do less swapping
vm.swappiness = 10
vm.dirty_ratio = 60
vm.dirty_background_ratio = 2

### GENERAL NETWORK SECURITY OPTIONS ###

# Number of times SYNACKs for passive TCP connection.
net.ipv4.tcp_synack_retries = 2

# Allowed local port range
net.ipv4.ip_local_port_range = 2000 65535

# Protect Against TCP Time-Wait
net.ipv4.tcp_rfc1337 = 1

# Decrease the time default value for tcp_fin_timeout connection
net.ipv4.tcp_fin_timeout = 15

# Decrease the time default value for connections to keep alive
net.ipv4.tcp_keepalive_time = 300
net.ipv4.tcp_keepalive_probes = 5
net.ipv4.tcp_keepalive_intvl = 15

### TUNING NETWORK PERFORMANCE ###

# Default Socket Receive Buffer
net.core.rmem_default = 31457280

# Maximum Socket Receive Buffer
net.core.rmem_max = 12582912

# Default Socket Send Buffer
net.core.wmem_default = 31457280

# Maximum Socket Send Buffer
net.core.wmem_max = 12582912

# Increase number of incoming connections
net.core.somaxconn = 40000

# Increase number of incoming connections backlog
net.core.netdev_max_backlog = 65536

# Increase the maximum amount of option memory buffers
net.core.optmem_max = 25165824

# Increase the maximum total buffer-space allocatable
# This is measured in units of pages (4096 bytes)
net.ipv4.tcp_mem = 65536 131072 262144
net.ipv4.udp_mem = 65536 131072 262144

# Increase the read-buffer space allocatable
net.ipv4.tcp_rmem= 10240 87380 12582912
net.ipv4.udp_rmem_min = 16384

# Increase the write-buffer-space allocatable
net.ipv4.tcp_wmem= 10240 87380 12582912
net.ipv4.udp_wmem_min = 16384

# Increase the tcp-time-wait buckets pool size to prevent simple DOS attacks
net.ipv4.tcp_max_tw_buckets = 1440000
net.ipv4.tcp_tw_recycle = 1
net.ipv4.tcp_tw_reuse = 1