Most off-the-shelf routers claim theoretical connection limits (often 250+), but real-world performance collapses much earlier. The Draytek 2829VN exemplifies this with these technical constraints:

// Pseudo-code showing connection overhead calculation
const MAX_THEORETICAL_CONNECTIONS = 254; // DHCP range limitation
const ACTUAL_THROUGHPUT_THRESHOLD = 0.85; // 85% utilization ceiling
const OVERHEAD_PER_CLIENT = 1.15; // Management frame multiplier

function calculateEffectiveLimit(bandwidthMbps, avgClientUsage) {
  return Math.floor(
    (bandwidthMbps * ACTUAL_THROUGHPUT_THRESHOLD) / 
    (avgClientUsage * OVERHEAD_PER_CLIENT)
  );
}
// Example: 50Mbps link with 2Mbps/iPad → ~20 stable connections

Your update proves the critical nature of channel planning. Here's how to programmatically scan optimal channels in Linux (works on Raspberry Pi APs):

#!/bin/bash
# WiFi channel optimizer for high-density deployments
CHANNELS=("1" "3" "6" "8" "11" "13")
INTERFACE="wlan0"

for chan in "${CHANNELS[@]}"; do
  iwconfig $INTERFACE channel $chan
  airodump-ng --channel $chan --write /tmp/scan_$chan $INTERFACE &
  sleep 10
  pkill airodump-ng
done

# Analyze results with least interference
grep -r "Beacon" /tmp/scan_* | awk '{print $4}' | sort -n > channel_analysis.txt

For those needing to automate multi-AP deployments, consider this Python snippet for coordinated channel management:

import paramiko
from multiprocessing import Pool

AP_CREDENTIALS = [
    {"host":"ap1.local","user":"admin","channel":3},
    {"host":"ap2.local","user":"admin","channel":8},
    {"host":"ap3.local","user":"admin","channel":13}
]

def configure_ap(ap):
    ssh = paramiko.SSHClient()
    ssh.set_missing_host_key_policy(paramiko.AutoAddPolicy())
    ssh.connect(ap["host"], username=ap["user"])
    stdin, stdout, stderr = ssh.exec_command(
        f"iwconfig wlan0 channel {ap['channel']}\n"
        "service hostapd restart"
    )
    return stdout.read()

if __name__ == "__main__":
    with Pool(3) as p:
        print(p.map(configure_ap, AP_CREDENTIALS))

The iPad connection delay you observed stems from aggressive channel scanning. This can be mitigated with proper WiFi configuration profiles:

<dict>
    <key>SSID_STR</key>
    <string>YourNetwork</string>
    <key>HIDDEN_NETWORK</key>
    <false/>
    <key>AutoJoin</key>
    <true/>
    <key>PreferredOrder</key>
    <integer>1</integer>
    <key>Channel</key>
    <integer>8</integer> <!-- Prevents full scan -->
</dict>

When dealing with high-density WiFi deployments, especially in programming environments or tech conferences, understanding router capacity is crucial. Most consumer-grade routers typically support 30-50 concurrent connections, while enterprise models can handle 100-250+.

Here's a Python snippet to visualize channel interference patterns:

import matplotlib.pyplot as plt

channels = [1, 6, 11]  # Standard non-overlapping channels
interference_range = 5  # Channels that may interfere

def check_interference(target_channel):
    return any(abs(target_channel - c) <= interference_range for c in channels)

# Test alternative channels
alt_channels = [3, 8, 13]
results = {chan: check_interference(chan) for chan in alt_channels}

print(f"Interference test results: {results}")

For JavaScript developers working with WiFi-enabled apps, here's how to monitor connection quality:

// Web-based WiFi quality monitor
navigator.connection.addEventListener('change', () => {
  const connection = navigator.connection;
  console.log(Effective connection type: ${connection.effectiveType});
  console.log(Downlink speed: ${connection.downlink} Mbps);
  console.log(Round-trip time: ${connection.rtt} ms);
});

// For iOS Safari (iPad specific)
if (window.webkit && webkit.messageHandlers) {
  webkit.messageHandlers.observeConnection.postMessage({
    action: 'startMonitoring',
    interval: 5000
  });
}

When configuring routers via SSH (common in developer setups):

# Basic router config for high-density environments
ssh admin@router_ip
configure terminal
wireless
 max-stations 100  # Set maximum connections
 band-steering enable  # Better load balancing
 channel width 20MHz  # Reduces interference
 power local  # Optimize transmission power
end
write memory

Signs your router is overwhelmed:

• Connection timeouts during API calls
• Increased packet loss affecting real-time apps
• DHCP lease issues (devices can't get IP addresses)

For Node.js developers creating WiFi management tools:

const wifi = require('node-wifi');

wifi.init({
  iface: null // auto-select interface
});

// Scan for best access point
wifi.scan((error, networks) => {
  if (error) {
    console.log(error);
  } else {
    const bestAP = networks
      .filter(n => !n.ssid.includes('_guest'))
      .sort((a, b) => b.quality - a.quality)[0];
    console.log(Best AP: ${bestAP.ssid} on channel ${bestAP.channel});
  }
});