WebSocket proxying in Nginx - Time & Space Complexity

Time Complexity: WebSocket proxying

O(n)

Understanding Time Complexity

When nginx proxies WebSocket connections, it handles data streams between clients and servers.

We want to understand how the work grows as more messages pass through the proxy.

Scenario Under Consideration

Analyze the time complexity of the following nginx WebSocket proxy configuration.

location /ws/ {
    proxy_pass http://backend_server;
    proxy_http_version 1.1;
    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection "upgrade";
    proxy_read_timeout 86400;
}
    

This config forwards WebSocket requests to a backend server, maintaining the connection for real-time data.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: nginx reads and forwards each WebSocket message between client and server.
• How many times: This happens for every message sent during the connection lifetime.

How Execution Grows With Input

As the number of messages increases, nginx processes each one in turn.

Input Size (n)	Approx. Operations
10 messages	10 forwarding operations
100 messages	100 forwarding operations
1000 messages	1000 forwarding operations

Pattern observation: The work grows directly with the number of messages passing through.

Final Time Complexity

Time Complexity: O(n)

This means the time to handle WebSocket proxying grows linearly with the number of messages.

Common Mistake

[X] Wrong: "nginx processes all WebSocket messages instantly regardless of count."

[OK] Correct: Each message requires processing and forwarding, so more messages mean more work.

Interview Connect

Understanding how nginx handles WebSocket streams helps you explain real-time proxying performance clearly and confidently.

Self-Check

"What if nginx buffered multiple WebSocket messages before forwarding? How would the time complexity change?"