Why MQTT is the IoT standard in IOT Protocols - Performance Analysis

Time Complexity: Why MQTT is the IoT standard

O(n)

Understanding Time Complexity

We want to understand how the time it takes to send messages using MQTT grows as more devices connect.

How does MQTT handle many devices without slowing down too much?

Scenario Under Consideration

Analyze the time complexity of the MQTT publish-subscribe message delivery.

// Simplified MQTT message delivery
function mqttPublish(topic, message) {
  let subscribers = getSubscribers(topic); // list of devices subscribed
  for (let device of subscribers) {
    sendMessage(device, message); // send message to each device
  }
}

This code sends a message to all devices subscribed to a topic.

Identify Repeating Operations

Look for repeated actions that take most time.

• Primary operation: Loop over all subscribed devices to send messages.
• How many times: Once for each subscribed device.

How Execution Grows With Input

As the number of subscribed devices grows, the number of send actions grows too.

Input Size (n)	Approx. Operations
10	10 sends
100	100 sends
1000	1000 sends

Pattern observation: The work grows directly with the number of subscribers.

Final Time Complexity

Time Complexity: O(n)

This means sending a message takes longer as more devices subscribe, growing in a straight line.

Common Mistake

[X] Wrong: "Sending one message always takes the same time no matter how many devices listen."

[OK] Correct: Each subscribed device needs its own message, so more devices mean more work.

Interview Connect

Understanding how MQTT scales helps you explain real IoT systems and shows you can think about efficiency in networks.

Self-Check

"What if MQTT used a broadcast method that sends one message to all devices at once? How would the time complexity change?"