Why MQTT is the IoT standard in Raspberry Pi - 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 and receive messages using MQTT grows as more devices connect.

How does MQTT handle many devices efficiently?

Scenario Under Consideration

Analyze the time complexity of this simple MQTT publish-subscribe example on a Raspberry Pi.

import paho.mqtt.client as mqtt

def on_message(client, userdata, message):
    print(f"Received message: {message.payload.decode()}")

client = mqtt.Client()
client.on_message = on_message
client.connect("broker.hivemq.com", 1883)
client.subscribe("home/temperature")
client.loop_start()

for i in range(100):
    client.publish("home/temperature", f"Temp {i}")

This code connects to an MQTT broker, subscribes to a topic, and publishes 100 messages.

Identify Repeating Operations

Look at what repeats in this code.

• Primary operation: Publishing messages in a loop.
• How many times: 100 times, once per loop iteration.

How Execution Grows With Input

As the number of messages to send grows, the time to send them grows roughly the same amount.

Input Size (n)	Approx. Operations
10	10 publish calls
100	100 publish calls
1000	1000 publish calls

Pattern observation: The time grows directly with the number of messages sent.

Final Time Complexity

Time Complexity: O(n)

This means if you double the messages, the time to send them roughly doubles too.

Common Mistake

[X] Wrong: "MQTT sends all messages instantly no matter how many devices or messages there are."

[OK] Correct: Each message takes some time to send, so more messages mean more time. MQTT is efficient but not instant.

Interview Connect

Understanding how MQTT scales with message count helps you explain real IoT system behavior clearly and confidently.

Self-Check

"What if we changed the code to publish messages in parallel using multiple threads? How would the time complexity change?"