API Gateway throttling in AWS - Time & Space Complexity

Time Complexity: API Gateway throttling

O(n)

Understanding Time Complexity

When using API Gateway throttling, we want to understand how the number of requests affects the system's behavior.

Specifically, how does the throttling process handle increasing request volumes?

Scenario Under Consideration

Analyze the time complexity of throttling requests in API Gateway.

// Pseudocode for API Gateway throttling
for each incoming request {
  if (currentRequestCount < throttleLimit) {
    allow request
    increment currentRequestCount
  } else {
    reject request with 429 error
  }
}

This sequence checks each request against a limit and either allows or rejects it.

Identify Repeating Operations

Identify the API calls, resource provisioning, data transfers that repeat.

• Primary operation: Checking and updating the current request count for each incoming request.
• How many times: Once per request received by the API Gateway.

How Execution Grows With Input

Each new request triggers one check and possibly an update. So, as requests increase, operations increase at the same rate.

Input Size (n)	Approx. Api Calls/Operations
10	10 checks and updates
100	100 checks and updates
1000	1000 checks and updates

Pattern observation: The number of operations grows directly with the number of requests.

Final Time Complexity

Time Complexity: O(n)

This means the work done grows linearly as more requests come in.

Common Mistake

[X] Wrong: "Throttling happens instantly without checking each request."

[OK] Correct: Each request must be checked against the limit, so the system does work proportional to the number of requests.

Interview Connect

Understanding how throttling scales helps you design systems that handle traffic smoothly and avoid overload.

Self-Check

"What if the throttle limit was dynamic and changed based on time of day? How would the time complexity change?"