Why API Gateway matters in AWS - Performance Analysis

Time Complexity: Why API Gateway matters

O(n)

Understanding Time Complexity

We want to understand how the work done by API Gateway grows as more requests come in.

How does the number of API calls affect the time it takes to handle requests?

Scenario Under Consideration

Analyze the time complexity of handling multiple API requests through API Gateway.

// Pseudocode for API Gateway handling requests
for each request in incomingRequests:
  validate request
  route to backend service
  apply throttling and caching
  send response

This sequence shows how API Gateway processes each incoming request step-by-step.

Identify Repeating Operations

Look at what happens repeatedly for each request.

• Primary operation: Processing each API request through validation, routing, and response.
• How many times: Once per incoming request.

How Execution Grows With Input

Each new request adds one more set of processing steps.

Input Size (n)	Approx. Api Calls/Operations
10	10 processing steps
100	100 processing steps
1000	1000 processing steps

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

Final Time Complexity

Time Complexity: O(n)

This means the time to handle requests grows in a straight line as more requests come in.

Common Mistake

[X] Wrong: "API Gateway processes all requests at once, so time stays the same no matter how many requests arrive."

[OK] Correct: Each request needs its own processing steps, so more requests mean more work and more time.

Interview Connect

Understanding how API Gateway scales with requests helps you design systems that handle traffic smoothly and predict performance.

Self-Check

"What if API Gateway used caching to reduce processing for repeated requests? How would the time complexity change?"