Rate limiting with sliding window in Redis - Time & Space Complexity

Time Complexity: Rate limiting with sliding window

O(n)

Understanding Time Complexity

When using Redis to limit how often a user can do something, we want to know how the time to check and update limits changes as more requests happen.

We ask: How does the work grow when many requests come in quickly?

Scenario Under Consideration

Analyze the time complexity of the following Redis commands for sliding window rate limiting.

-- Current timestamp in milliseconds
local current_time = redis.call('TIME')
local now = tonumber(current_time[1]) * 1000 + tonumber(current_time[2]) / 1000
local key = KEYS[1]
local window = tonumber(ARGV[1])
local limit = tonumber(ARGV[2])

-- Remove old entries outside the window
redis.call('ZREMRANGEBYSCORE', key, 0, now - window)

-- Add current request timestamp
redis.call('ZADD', key, now, now)

-- Count requests in window
local count = redis.call('ZCOUNT', key, now - window, now)

return count <= limit
    

This code keeps timestamps of requests in a sorted set, removes old ones, adds the new one, and checks if the count is within the limit.

Identify Repeating Operations

Look for repeated work that depends on input size.

• Primary operation: Removing old timestamps with ZREMRANGEBYSCORE and counting with ZCOUNT.
• How many times: The removal scans all timestamps outside the window, which depends on how many old requests exist.

How Execution Grows With Input

As more requests happen, the sorted set grows, but old entries get removed.

Input Size (n)	Approx. Operations
10	About 10 removals and O(1) count
100	About 100 removals and O(1) count
1000	About 1000 removals and O(1) count

Pattern observation: The work grows roughly with the number of stored timestamps, which depends on the request rate and window size.

Final Time Complexity

Time Complexity: O(n)

This means the time to check and update the limit grows linearly with the number of requests stored in the window.

Common Mistake

[X] Wrong: "The operations always take constant time regardless of request count."

[OK] Correct: Removing old entries and counting depend on how many timestamps are stored, so more requests mean more work.

Interview Connect

Understanding how Redis commands scale with data size helps you design efficient rate limiting, a common real-world problem.

Self-Check

What if we used a fixed-size queue instead of a sorted set? How would the time complexity change?

Practice

1. What is the main purpose of using a sliding window in rate limiting with Redis?

easy

A. To count actions within a moving time frame for fair limits

B. To store user passwords securely

C. To permanently block users after one action

D. To sort data alphabetically

Solution

1. Step 1: Understand sliding window concept

   Sliding window rate limiting counts actions in a recent time frame that moves forward as time passes.

2. Step 2: Identify purpose in Redis context

   Redis uses sorted sets to track timestamps of actions to enforce limits fairly over time.

3. Final Answer:

   To count actions within a moving time frame for fair limits -> Option A

4. Quick Check:

   Sliding window = moving time frame count [OK]

Hint: Sliding window means counting recent actions, not all time [OK]

Common Mistakes:

• Thinking sliding window blocks permanently
• Confusing with password storage
• Assuming it sorts data alphabetically

2. Which Redis command is essential to add a timestamp to a sorted set for sliding window rate limiting?

easy

A. ZADD

B. GET

C. HSET

D. LPUSH

Solution

1. Step 1: Identify command to add to sorted set

   ZADD adds members with scores (timestamps) to a sorted set in Redis.

2. Step 2: Confirm other commands' purpose

   GET retrieves string values, HSET sets hash fields, LPUSH adds to lists, none add to sorted sets.

3. Final Answer:

   ZADD -> Option A

4. Quick Check:

   ZADD adds to sorted set [OK]

Hint: Use ZADD to add timestamps to sorted sets [OK]

Common Mistakes:

• Using GET which only reads strings
• Confusing HSET (hashes) with sorted sets
• Using LPUSH which is for lists

3. Given this Redis Lua script snippet for sliding window rate limiting:

local now = tonumber(redis.call('TIME')[1])
redis.call('ZREMRANGEBYSCORE', key, 0, now - window)
local count = redis.call('ZCARD', key)
if count < limit then
  redis.call('ZADD', key, now, now)
  return 1
else
  return 0
end

What will be the return value if the current count is equal to the limit?

medium

A. 1

B. nil

C. 0

D. An error

Solution

1. Step 1: Analyze the condition count < limit

   If count is equal to limit, the condition count < limit is false.

2. Step 2: Determine return value when condition is false

   When false, the script returns 0, indicating rate limit reached.

3. Final Answer:

   0 -> Option C

4. Quick Check:

   count == limit returns 0 [OK]

Hint: If count equals limit, return 0 (limit reached) [OK]

Common Mistakes:

• Assuming count == limit returns 1
• Expecting an error instead of 0
• Thinking nil is returned

4. You have this Redis Lua script for sliding window rate limiting:

local now = tonumber(redis.call('TIME')[1])
redis.call('ZREMRANGEBYSCORE', key, 0, now - window)
local count = redis.call('ZCARD', key)
if count <= limit then
  redis.call('ZADD', key, now, now)
  return 1
else
  return 0
end

What is the bug in this script?

medium

A. ZREMRANGEBYSCORE is used incorrectly

B. Using <= allows one extra request beyond limit

C. ZADD should use a string member, not number

D. TIME command returns a string, not number

Solution

1. Step 1: Check condition count <= limit

   This condition allows adding a request when count equals limit, exceeding limit by one.

2. Step 2: Verify other commands usage

   ZREMRANGEBYSCORE usage is correct to remove old timestamps; ZADD accepts numbers as members; TIME returns array with string seconds converted to number.

3. Final Answer:

   Using <= allows one extra request beyond limit -> Option B

4. Quick Check:

   count <= limit allows limit+1 requests [OK]

Hint: Use < not <= to enforce strict limit [OK]

Common Mistakes:

• Thinking ZREMRANGEBYSCORE is wrong here
• Believing ZADD can't use numbers as members
• Confusing TIME return type

5. You want to implement a sliding window rate limiter in Redis that allows 100 requests per 60 seconds. Which sequence of Redis commands best enforces this limit efficiently?

hard

A. HSET to store count, GET to read count, INCR to increment count

B. LPUSH to add timestamp, LLEN to count, LTRIM to remove old timestamps

C. SETNX to set a flag, EXPIRE to reset after 60 seconds

D. ZREMRANGEBYSCORE to remove old timestamps, ZCARD to count, ZADD to add current timestamp

Solution

1. Step 1: Understand sliding window enforcement

   Use sorted sets to store timestamps, remove old ones, count current requests, and add new timestamp.

2. Step 2: Evaluate each option's commands

   ZREMRANGEBYSCORE to remove old timestamps, ZCARD to count, ZADD to add current timestamp uses ZREMRANGEBYSCORE, ZCARD, ZADD correctly for sliding window. LPUSH to add timestamp, LLEN to count, LTRIM to remove old timestamps uses lists which are less efficient for range removals. HSET to store count, GET to read count, INCR to increment count uses hashes and counters, not suitable for sliding window. SETNX to set a flag, EXPIRE to reset after 60 seconds uses simple flags, not counting requests.

3. Final Answer:

   ZREMRANGEBYSCORE, ZCARD, ZADD sequence -> Option D

4. Quick Check:

   Sorted sets + remove old + count + add = correct [OK]

Hint: Use sorted sets with ZREMRANGEBYSCORE, ZCARD, ZADD [OK]

Common Mistakes:

• Using lists which are inefficient for sliding windows
• Using counters without timestamps
• Using flags without counting requests