Rate Limiting, Cells, and GCRA

Sep 18, 2015

Rate limiting is a mechanism that many developers (especially those running services) may find themselves looking into at some point in their careers. It’s useful for a variety of purposes, some of which might be:

  1. Sharing access to limited resources. e.g. Requests made to an API where the limited resources are your server capacity, database load, etc.
  2. Security. e.g. Limiting the number of second factor attempts that a user is allowed to perform, or the number of times they’re allowed to get their password wrong.
  3. Revenue. Certain services might want to limit actions based on the tier of their customer’s service, and thus create a revenue model based on rate limiting.

Here we’ll explore a few different rate limiting algorithms and culminate at a sophisticated one called GCRA.

A very simple rate limiting implementation is to store a remaining limit in a bucket that will expire after a certain amount of time. We can do this by starting a bucket when the first action comes in, decrementing its value as more actions appear, and make sure it expires after the configured rate limiting period. The pseudo-code looks like:

# 5000 allowed actions per hour
RATE_BURST  = 5000
RATE_PERIOD = 1.hour

def rate_limit?(bucket)
  if !bucket.exists?

  if bucket.value > 0

The Redis SETEX command makes this trivial to implement; just set a key containing the remaining limit with the appropriate expiry and let Redis take care of clean-up.

This method can be somewhat unforgiving for users because it allows a buggy or rogue script to burn an account’s entire rate limit immediately, and force them to wait for the bucket’s expiry to get access back.

By the same principle, the algorithm can be dangerous to the server as well. Consider an antisocial script that can make enough concurrent requests that it can exhaust its rate limit in short order and which is regularly overlimit. Once an hour as the limit resets, the script bombards the server with a new series of requests until its rate is exhausted once again. In this scenario the server always needs enough extra capacity to handle these short intense bursts and which will likely go to waste during the rest of the hour. This wouldn’t be the case if we could find an algorithm that would force these requests to be more evenly spaced out.

GitHub’s API is one such service that implements this naive algorithm (I will randomly pick on them, but many others do this as well), and I can use a benchmarking tool to help demonstrate the problem 1. After my 5000 requests are through I’ll be locked out for the next hour:

$ curl --silent --head -i -H "Authorization: token $GITHUB_TOKEN" \
    https://api.github.com/users/brandur | grep RateLimit
X-RateLimit-Limit: 5000
X-RateLimit-Remaining: 0
X-RateLimit-Reset: 1442423816

$ RESET=1442423816 ruby -e 'puts "%.0f minute(s) before reset" % \
    ((Time.at(ENV["RESET"].to_i) - Time.now) / 60)'
51 minute(s) before reset

Luckily, an algorithm exists that can take care of the problem of this sort of jagged rate limiting called the leaky bucket. It’s intuitive to understand by comparing it to its real-world namesake: imagine a bucket partially filled with water and which has some fixed capacity (τ). The bucket has a leak so that some amount of water is escaping at a constant rate (T). Whenever an action that should be rate limited occurs, some amount of water flows into the bucket, with the amount being proportional to its relative costliness. If the amount of water entering the bucket is greater than the amount leaving through the leak, the bucket starts to fill. Actions are disallowed if the bucket is full.

A visualization of the
A visualization of the "leaky bucket" analog, where water is symbolic of rate-limited actions.

The leaky bucket produces a very smooth rate limiting effect. A user can still exhaust their entire quota by filling their entire bucket nearly instantaneously, but after realizing the error, they should still have access to more quota quickly as the leak starts to drain the bucket.

The leaky bucket is normally implemented using a background process that simulates a leak. It looks for any active buckets that need to be drained, and drains each one in turn. In Redis, this might look like a hash that groups all buckets under a type of rate limit and which is dripped by iterating each key and decrementing it.

The naive leaky bucket’s greatest weakness is its “drip” process. If it goes offline or gets to a capacity limit where it can’t drip all the buckets that need to be dripped, then new incoming requests might be limited incorrectly. There are a number of strategies to help avoid this danger, but if we could build an algorithm without a drip, it would be fundamentally more stable.

This leads us to the leaky bucket variant called “Generic Cell Rate Algorithm” (GCRA). The name “cell” comes from a communications technology called Asynchronous Transfer Mode (ATM) which encoded data into small packets of fixed size called “cells” (as opposed to the variable size frames of IP). GCRA was the algorithm recommended by the ATM Forum for use in an ATM network’s scheduler so that it could either delay or drop cells that came in over their rate limit. Although today ATM is dead, we still catch occasional glimpses of its past innovation with examples like GCRA.

GCRA works by tracking remaining limit through a time called the “theoretical arrival time” (TAT), which is seeded on the first request by adding a duration representing its cost to the current time. The cost is calculated as a multiplier of our “emission interval” (T), which is derived from the rate at which we want the bucket to refill. When any subsequent request comes in, we take the existing TAT, subtract a fixed buffer representing the limit’s total burst capacity from it (τ + T), and compare the result to the current time. This result represents the next time to allow a request. If it’s in the past, we allow the incoming request, and if it’s in the future, we don’t. After a successful request, a new TAT is calculated by adding T.

The pseudo-code for the algorithm can look a little daunting, so instead of showing it, I’ll recommend taking a look at our reference implementation Throttled (more on this below) which is free of heavy abstractions and straightforward to read. Instead, let’s take a look at visual representation of the timeline and various variables for successful request. Here we see an allowed request where t0 is within the bounds of TAT - (τ + T) (i.e. the time of the next allowed request):

A visualization of an allowed request under GCRA. A request at time t0 is successful.
A visualization of an allowed request under GCRA. A request at time t0 is successful.

For a failed request, the time of the next allowed request is in the future, prompting us to deny the request:

A visualization of a denied request under GCRA. A request at time t0 is rejected.
A visualization of a denied request under GCRA. A request at time t0 is rejected.

Because GCRA is so dependent on time, it’s critical to have a strategy for making sure that the current time is consistent if rate limits are being tracked from multiple deployments. Clock drift between machines could throw off the algorithm and lead to false positives (i.e. users locked out of their accounts). One easy strategy here is to use the store’s time for synchronization (for example, by accessing the TIME command in Redis).

My colleague Andrew Metcalf recently upgraded the open-source Golang library Throttled 2 from a naive rate limiting implementation to the one using GCRA. The package is well-documented and well-tested, and should serve as a pretty intuitive reference implementation for the curious. It’s already taking production traffic at Stripe and should be soon at Heroku as well. In particular, check out rate.go where the bulk of the implementation of GCRA is located.

And of course, if you need a rate limiting module and have some Go in your stack, we’d love for you to give Throttled a whirl and let us know how it went.

1 Note that it appears that GitHub also has a secondary limiting mechanism that protects its API from fast instantaneous bursts. I’m still using them as an example because although this does help protect them, it doesn’t help very much in protecting me from myself (i.e. blowing through my entire limit with a buggy script).

2 I am also a maintainer of Throttled.

Did I make a mistake? Please consider sending a pull request.