FA-73656 / Rate limiter algorithms / Open access
Reservation limiter with stored permits: stored permits never consumed · case 01
A burst allowance is reused by every request, so the limiter never throttles after idleness.
ROOT CAUSE
Stored permits used by a request are not subtracted.
THE FAILURE
Stored permits used by a request are not subtracted.
Unsuccessful approach: Subtracting the full request drives the stored balance negative.
Case contract
Input {rate (permits per second), max_burst_s, requests [[t_ms, permits]]} with nondecreasing t. The interval is I = 1000/rate ms. When t is past next_free, idle time is converted into stored permits (capped at max_burst_s*rate) and next_free moves to t. A request waits max(0, next_free - t), i.e. it pays for the previous reservation, then consumes stored permits first and pushes next_free by I per fresh permit. Return [ceil waits in ms, stored, next_free] with exact fractions as strings.
Why this case matters
Client-side reservation limiters (as in smooth-bursty designs) let a large request proceed now and make the next caller wait; getting who pays wrong starves or floods the backend.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
rate = x['rate']
I = Fraction(1000, rate)
max_stored = Fraction(x['max_burst_s'] * rate)
stored = Fraction(0)
next_free = Fraction(0)
out = []
for t, p in x['requests']:
if t > next_free:
stored = min(max_stored, stored + (t - next_free) / I)
next_free = Fraction(t)
wait = max(Fraction(0), next_free - t)
use = min(Fraction(p), stored)
fresh = p - use
next_free += fresh * I
out.append(math.ceil(wait))
return [out, str(stored), str(next_free)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [101, 1], [5000, 1]]},
[[0, 2000, 2099, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10001, 1]]},
[[0, 0, 500, 999], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3001, 1]]},
[[0, 0, 0, 499], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4001, 2], [4001, 4]]},
[[0, 0, 0, 0, 0], '3', '4001']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [11, 1], [20, 2]]},
[[0, 334, 656, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[610, 3],
[1148, 4],
[1339, 3],
[2090, 3],
[2093, 2],
[2589, 1],
[2607, 4],
[2941, 2],
[3090, 2]]},
[[0, 352, 2161, 2910, 4407, 4911, 5393, 7059, 7910], '0', '12000']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [102, 1], [5000, 1]]},
[[0, 2000, 2098, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10002, 1]]},
[[0, 0, 500, 998], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3002, 1]]},
[[0, 0, 0, 498], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4002, 2], [4002, 4]]},
[[0, 0, 0, 0, 0], '3', '4002']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [12, 1], [20, 2]]},
[[0, 334, 655, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[142, 4],
[325, 1],
[548, 2],
[901, 1],
[1366, 1],
[1827, 2],
[1998, 3],
[2374, 1],
[2914, 2]]},
[[0, 1675, 1952, 2599, 2634, 2673, 3502, 4626, 4586], '0', '8500']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [103, 1], [5000, 1]]},
[[0, 2000, 2097, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10003, 1]]},
[[0, 0, 500, 997], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3003, 1]]},
[[0, 0, 0, 497], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4003, 2], [4003, 4]]},
[[0, 0, 0, 0, 0], '3', '4003']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [13, 1], [20, 2]]},
[[0, 334, 654, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[644, 4],
[886, 4],
[910, 3],
[1485, 1],
[1585, 2],
[1776, 4],
[2163, 2],
[2628, 3],
[2698, 2]]},
[[0, 1114, 3090, 4015, 4415, 5224, 6837, 7372, 8802], '0', '12500']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [104, 1], [5000, 1]]},
[[0, 2000, 2096, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10004, 1]]},
[[0, 0, 500, 996], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3004, 1]]},
[[0, 0, 0, 496], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4004, 2], [4004, 4]]},
[[0, 0, 0, 0, 0], '3', '4004']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [14, 1], [20, 2]]},
[[0, 334, 653, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[106, 2],
[1122, 1],
[1604, 3],
[1998, 1],
[2099, 1],
[2549, 2],
[2752, 1],
[2983, 1],
[3690, 4]]},
[[0, 0, 0, 1002, 1401, 1451, 2248, 2517, 2310], '0', '8000']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [105, 1], [5000, 1]]},
[[0, 2000, 2095, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10005, 1]]},
[[0, 0, 500, 995], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3005, 1]]},
[[0, 0, 0, 495], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4005, 2], [4005, 4]]},
[[0, 0, 0, 0, 0], '3', '4005']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [15, 1], [20, 2]]},
[[0, 334, 652, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[2392, 4],
[2748, 2],
[3147, 1],
[3291, 2],
[3293, 2],
[3431, 2],
[3441, 1],
[3672, 1],
[3732, 4]]},
[[0, 0, 245, 601, 1599, 2461, 3451, 3720, 4160], '0', '9892']]]]
for label, args, expected in cases[N - 1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| pay later for big request | [[0, 2000, 2099, 0], '0', '5200'] | [[0, 2000, 2099, 0], '0', '5200'] | Passed |
| stored permits capped | [[0, 0, 500, 499], '2', '10500'] | [[0, 0, 500, 999], '0', '11500'] | Failed |
| stored permits consumed | [[0, 0, 0, 0], '8', '3001'] | [[0, 0, 0, 499], '0', '3750'] | Failed |
| resync after idle | [[0, 0, 0, 0, 0], '9', '4001'] | [[0, 0, 0, 0, 0], '3', '4001'] | Failed |
| fractional waits | [[0, 334, 656, 980], '0', '5000/3'] | [[0, 334, 656, 980], '0', '5000/3'] | Passed |
| random acquires | [[0, 352, 1551, 1690, 2577, 2471, 2453, 3509, 3750], '61/50', '7230'] | [[0, 352, 2161, 2910, 4407, 4911, 5393, 7059, 7910], '0', '12000'] | Failed |
SHA-256 / 3da28232b2bf4c6d4b2a81855d4bb2fb294b1fe6979cc25c45405cba2671ca91
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
rate = x['rate']
I = Fraction(1000, rate)
max_stored = Fraction(x['max_burst_s'] * rate)
stored = Fraction(0)
next_free = Fraction(0)
out = []
for t, p in x['requests']:
if t > next_free:
stored = min(max_stored, stored + (t - next_free) / I)
next_free = Fraction(t)
wait = max(Fraction(0), next_free - t)
use = min(Fraction(p), stored)
fresh = p - use
next_free += fresh * I
stored -= p
out.append(math.ceil(wait))
return [out, str(stored), str(next_free)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [101, 1], [5000, 1]]},
[[0, 2000, 2099, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10001, 1]]},
[[0, 0, 500, 999], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3001, 1]]},
[[0, 0, 0, 499], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4001, 2], [4001, 4]]},
[[0, 0, 0, 0, 0], '3', '4001']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [11, 1], [20, 2]]},
[[0, 334, 656, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[610, 3],
[1148, 4],
[1339, 3],
[2090, 3],
[2093, 2],
[2589, 1],
[2607, 4],
[2941, 2],
[3090, 2]]},
[[0, 352, 2161, 2910, 4407, 4911, 5393, 7059, 7910], '0', '12000']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [102, 1], [5000, 1]]},
[[0, 2000, 2098, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10002, 1]]},
[[0, 0, 500, 998], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3002, 1]]},
[[0, 0, 0, 498], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4002, 2], [4002, 4]]},
[[0, 0, 0, 0, 0], '3', '4002']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [12, 1], [20, 2]]},
[[0, 334, 655, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[142, 4],
[325, 1],
[548, 2],
[901, 1],
[1366, 1],
[1827, 2],
[1998, 3],
[2374, 1],
[2914, 2]]},
[[0, 1675, 1952, 2599, 2634, 2673, 3502, 4626, 4586], '0', '8500']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [103, 1], [5000, 1]]},
[[0, 2000, 2097, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10003, 1]]},
[[0, 0, 500, 997], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3003, 1]]},
[[0, 0, 0, 497], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4003, 2], [4003, 4]]},
[[0, 0, 0, 0, 0], '3', '4003']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [13, 1], [20, 2]]},
[[0, 334, 654, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[644, 4],
[886, 4],
[910, 3],
[1485, 1],
[1585, 2],
[1776, 4],
[2163, 2],
[2628, 3],
[2698, 2]]},
[[0, 1114, 3090, 4015, 4415, 5224, 6837, 7372, 8802], '0', '12500']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [104, 1], [5000, 1]]},
[[0, 2000, 2096, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10004, 1]]},
[[0, 0, 500, 996], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3004, 1]]},
[[0, 0, 0, 496], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4004, 2], [4004, 4]]},
[[0, 0, 0, 0, 0], '3', '4004']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [14, 1], [20, 2]]},
[[0, 334, 653, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[106, 2],
[1122, 1],
[1604, 3],
[1998, 1],
[2099, 1],
[2549, 2],
[2752, 1],
[2983, 1],
[3690, 4]]},
[[0, 0, 0, 1002, 1401, 1451, 2248, 2517, 2310], '0', '8000']]],
[['pay later for big request',
{'max_burst_s': 0, 'rate': 5, 'requests': [[0, 10], [0, 1], [105, 1], [5000, 1]]},
[[0, 2000, 2095, 0], '0', '5200']],
['stored permits capped',
{'max_burst_s': 1, 'rate': 2, 'requests': [[0, 1], [10000, 3], [10000, 1], [10005, 1]]},
[[0, 0, 500, 995], '0', '11500']],
['stored permits consumed',
{'max_burst_s': 2, 'rate': 4, 'requests': [[0, 1], [3000, 5], [3000, 5], [3005, 1]]},
[[0, 0, 0, 495], '0', '3750']],
['resync after idle',
{'max_burst_s': 3, 'rate': 3, 'requests': [[0, 1], [2000, 1], [2100, 1], [4005, 2], [4005, 4]]},
[[0, 0, 0, 0, 0], '3', '4005']],
['fractional waits',
{'max_burst_s': 0, 'rate': 3, 'requests': [[0, 1], [0, 1], [15, 1], [20, 2]]},
[[0, 334, 652, 980], '0', '5000/3']],
['random acquires',
{'max_burst_s': 2,
'rate': 2,
'requests': [[2392, 4],
[2748, 2],
[3147, 1],
[3291, 2],
[3293, 2],
[3431, 2],
[3441, 1],
[3672, 1],
[3732, 4]]},
[[0, 0, 245, 601, 1599, 2461, 3451, 3720, 4160], '0', '9892']]]]
for label, args, expected in cases[N - 1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| pay later for big request | [[0, 2000, 4099, 1600], '-13', '9200'] | [[0, 2000, 2099, 0], '0', '5200'] | Failed |
| stored permits capped | [[0, 0, 500, 1499], '-3', '13000'] | [[0, 0, 500, 999], '0', '11500'] | Failed |
| stored permits consumed | [[0, 0, 0, 499], '-3', '4250'] | [[0, 0, 0, 499], '0', '3750'] | Failed |
| resync after idle | [[0, 0, 0, 0, 0], '2003/1000', '4001'] | [[0, 0, 0, 0, 0], '3', '4001'] | Failed |
| fractional waits | [[0, 334, 989, 1980], '-5', '11000/3'] | [[0, 334, 656, 980], '0', '5000/3'] | Failed |
| random acquires | [[0, 352, 3051, 6690, 12577, 18971, 26343, 35399, 45640], '-1139/50', '60120'] | [[0, 352, 2161, 2910, 4407, 4911, 5393, 7059, 7910], '0', '12000'] | Failed |
SHA-256 / a282d8b9550043d857978c0ccaf88e6bae78afe1b0746ea05e367582ce7033bb
HELD IN THE MEMBER ARCHIVE
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This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
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Sign in to the archive ↗Verification & scope
A deterministic, bounded teaching model with stipulated constants and pre-hashed or explicitly hashed inputs; it is not a production implementation and makes no claim of conformance to any library or paper beyond the stated contract. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:48:49.602498+00:00.
Case digest / 471ef631b6d61491b31df9067eca90a44cab85aff5cd1c54c88fc316b7518cf0