FA-73371 / Rate limiter algorithms / Open access
Generic cell rate algorithm limiter: idle time banks unlimited credit · case 01
After a quiet period the limiter admits an unbounded burst because TAT lags far behind now.
ROOT CAUSE
The theoretical arrival time is not advanced to now before adding the increment.
VERIFIED REPAIR
Start from max(TAT, t).
Unsuccessful approach: Anchoring at t - T grants one extra emission interval of credit after idleness.
Case contract
Input {period_ms T, burst B, requests [[t, quantity]]}. State TAT starts at 0. A quantity above B is ["never", 0, 0]. Otherwise tat = max(TAT, t) and new_tat = tat + q*T; the request is allowed iff new_tat - t <= B*T, in which case TAT = new_tat and remaining = floor((B*T - (TAT - t))/T). A denied request leaves TAT unchanged and reports retry_after = new_tat - B*T - t and remaining floor((B*T - (tat - t))/T). Return [[decision, retry_after, remaining]].
Why this case matters
GCRA limiters store a single theoretical-arrival timestamp per key; every decision and header value is derived from it, so small formula errors leak bursts or starve clients.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
T = x['period_ms']
B = x['burst']
TAT = 0
out = []
for t, q in x['requests']:
if q > B:
out.append(['never', 0, 0])
continue
tat = TAT
new_tat = tat + q * T
if new_tat - t <= B * T:
TAT = new_tat
out.append(['allow', 0, (B * T - (TAT - t)) // T])
else:
out.append(['deny', new_tat - B * T - t, (B * T - (tat - t)) // T])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10010, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 40, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [41, 2], [5, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [201, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[8, 2],
[57, 1],
[84, 2],
[163, 2],
[383, 1],
[525, 2],
[624, 2],
[997, 1],
[1402, 2],
[1869, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['deny', 24, 1],
['allow', 0, 0],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 2]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10020, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 30, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [42, 2], [10, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [202, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[67, 2],
[137, 1],
[249, 1],
[594, 1],
[681, 2],
[826, 1],
[1250, 1],
[1428, 1],
[1433, 2],
[1483, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 3],
['allow', 0, 1],
['deny', 45, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10030, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 20, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [43, 2], [15, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [203, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[56, 1],
[339, 2],
[932, 1],
[1203, 2],
[1327, 2],
[1505, 1],
[1614, 2],
[1774, 2],
[1930, 1],
[1938, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 1],
['deny', 65, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10040, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 10, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [44, 2], [20, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [204, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[415, 1],
[479, 1],
[592, 1],
[602, 2],
[683, 2],
[973, 2],
[1658, 1],
[1708, 2],
[1784, 1],
[1789, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 0],
['deny', 32, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 1],
['deny', 69, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10050, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['allow', 0, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [45, 2], [25, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [205, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[293, 2],
[620, 2],
[635, 1],
[1275, 2],
[1525, 2],
[1565, 1],
[1595, 2],
[1614, 1],
[1806, 2],
[1874, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['deny', 30, 1],
['allow', 0, 0],
['allow', 0, 0],
['allow', 0, 0]]]]]
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 |
|---|---|---|---|
| burst of five | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| idle credit bounded | [['allow', 0, 2], ['allow', 0, 201], ['allow', 0, 200], ['allow', 0, 199], ['allow', 0, 198], ['allow', 0, 197]] | [['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 50, 0], ['deny', 40, 0]] | Failed |
| denied requests do not push tat | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| multi-unit request | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | Passed |
| exact tolerance edge | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | Passed |
| random traffic | [['allow', 0, 2], ['allow', 0, 1], ['deny', 16, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 5], ['allow', 0, 7]] | [['allow', 0, 2], ['allow', 0, 1], ['deny', 24, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 2]] | Failed |
SHA-256 / 6fe115b2683a9e8ad7e01447800aeb70472b196ac9684fb7f48a505d0ab8b9ec
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
T = x['period_ms']
B = x['burst']
TAT = 0
out = []
for t, q in x['requests']:
if q > B:
out.append(['never', 0, 0])
continue
tat = max(TAT, t - T)
new_tat = tat + q * T
if new_tat - t <= B * T:
TAT = new_tat
out.append(['allow', 0, (B * T - (TAT - t)) // T])
else:
out.append(['deny', new_tat - B * T - t, (B * T - (tat - t)) // T])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10010, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 40, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [41, 2], [5, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [201, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[8, 2],
[57, 1],
[84, 2],
[163, 2],
[383, 1],
[525, 2],
[624, 2],
[997, 1],
[1402, 2],
[1869, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['deny', 24, 1],
['allow', 0, 0],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 2]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10020, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 30, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [42, 2], [10, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [202, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[67, 2],
[137, 1],
[249, 1],
[594, 1],
[681, 2],
[826, 1],
[1250, 1],
[1428, 1],
[1433, 2],
[1483, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 3],
['allow', 0, 1],
['deny', 45, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10030, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 20, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [43, 2], [15, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [203, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[56, 1],
[339, 2],
[932, 1],
[1203, 2],
[1327, 2],
[1505, 1],
[1614, 2],
[1774, 2],
[1930, 1],
[1938, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 1],
['deny', 65, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10040, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 10, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [44, 2], [20, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [204, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[415, 1],
[479, 1],
[592, 1],
[602, 2],
[683, 2],
[973, 2],
[1658, 1],
[1708, 2],
[1784, 1],
[1789, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 0],
['deny', 32, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 1],
['deny', 69, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10050, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['allow', 0, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [45, 2], [25, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [205, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[293, 2],
[620, 2],
[635, 1],
[1275, 2],
[1525, 2],
[1565, 1],
[1595, 2],
[1614, 1],
[1806, 2],
[1874, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['deny', 30, 1],
['allow', 0, 0],
['allow', 0, 0],
['allow', 0, 0]]]]]
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 |
|---|---|---|---|
| burst of five | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| idle credit bounded | [['allow', 0, 2], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 40, 0]] | [['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 50, 0], ['deny', 40, 0]] | Failed |
| denied requests do not push tat | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| multi-unit request | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | Passed |
| exact tolerance edge | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | Passed |
| random traffic | [['allow', 0, 2], ['allow', 0, 1], ['deny', 16, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 3], ['allow', 0, 3]] | [['allow', 0, 2], ['allow', 0, 1], ['deny', 24, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 2]] | Failed |
SHA-256 / 94e21cbde74ef6675fec52f7d3aaf13fff449c7db526cb72c0ef82792786ef4b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
T = x['period_ms']
B = x['burst']
TAT = 0
out = []
for t, q in x['requests']:
if q > B:
out.append(['never', 0, 0])
continue
tat = max(TAT, t)
new_tat = tat + q * T
if new_tat - t <= B * T:
TAT = new_tat
out.append(['allow', 0, (B * T - (TAT - t)) // T])
else:
out.append(['deny', new_tat - B * T - t, (B * T - (tat - t)) // T])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10010, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 40, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [101, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [41, 2], [5, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [201, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[8, 2],
[57, 1],
[84, 2],
[163, 2],
[383, 1],
[525, 2],
[624, 2],
[997, 1],
[1402, 2],
[1869, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['deny', 24, 1],
['allow', 0, 0],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 2]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10020, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 30, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [102, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [42, 2], [10, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [202, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[67, 2],
[137, 1],
[249, 1],
[594, 1],
[681, 2],
[826, 1],
[1250, 1],
[1428, 1],
[1433, 2],
[1483, 2]]},
[['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 1],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 3],
['allow', 0, 1],
['deny', 45, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10030, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 20, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [103, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [43, 2], [15, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [203, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[56, 1],
[339, 2],
[932, 1],
[1203, 2],
[1327, 2],
[1505, 1],
[1614, 2],
[1774, 2],
[1930, 1],
[1938, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['allow', 0, 1],
['deny', 65, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10040, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['deny', 10, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [104, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [44, 2], [20, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [204, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[415, 1],
[479, 1],
[592, 1],
[602, 2],
[683, 2],
[973, 2],
[1658, 1],
[1708, 2],
[1784, 1],
[1789, 2]]},
[['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 0],
['deny', 32, 1],
['allow', 0, 2],
['allow', 0, 3],
['allow', 0, 1],
['allow', 0, 1],
['deny', 69, 1]]]],
[['burst of five',
{'burst': 5,
'period_ms': 100,
'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [250, 1]]},
[['allow', 0, 4],
['allow', 0, 3],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['idle credit bounded',
{'burst': 3,
'period_ms': 50,
'requests': [[0, 1], [10000, 1], [10000, 1], [10000, 1], [10000, 1], [10050, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 0],
['deny', 50, 0],
['allow', 0, 0]]],
['denied requests do not push tat',
{'burst': 2, 'period_ms': 100, 'requests': [[0, 1], [0, 1], [0, 1], [0, 1], [105, 1], [200, 1]]},
[['allow', 0, 1],
['allow', 0, 0],
['deny', 100, 0],
['deny', 100, 0],
['allow', 0, 0],
['allow', 0, 0]]],
['multi-unit request',
{'burst': 4, 'period_ms': 20, 'requests': [[0, 3], [0, 2], [45, 2], [25, 5]]},
[['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]]],
['exact tolerance edge',
{'burst': 3, 'period_ms': 100, 'requests': [[0, 3], [100, 1], [150, 1], [205, 1]]},
[['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]]],
['random traffic',
{'burst': 4,
'period_ms': 100,
'requests': [[293, 2],
[620, 2],
[635, 1],
[1275, 2],
[1525, 2],
[1565, 1],
[1595, 2],
[1614, 1],
[1806, 2],
[1874, 1]]},
[['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['allow', 0, 2],
['allow', 0, 2],
['allow', 0, 1],
['deny', 30, 1],
['allow', 0, 0],
['allow', 0, 0],
['allow', 0, 0]]]]]
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 |
|---|---|---|---|
| burst of five | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 4], ['allow', 0, 3], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| idle credit bounded | [['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 50, 0], ['deny', 40, 0]] | [['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 1], ['allow', 0, 0], ['deny', 50, 0], ['deny', 40, 0]] | Passed |
| denied requests do not push tat | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | [['allow', 0, 1], ['allow', 0, 0], ['deny', 100, 0], ['deny', 100, 0], ['allow', 0, 0], ['allow', 0, 0]] | Passed |
| multi-unit request | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | [['allow', 0, 1], ['deny', 20, 1], ['allow', 0, 1], ['never', 0, 0]] | Passed |
| exact tolerance edge | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | [['allow', 0, 0], ['allow', 0, 0], ['deny', 50, 0], ['allow', 0, 0]] | Passed |
| random traffic | [['allow', 0, 2], ['allow', 0, 1], ['deny', 24, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 2]] | [['allow', 0, 2], ['allow', 0, 1], ['deny', 24, 1], ['allow', 0, 0], ['allow', 0, 1], ['allow', 0, 1], ['allow', 0, 0], ['allow', 0, 2], ['allow', 0, 2], ['allow', 0, 2]] | Passed |
SHA-256 / 4813819e5702a7ff6ba793d3d1f2ce7cee700f3f6586f8372b17a723b314ce6d
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 2026-09-29T14:48:46.919047+00:00.
Case digest / b61a70ac8c84d40139297ba93fcb8320d1fc9d9b84df65196f2bd248c6446f71