FA-68201 / Traffic signal timing plans / Open access

Transit signal priority decision: the lockout window lets the boundary cycle through · case 01

Transit signal priority decision returns a wrong result when the lockout window lets the boundary cycle through.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

A request exactly lockout cycles after the last grant is served, granting priority more often than allowed.

THE FAILURE

A request exactly lockout cycles after the last grant is served, granting priority more often than allowed.

Unsuccessful approach: Comparing the cycle index alone ignores when priority was last granted.

Case contract

Input {cycle, green_start, green_end (exclusive), max_ext, max_early, arrival (seconds, reduced modulo cycle), last_granted (cycle index or null), cycle_index, lockout}. A request within lockout cycles of the last grant (difference <= lockout) returns ['locked', 0]. Arrival in green needs nothing. If the arrival is less than max_ext seconds after green end (cyclically) green is extended through the arrival second: ['extend', d+1]. Otherwise green starts early by min(max_early, seconds until next green start).

Why this case matters

Signal timing arithmetic is exact and integer or rational; a wrong rule silently produces unsafe or inefficient timing plans.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    C = x['cycle']
    a = x['arrival'] % C
    last = x['last_granted']
    if last is not None and x['cycle_index'] - last < x['lockout']:
        return ['locked', 0]
    gs, ge = x['green_start'], x['green_end']
    if gs <= a < ge:
        return ['none', 0]
    d = (a - ge) % C
    if d < x['max_ext']:
        return ['extend', d + 1]
    wait = (gs - a) % C
    return ['early', min(x['max_early'], wait)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 80, 'green_start': 21, 'green_end': 54, 'max_ext': 11, 'max_early': 20, 'arrival': 204, 'last_granted': 18, 'cycle_index': 3, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 140, 'green_start': 22, 'green_end': 82, 'max_ext': 20, 'max_early': 12, 'arrival': 98, 'last_granted': 4, 'cycle_index': 5, 'lockout': 1}, ['locked', 0]), ({'cycle': 90, 'green_start': 7, 'green_end': 37, 'max_ext': 16, 'max_early': 14, 'arrival': 165, 'last_granted': 5, 'cycle_index': 6, 'lockout': 1}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 120, 'green_start': 14, 'green_end': 37, 'max_ext': 18, 'max_early': 14, 'arrival': 190, 'last_granted': 12, 'cycle_index': 14, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 90, 'green_start': 8, 'green_end': 29, 'max_ext': 13, 'max_early': 20, 'arrival': 146, 'last_granted': 5, 'cycle_index': 8, 'lockout': 3}, ['locked', 0])], [({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 130, 'green_start': 43, 'green_end': 58, 'max_ext': 17, 'max_early': 10, 'arrival': 7, 'last_granted': 1, 'cycle_index': 7, 'lockout': 1}, ['early', 10]), ({'cycle': 80, 'green_start': 28, 'green_end': 64, 'max_ext': 6, 'max_early': 7, 'arrival': 101, 'last_granted': 9, 'cycle_index': 7, 'lockout': 1}, ['locked', 0]), ({'cycle': 130, 'green_start': 19, 'green_end': 74, 'max_ext': 12, 'max_early': 14, 'arrival': 130, 'last_granted': 14, 'cycle_index': 17, 'lockout': 3}, ['locked', 0]), ({'cycle': 120, 'green_start': 28, 'green_end': 69, 'max_ext': 17, 'max_early': 18, 'arrival': 81, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['extend', 13]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 140, 'green_start': 29, 'green_end': 54, 'max_ext': 14, 'max_early': 5, 'arrival': 42, 'last_granted': 10, 'cycle_index': 13, 'lockout': 3}, ['locked', 0])], [({'cycle': 130, 'green_start': 26, 'green_end': 46, 'max_ext': 9, 'max_early': 13, 'arrival': 214, 'last_granted': 6, 'cycle_index': 19, 'lockout': 3}, ['early', 13]), ({'cycle': 90, 'green_start': 25, 'green_end': 47, 'max_ext': 13, 'max_early': 7, 'arrival': 220, 'last_granted': 5, 'cycle_index': 7, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 110, 'green_start': 46, 'green_end': 71, 'max_ext': 20, 'max_early': 9, 'arrival': 55, 'last_granted': None, 'cycle_index': 12, 'lockout': 3}, ['none', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 100, 'green_start': 19, 'green_end': 35, 'max_ext': 18, 'max_early': 15, 'arrival': 139, 'last_granted': None, 'cycle_index': 0, 'lockout': 3}, ['extend', 5]), ({'cycle': 140, 'green_start': 4, 'green_end': 57, 'max_ext': 20, 'max_early': 19, 'arrival': 89, 'last_granted': 18, 'cycle_index': 21, 'lockout': 3}, ['locked', 0])], [({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 90, 'green_start': 24, 'green_end': 45, 'max_ext': 5, 'max_early': 8, 'arrival': 267, 'last_granted': 2, 'cycle_index': 5, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 36, 'max_ext': 5, 'max_early': 15, 'arrival': 137, 'last_granted': 16, 'cycle_index': 18, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 120, 'green_start': 13, 'green_end': 64, 'max_ext': 7, 'max_early': 14, 'arrival': 151, 'last_granted': 17, 'cycle_index': 19, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 53, 'green_end': 103, 'max_ext': 15, 'max_early': 10, 'arrival': 298, 'last_granted': 3, 'cycle_index': 4, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 45, 'green_end': 69, 'max_ext': 12, 'max_early': 17, 'arrival': 116, 'last_granted': 5, 'cycle_index': 5, 'lockout': 1}, ['locked', 0])], [({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 100, 'green_start': 13, 'green_end': 36, 'max_ext': 18, 'max_early': 7, 'arrival': 201, 'last_granted': 13, 'cycle_index': 15, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 23, 'green_end': 49, 'max_ext': 16, 'max_early': 17, 'arrival': 420, 'last_granted': 19, 'cycle_index': 3, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 12, 'green_end': 42, 'max_ext': 7, 'max_early': 13, 'arrival': 45, 'last_granted': 6, 'cycle_index': 8, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 80, 'green_start': 24, 'green_end': 55, 'max_ext': 13, 'max_early': 19, 'arrival': 191, 'last_granted': 1, 'cycle_index': 18, 'lockout': 2}, ['none', 0]), ({'cycle': 120, 'green_start': 52, 'green_end': 74, 'max_ext': 20, 'max_early': 13, 'arrival': 248, 'last_granted': None, 'cycle_index': 12, 'lockout': 1}, ['early', 13])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, 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
timing oracle 0	`['locked', 0]`	`['locked', 0]`	Passed
timing oracle 1	`['early', 2]`	`['early', 2]`	Passed
timing oracle 2	`['extend', 17]`	`['locked', 0]`	Failed
timing oracle 3	`['early', 14]`	`['locked', 0]`	Failed
timing oracle 4	`['none', 0]`	`['none', 0]`	Passed
timing oracle 5	`['locked', 0]`	`['locked', 0]`	Passed
timing oracle 6	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 7	`['early', 20]`	`['locked', 0]`	Failed

SHA-256 / 9a4b522fa410bf0fc5bc2e3d272f68a10a7737b1d6277a0eae827cf40c53f933

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    C = x['cycle']
    a = x['arrival'] % C
    last = x['last_granted']
    if last is not None and x['cycle_index'] <= x['lockout']:
        return ['locked', 0]
    gs, ge = x['green_start'], x['green_end']
    if gs <= a < ge:
        return ['none', 0]
    d = (a - ge) % C
    if d < x['max_ext']:
        return ['extend', d + 1]
    wait = (gs - a) % C
    return ['early', min(x['max_early'], wait)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 80, 'green_start': 21, 'green_end': 54, 'max_ext': 11, 'max_early': 20, 'arrival': 204, 'last_granted': 18, 'cycle_index': 3, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 140, 'green_start': 22, 'green_end': 82, 'max_ext': 20, 'max_early': 12, 'arrival': 98, 'last_granted': 4, 'cycle_index': 5, 'lockout': 1}, ['locked', 0]), ({'cycle': 90, 'green_start': 7, 'green_end': 37, 'max_ext': 16, 'max_early': 14, 'arrival': 165, 'last_granted': 5, 'cycle_index': 6, 'lockout': 1}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 120, 'green_start': 14, 'green_end': 37, 'max_ext': 18, 'max_early': 14, 'arrival': 190, 'last_granted': 12, 'cycle_index': 14, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 90, 'green_start': 8, 'green_end': 29, 'max_ext': 13, 'max_early': 20, 'arrival': 146, 'last_granted': 5, 'cycle_index': 8, 'lockout': 3}, ['locked', 0])], [({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 130, 'green_start': 43, 'green_end': 58, 'max_ext': 17, 'max_early': 10, 'arrival': 7, 'last_granted': 1, 'cycle_index': 7, 'lockout': 1}, ['early', 10]), ({'cycle': 80, 'green_start': 28, 'green_end': 64, 'max_ext': 6, 'max_early': 7, 'arrival': 101, 'last_granted': 9, 'cycle_index': 7, 'lockout': 1}, ['locked', 0]), ({'cycle': 130, 'green_start': 19, 'green_end': 74, 'max_ext': 12, 'max_early': 14, 'arrival': 130, 'last_granted': 14, 'cycle_index': 17, 'lockout': 3}, ['locked', 0]), ({'cycle': 120, 'green_start': 28, 'green_end': 69, 'max_ext': 17, 'max_early': 18, 'arrival': 81, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['extend', 13]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 140, 'green_start': 29, 'green_end': 54, 'max_ext': 14, 'max_early': 5, 'arrival': 42, 'last_granted': 10, 'cycle_index': 13, 'lockout': 3}, ['locked', 0])], [({'cycle': 130, 'green_start': 26, 'green_end': 46, 'max_ext': 9, 'max_early': 13, 'arrival': 214, 'last_granted': 6, 'cycle_index': 19, 'lockout': 3}, ['early', 13]), ({'cycle': 90, 'green_start': 25, 'green_end': 47, 'max_ext': 13, 'max_early': 7, 'arrival': 220, 'last_granted': 5, 'cycle_index': 7, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 110, 'green_start': 46, 'green_end': 71, 'max_ext': 20, 'max_early': 9, 'arrival': 55, 'last_granted': None, 'cycle_index': 12, 'lockout': 3}, ['none', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 100, 'green_start': 19, 'green_end': 35, 'max_ext': 18, 'max_early': 15, 'arrival': 139, 'last_granted': None, 'cycle_index': 0, 'lockout': 3}, ['extend', 5]), ({'cycle': 140, 'green_start': 4, 'green_end': 57, 'max_ext': 20, 'max_early': 19, 'arrival': 89, 'last_granted': 18, 'cycle_index': 21, 'lockout': 3}, ['locked', 0])], [({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 90, 'green_start': 24, 'green_end': 45, 'max_ext': 5, 'max_early': 8, 'arrival': 267, 'last_granted': 2, 'cycle_index': 5, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 36, 'max_ext': 5, 'max_early': 15, 'arrival': 137, 'last_granted': 16, 'cycle_index': 18, 'lockout': 3}, ['locked', 0]), ({'cycle': 90, 'green_start': 0, 'green_end': 40, 'max_ext': 12, 'max_early': 8, 'arrival': 40, 'last_granted': None, 'cycle_index': 0, 'lockout': 1}, ['extend', 1]), ({'cycle': 120, 'green_start': 13, 'green_end': 64, 'max_ext': 7, 'max_early': 14, 'arrival': 151, 'last_granted': 17, 'cycle_index': 19, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 53, 'green_end': 103, 'max_ext': 15, 'max_early': 10, 'arrival': 298, 'last_granted': 3, 'cycle_index': 4, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 45, 'green_end': 69, 'max_ext': 12, 'max_early': 17, 'arrival': 116, 'last_granted': 5, 'cycle_index': 5, 'lockout': 1}, ['locked', 0])], [({'cycle': 100, 'green_start': 10, 'green_end': 45, 'max_ext': 10, 'max_early': 10, 'arrival': 110, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['none', 0]), ({'cycle': 100, 'green_start': 13, 'green_end': 36, 'max_ext': 18, 'max_early': 7, 'arrival': 201, 'last_granted': 13, 'cycle_index': 15, 'lockout': 2}, ['locked', 0]), ({'cycle': 140, 'green_start': 23, 'green_end': 49, 'max_ext': 16, 'max_early': 17, 'arrival': 420, 'last_granted': 19, 'cycle_index': 3, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 12, 'green_end': 42, 'max_ext': 7, 'max_early': 13, 'arrival': 45, 'last_granted': 6, 'cycle_index': 8, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 10, 'green_end': 50, 'max_ext': 10, 'max_early': 10, 'arrival': 250, 'last_granted': 3, 'cycle_index': 5, 'lockout': 2}, ['locked', 0]), ({'cycle': 100, 'green_start': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2]), ({'cycle': 80, 'green_start': 24, 'green_end': 55, 'max_ext': 13, 'max_early': 19, 'arrival': 191, 'last_granted': 1, 'cycle_index': 18, 'lockout': 2}, ['none', 0]), ({'cycle': 120, 'green_start': 52, 'green_end': 74, 'max_ext': 20, 'max_early': 13, 'arrival': 248, 'last_granted': None, 'cycle_index': 12, 'lockout': 1}, ['early', 13])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, 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
timing oracle 0	`['none', 0]`	`['locked', 0]`	Failed
timing oracle 1	`['early', 2]`	`['early', 2]`	Passed
timing oracle 2	`['extend', 17]`	`['locked', 0]`	Failed
timing oracle 3	`['early', 14]`	`['locked', 0]`	Failed
timing oracle 4	`['none', 0]`	`['none', 0]`	Passed
timing oracle 5	`['early', 14]`	`['locked', 0]`	Failed
timing oracle 6	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 7	`['early', 20]`	`['locked', 0]`	Failed

SHA-256 / 3fd6aff7a4ba0ae9de474bd772d604d044646aae08307dbce985c20431f3852e

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This mechanism has 8 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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Verification & scope

A deterministic, bounded toy model with a stipulated contract; it makes no claim of conformance to any agency manual or standard. 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 2026-09-29T14:47:59.874964+00:00.

Case digest / 162d5ecf4d00ff8e04e02c6725685ab42d9d00f9a8c76ed60591eaa48f797635