FA-68226 / Traffic signal timing plans / Open access

Transit signal priority decision: time to next green is measured backwards · case 01

Transit signal priority decision returns a wrong result when time to next green is measured backwards.

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

ROOT CAUSE

The wait is computed from green start to arrival, reversing the direction around the cycle.

THE FAILURE

The wait is computed from green start to arrival, reversing the direction around the cycle.

Unsuccessful approach: Without the modulo, arrivals after green start in the same cycle get a negative wait.

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 = (a - gs) % 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': 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': 130, 'green_start': 5, 'green_end': 23, 'max_ext': 5, 'max_early': 14, 'arrival': 261, 'last_granted': 0, 'cycle_index': 12, 'lockout': 1}, ['early', 4]), ({'cycle': 120, 'green_start': 28, 'green_end': 81, 'max_ext': 11, 'max_early': 16, 'arrival': 17, 'last_granted': None, 'cycle_index': 17, 'lockout': 2}, ['early', 11]), ({'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': 90, 'green_start': 2, 'green_end': 24, 'max_ext': 19, 'max_early': 10, 'arrival': 151, 'last_granted': None, 'cycle_index': 3, 'lockout': 2}, ['early', 10]), ({'cycle': 140, 'green_start': 23, 'green_end': 39, 'max_ext': 18, 'max_early': 10, 'arrival': 206, 'last_granted': 1, 'cycle_index': 18, 'lockout': 3}, ['early', 10]), ({'cycle': 140, 'green_start': 36, 'green_end': 98, 'max_ext': 10, 'max_early': 15, 'arrival': 23, 'last_granted': 10, 'cycle_index': 13, 'lockout': 1}, ['early', 13])], [({'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': 110, 'green_start': 49, 'green_end': 88, 'max_ext': 8, 'max_early': 20, 'arrival': 36, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['early', 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': 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': 80, 'green_start': 13, 'green_end': 42, 'max_ext': 10, 'max_early': 5, 'arrival': 66, 'last_granted': None, 'cycle_index': 10, 'lockout': 3}, ['early', 5]), ({'cycle': 100, 'green_start': 24, 'green_end': 51, 'max_ext': 20, 'max_early': 20, 'arrival': 87, 'last_granted': 4, 'cycle_index': 17, 'lockout': 1}, ['early', 20]), ({'cycle': 80, 'green_start': 10, 'green_end': 38, 'max_ext': 10, 'max_early': 16, 'arrival': 157, 'last_granted': 17, 'cycle_index': 22, 'lockout': 2}, ['early', 13]), ({'cycle': 110, 'green_start': 9, 'green_end': 41, 'max_ext': 17, 'max_early': 18, 'arrival': 115, 'last_granted': None, 'cycle_index': 18, 'lockout': 3}, ['early', 4])], [({'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': 140, 'green_start': 4, 'green_end': 36, 'max_ext': 15, 'max_early': 11, 'arrival': 99, 'last_granted': None, 'cycle_index': 6, 'lockout': 1}, ['early', 11]), ({'cycle': 90, 'green_start': 25, 'green_end': 40, 'max_ext': 8, 'max_early': 9, 'arrival': 60, 'last_granted': None, 'cycle_index': 20, 'lockout': 1}, ['early', 9]), ({'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': 2, 'green_end': 30, 'max_ext': 12, 'max_early': 13, 'arrival': 297, 'last_granted': None, 'cycle_index': 10, 'lockout': 3}, ['early', 5]), ({'cycle': 120, 'green_start': 50, 'green_end': 90, 'max_ext': 11, 'max_early': 8, 'arrival': 49, 'last_granted': 4, 'cycle_index': 13, 'lockout': 3}, ['early', 1]), ({'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': 42, 'green_end': 86, 'max_ext': 9, 'max_early': 11, 'arrival': 38, 'last_granted': None, 'cycle_index': 16, 'lockout': 3}, ['early', 4])], [({'cycle': 90, 'green_start': 42, 'green_end': 78, 'max_ext': 18, 'max_early': 14, 'arrival': 209, 'last_granted': None, 'cycle_index': 8, 'lockout': 2}, ['early', 13]), ({'cycle': 100, 'green_start': 1, 'green_end': 27, 'max_ext': 13, 'max_early': 8, 'arrival': 261, 'last_granted': None, 'cycle_index': 2, 'lockout': 3}, ['early', 8]), ({'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': 26, 'green_end': 44, 'max_ext': 5, 'max_early': 15, 'arrival': 251, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['early', 15]), ({'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': 120, 'green_start': 18, 'green_end': 55, 'max_ext': 12, 'max_early': 18, 'arrival': 126, 'last_granted': None, 'cycle_index': 20, 'lockout': 1}, ['early', 12]), ({'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': 4, 'green_end': 40, 'max_ext': 12, 'max_early': 20, 'arrival': 388, 'last_granted': None, 'cycle_index': 10, 'lockout': 1}, ['early', 6])], [({'cycle': 90, 'green_start': 29, 'green_end': 48, 'max_ext': 19, 'max_early': 20, 'arrival': 14, 'last_granted': 6, 'cycle_index': 10, 'lockout': 1}, ['early', 15]), ({'cycle': 130, 'green_start': 18, 'green_end': 48, 'max_ext': 17, 'max_early': 6, 'arrival': 257, 'last_granted': 19, 'cycle_index': 0, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 9, 'green_end': 40, 'max_ext': 10, 'max_early': 11, 'arrival': 349, 'last_granted': None, 'cycle_index': 1, 'lockout': 1}, ['early', 11]), ({'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': 130, 'green_start': 33, 'green_end': 59, 'max_ext': 11, 'max_early': 17, 'arrival': 153, 'last_granted': None, 'cycle_index': 10, 'lockout': 1}, ['early', 10]), ({'cycle': 140, 'green_start': 23, 'green_end': 87, 'max_ext': 18, 'max_early': 8, 'arrival': 409, 'last_granted': 8, 'cycle_index': 17, 'lockout': 2}, ['early', 8]), ({'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': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2])]]
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', 14]`	`['early', 4]`	Failed
timing oracle 2	`['early', 16]`	`['early', 11]`	Failed
timing oracle 3	`['none', 0]`	`['none', 0]`	Passed
timing oracle 4	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 5	`['early', 10]`	`['early', 10]`	Passed
timing oracle 6	`['early', 10]`	`['early', 10]`	Passed
timing oracle 7	`['early', 15]`	`['early', 13]`	Failed

SHA-256 / 5b8bb595b9b1a8de890e11935b64c6fa9fdaa5cf534b5062f3c0b32d08ff5783

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'] - 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
    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': 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': 130, 'green_start': 5, 'green_end': 23, 'max_ext': 5, 'max_early': 14, 'arrival': 261, 'last_granted': 0, 'cycle_index': 12, 'lockout': 1}, ['early', 4]), ({'cycle': 120, 'green_start': 28, 'green_end': 81, 'max_ext': 11, 'max_early': 16, 'arrival': 17, 'last_granted': None, 'cycle_index': 17, 'lockout': 2}, ['early', 11]), ({'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': 90, 'green_start': 2, 'green_end': 24, 'max_ext': 19, 'max_early': 10, 'arrival': 151, 'last_granted': None, 'cycle_index': 3, 'lockout': 2}, ['early', 10]), ({'cycle': 140, 'green_start': 23, 'green_end': 39, 'max_ext': 18, 'max_early': 10, 'arrival': 206, 'last_granted': 1, 'cycle_index': 18, 'lockout': 3}, ['early', 10]), ({'cycle': 140, 'green_start': 36, 'green_end': 98, 'max_ext': 10, 'max_early': 15, 'arrival': 23, 'last_granted': 10, 'cycle_index': 13, 'lockout': 1}, ['early', 13])], [({'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': 110, 'green_start': 49, 'green_end': 88, 'max_ext': 8, 'max_early': 20, 'arrival': 36, 'last_granted': None, 'cycle_index': 4, 'lockout': 1}, ['early', 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': 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': 80, 'green_start': 13, 'green_end': 42, 'max_ext': 10, 'max_early': 5, 'arrival': 66, 'last_granted': None, 'cycle_index': 10, 'lockout': 3}, ['early', 5]), ({'cycle': 100, 'green_start': 24, 'green_end': 51, 'max_ext': 20, 'max_early': 20, 'arrival': 87, 'last_granted': 4, 'cycle_index': 17, 'lockout': 1}, ['early', 20]), ({'cycle': 80, 'green_start': 10, 'green_end': 38, 'max_ext': 10, 'max_early': 16, 'arrival': 157, 'last_granted': 17, 'cycle_index': 22, 'lockout': 2}, ['early', 13]), ({'cycle': 110, 'green_start': 9, 'green_end': 41, 'max_ext': 17, 'max_early': 18, 'arrival': 115, 'last_granted': None, 'cycle_index': 18, 'lockout': 3}, ['early', 4])], [({'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': 140, 'green_start': 4, 'green_end': 36, 'max_ext': 15, 'max_early': 11, 'arrival': 99, 'last_granted': None, 'cycle_index': 6, 'lockout': 1}, ['early', 11]), ({'cycle': 90, 'green_start': 25, 'green_end': 40, 'max_ext': 8, 'max_early': 9, 'arrival': 60, 'last_granted': None, 'cycle_index': 20, 'lockout': 1}, ['early', 9]), ({'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': 2, 'green_end': 30, 'max_ext': 12, 'max_early': 13, 'arrival': 297, 'last_granted': None, 'cycle_index': 10, 'lockout': 3}, ['early', 5]), ({'cycle': 120, 'green_start': 50, 'green_end': 90, 'max_ext': 11, 'max_early': 8, 'arrival': 49, 'last_granted': 4, 'cycle_index': 13, 'lockout': 3}, ['early', 1]), ({'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': 42, 'green_end': 86, 'max_ext': 9, 'max_early': 11, 'arrival': 38, 'last_granted': None, 'cycle_index': 16, 'lockout': 3}, ['early', 4])], [({'cycle': 90, 'green_start': 42, 'green_end': 78, 'max_ext': 18, 'max_early': 14, 'arrival': 209, 'last_granted': None, 'cycle_index': 8, 'lockout': 2}, ['early', 13]), ({'cycle': 100, 'green_start': 1, 'green_end': 27, 'max_ext': 13, 'max_early': 8, 'arrival': 261, 'last_granted': None, 'cycle_index': 2, 'lockout': 3}, ['early', 8]), ({'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': 26, 'green_end': 44, 'max_ext': 5, 'max_early': 15, 'arrival': 251, 'last_granted': None, 'cycle_index': 7, 'lockout': 3}, ['early', 15]), ({'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': 120, 'green_start': 18, 'green_end': 55, 'max_ext': 12, 'max_early': 18, 'arrival': 126, 'last_granted': None, 'cycle_index': 20, 'lockout': 1}, ['early', 12]), ({'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': 4, 'green_end': 40, 'max_ext': 12, 'max_early': 20, 'arrival': 388, 'last_granted': None, 'cycle_index': 10, 'lockout': 1}, ['early', 6])], [({'cycle': 90, 'green_start': 29, 'green_end': 48, 'max_ext': 19, 'max_early': 20, 'arrival': 14, 'last_granted': 6, 'cycle_index': 10, 'lockout': 1}, ['early', 15]), ({'cycle': 130, 'green_start': 18, 'green_end': 48, 'max_ext': 17, 'max_early': 6, 'arrival': 257, 'last_granted': 19, 'cycle_index': 0, 'lockout': 1}, ['locked', 0]), ({'cycle': 120, 'green_start': 9, 'green_end': 40, 'max_ext': 10, 'max_early': 11, 'arrival': 349, 'last_granted': None, 'cycle_index': 1, 'lockout': 1}, ['early', 11]), ({'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': 130, 'green_start': 33, 'green_end': 59, 'max_ext': 11, 'max_early': 17, 'arrival': 153, 'last_granted': None, 'cycle_index': 10, 'lockout': 1}, ['early', 10]), ({'cycle': 140, 'green_start': 23, 'green_end': 87, 'max_ext': 18, 'max_early': 8, 'arrival': 409, 'last_granted': 8, 'cycle_index': 17, 'lockout': 2}, ['early', 8]), ({'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': 30, 'green_end': 45, 'max_ext': 20, 'max_early': 10, 'arrival': 28, 'last_granted': 1, 'cycle_index': 6, 'lockout': 2}, ['early', 2])]]
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', 4]`	`['early', 4]`	Passed
timing oracle 2	`['early', 11]`	`['early', 11]`	Passed
timing oracle 3	`['none', 0]`	`['none', 0]`	Passed
timing oracle 4	`['extend', 1]`	`['extend', 1]`	Passed
timing oracle 5	`['early', -59]`	`['early', 10]`	Failed
timing oracle 6	`['early', -43]`	`['early', 10]`	Failed
timing oracle 7	`['early', 13]`	`['early', 13]`	Passed

SHA-256 / 435aaf33b8622ee6d223bdd2031261239faab52ac79bab2f2f5bb8395cc1265f

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The verified repair and its recorded checks are member-only.

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 2026-09-29T14:48:00.252145+00:00.

Case digest / 42bdd6469fb5a2dcd87bdd97ceffe7bdd2071768ee626193fb2dd05445db1979