FA-68136 / Traffic signal timing plans / Open access

Uniform delay level of service: the delay denominator uses uncapped X · case 01

Uniform delay level of service returns a wrong result when the delay denominator uses uncapped X.

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

ROOT CAUSE

Without capping X at one, oversaturated movements get a negative or exploding uniform delay.

VERIFIED REPAIR

Restore the degree of saturation cap rule so that the step reads `min(1, X) * lam`.

Unsuccessful approach: Capping the product instead of X lets X*lam approach one and the delay grow without bound.

Case contract

Input {cycle, green, volume, sat_per_lane, lanes}. lam = green/cycle, capacity = sat*lanes*lam, X = volume/capacity, uniform delay d = 0.5*C*(1-lam)^2/(1 - min(1,X)*lam) rounded half up to tenths. LOS thresholds on tenths: <=100 A, <=200 B, <=350 C, <=550 D, <=800 E, else F; any X > 1 is F. Return {vc_milli: floor(1000X), delay_tenths, los}.

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
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    C, g = x['cycle'], x['green']
    lam = Fraction(g, C)
    cap = x['sat_per_lane'] * x['lanes'] * lam
    X = Fraction(x['volume']) / cap
    d = Fraction(1, 2) * C * (1 - lam) ** 2 / (1 - X * lam)
    tenths = int(d * 10 + Fraction(1, 2))
    if X > 1:
        los = 'F'
    else:
        los = 'F'
        for lim, lab in ((100, 'A'), (200, 'B'), (350, 'C'), (550, 'D'), (800, 'E')):
            if tenths <= lim:
                los = lab
                break
    return {'vc_milli': int(X * 1000), 'delay_tenths': tenths, 'los': los}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 150, 'green': 101, 'volume': 2622, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1024, 'delay_tenths': 245, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 90, 'green': 26, 'volume': 553, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1007, 'delay_tenths': 320, 'los': 'F'}), ({'cycle': 120, 'green': 86, 'volume': 1979, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 541, 'delay_tenths': 79, 'los': 'A'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'}), ({'cycle': 120, 'green': 29, 'volume': 647, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 495, 'delay_tenths': 392, 'los': 'D'}), ({'cycle': 120, 'green': 54, 'volume': 4200, 'sat_per_lane': 1900, 'lanes': 3}, {'vc_milli': 1637, 'delay_tenths': 330, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 120, 'green': 26, 'volume': 376, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 964, 'delay_tenths': 465, 'los': 'D'}), ({'cycle': 60, 'green': 33, 'volume': 1900, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 1016, 'delay_tenths': 135, 'los': 'F'}), ({'cycle': 140, 'green': 88, 'volume': 765, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 640, 'delay_tenths': 162, 'los': 'B'}), ({'cycle': 90, 'green': 60, 'volume': 1689, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1407, 'delay_tenths': 150, 'los': 'F'}), ({'cycle': 130, 'green': 69, 'volume': 1045, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1036, 'delay_tenths': 305, 'los': 'F'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 2309, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 641, 'delay_tenths': 58, 'los': 'A'}), ({'cycle': 130, 'green': 28, 'volume': 848, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 1093, 'delay_tenths': 510, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 15, 'volume': 386, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1218, 'delay_tenths': 375, 'los': 'F'}), ({'cycle': 100, 'green': 37, 'volume': 509, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 271, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 670, 'sat_per_lane': 1700, 'lanes': 1}, {'vc_milli': 1970, 'delay_tenths': 320, 'los': 'F'})], [({'cycle': 140, 'green': 41, 'volume': 539, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 511, 'delay_tenths': 412, 'los': 'D'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 80, 'green': 24, 'volume': 865, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1601, 'delay_tenths': 280, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 130, 'green': 95, 'volume': 3055, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1100, 'delay_tenths': 175, 'los': 'F'}), ({'cycle': 80, 'green': 41, 'volume': 5005, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 1808, 'delay_tenths': 195, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 47, 'volume': 1141, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 404, 'delay_tenths': 130, 'los': 'B'})], [({'cycle': 120, 'green': 62, 'volume': 674, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 224, 'los': 'C'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 34, 'volume': 2059, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1593, 'delay_tenths': 330, 'los': 'F'}), ({'cycle': 120, 'green': 51, 'volume': 1172, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1451, 'delay_tenths': 345, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 110, 'green': 46, 'volume': 726, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 510, 'delay_tenths': 237, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 1796, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 1760, 'delay_tenths': 320, 'los': 'F'})]]
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	`{'delay_tenths': 258, 'los': 'F', 'vc_milli': 1024}`	`{'delay_tenths': 245, 'los': 'F', 'vc_milli': 1024}`	Failed
timing oracle 1	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	Passed
timing oracle 2	`{'delay_tenths': 321, 'los': 'F', 'vc_milli': 1007}`	`{'delay_tenths': 320, 'los': 'F', 'vc_milli': 1007}`	Failed
timing oracle 3	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	Passed
timing oracle 4	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	Passed
timing oracle 5	`{'delay_tenths': 405, 'los': 'F', 'vc_milli': 1026}`	`{'delay_tenths': 400, 'los': 'F', 'vc_milli': 1026}`	Failed
timing oracle 6	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	Passed
timing oracle 7	`{'delay_tenths': 690, 'los': 'F', 'vc_milli': 1637}`	`{'delay_tenths': 330, 'los': 'F', 'vc_milli': 1637}`	Failed

SHA-256 / e6dfd371f45bcfbe437218c9eef904ab94ee505214dd94fac718449389980eaa

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    C, g = x['cycle'], x['green']
    lam = Fraction(g, C)
    cap = x['sat_per_lane'] * x['lanes'] * lam
    X = Fraction(x['volume']) / cap
    d = Fraction(1, 2) * C * (1 - lam) ** 2 / (1 - min(1, X * lam))
    tenths = int(d * 10 + Fraction(1, 2))
    if X > 1:
        los = 'F'
    else:
        los = 'F'
        for lim, lab in ((100, 'A'), (200, 'B'), (350, 'C'), (550, 'D'), (800, 'E')):
            if tenths <= lim:
                los = lab
                break
    return {'vc_milli': int(X * 1000), 'delay_tenths': tenths, 'los': los}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 150, 'green': 101, 'volume': 2622, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1024, 'delay_tenths': 245, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 90, 'green': 26, 'volume': 553, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1007, 'delay_tenths': 320, 'los': 'F'}), ({'cycle': 120, 'green': 86, 'volume': 1979, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 541, 'delay_tenths': 79, 'los': 'A'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'}), ({'cycle': 120, 'green': 29, 'volume': 647, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 495, 'delay_tenths': 392, 'los': 'D'}), ({'cycle': 120, 'green': 54, 'volume': 4200, 'sat_per_lane': 1900, 'lanes': 3}, {'vc_milli': 1637, 'delay_tenths': 330, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 120, 'green': 26, 'volume': 376, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 964, 'delay_tenths': 465, 'los': 'D'}), ({'cycle': 60, 'green': 33, 'volume': 1900, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 1016, 'delay_tenths': 135, 'los': 'F'}), ({'cycle': 140, 'green': 88, 'volume': 765, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 640, 'delay_tenths': 162, 'los': 'B'}), ({'cycle': 90, 'green': 60, 'volume': 1689, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1407, 'delay_tenths': 150, 'los': 'F'}), ({'cycle': 130, 'green': 69, 'volume': 1045, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1036, 'delay_tenths': 305, 'los': 'F'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 2309, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 641, 'delay_tenths': 58, 'los': 'A'}), ({'cycle': 130, 'green': 28, 'volume': 848, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 1093, 'delay_tenths': 510, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 15, 'volume': 386, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1218, 'delay_tenths': 375, 'los': 'F'}), ({'cycle': 100, 'green': 37, 'volume': 509, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 271, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 670, 'sat_per_lane': 1700, 'lanes': 1}, {'vc_milli': 1970, 'delay_tenths': 320, 'los': 'F'})], [({'cycle': 140, 'green': 41, 'volume': 539, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 511, 'delay_tenths': 412, 'los': 'D'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 80, 'green': 24, 'volume': 865, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1601, 'delay_tenths': 280, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 130, 'green': 95, 'volume': 3055, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1100, 'delay_tenths': 175, 'los': 'F'}), ({'cycle': 80, 'green': 41, 'volume': 5005, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 1808, 'delay_tenths': 195, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 47, 'volume': 1141, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 404, 'delay_tenths': 130, 'los': 'B'})], [({'cycle': 120, 'green': 62, 'volume': 674, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 224, 'los': 'C'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 34, 'volume': 2059, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1593, 'delay_tenths': 330, 'los': 'F'}), ({'cycle': 120, 'green': 51, 'volume': 1172, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1451, 'delay_tenths': 345, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 110, 'green': 46, 'volume': 726, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 510, 'delay_tenths': 237, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 1796, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 1760, 'delay_tenths': 320, 'los': 'F'})]]
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	`{'delay_tenths': 258, 'los': 'F', 'vc_milli': 1024}`	`{'delay_tenths': 245, 'los': 'F', 'vc_milli': 1024}`	Failed
timing oracle 1	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	Passed
timing oracle 2	`{'delay_tenths': 321, 'los': 'F', 'vc_milli': 1007}`	`{'delay_tenths': 320, 'los': 'F', 'vc_milli': 1007}`	Failed
timing oracle 3	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	Passed
timing oracle 4	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	Passed
timing oracle 5	`{'delay_tenths': 405, 'los': 'F', 'vc_milli': 1026}`	`{'delay_tenths': 400, 'los': 'F', 'vc_milli': 1026}`	Failed
timing oracle 6	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	Passed
timing oracle 7	`{'delay_tenths': 690, 'los': 'F', 'vc_milli': 1637}`	`{'delay_tenths': 330, 'los': 'F', 'vc_milli': 1637}`	Failed

SHA-256 / 2795d0cabfdefb75c324323d9ae4a24fc22eaf8bb3a0f9ff4e75b03fb0315434

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    C, g = x['cycle'], x['green']
    lam = Fraction(g, C)
    cap = x['sat_per_lane'] * x['lanes'] * lam
    X = Fraction(x['volume']) / cap
    d = Fraction(1, 2) * C * (1 - lam) ** 2 / (1 - min(1, X) * lam)
    tenths = int(d * 10 + Fraction(1, 2))
    if X > 1:
        los = 'F'
    else:
        los = 'F'
        for lim, lab in ((100, 'A'), (200, 'B'), (350, 'C'), (550, 'D'), (800, 'E')):
            if tenths <= lim:
                los = lab
                break
    return {'vc_milli': int(X * 1000), 'delay_tenths': tenths, 'los': los}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'cycle': 150, 'green': 101, 'volume': 2622, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1024, 'delay_tenths': 245, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 90, 'green': 26, 'volume': 553, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1007, 'delay_tenths': 320, 'los': 'F'}), ({'cycle': 120, 'green': 86, 'volume': 1979, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 541, 'delay_tenths': 79, 'los': 'A'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'}), ({'cycle': 120, 'green': 29, 'volume': 647, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 495, 'delay_tenths': 392, 'los': 'D'}), ({'cycle': 120, 'green': 54, 'volume': 4200, 'sat_per_lane': 1900, 'lanes': 3}, {'vc_milli': 1637, 'delay_tenths': 330, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 120, 'green': 26, 'volume': 376, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 964, 'delay_tenths': 465, 'los': 'D'}), ({'cycle': 60, 'green': 33, 'volume': 1900, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 1016, 'delay_tenths': 135, 'los': 'F'}), ({'cycle': 140, 'green': 88, 'volume': 765, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 640, 'delay_tenths': 162, 'los': 'B'}), ({'cycle': 90, 'green': 60, 'volume': 1689, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1407, 'delay_tenths': 150, 'los': 'F'}), ({'cycle': 130, 'green': 69, 'volume': 1045, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1036, 'delay_tenths': 305, 'los': 'F'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 120, 'green': 40, 'volume': 1300, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1026, 'delay_tenths': 400, 'los': 'F'})], [({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 2309, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 641, 'delay_tenths': 58, 'los': 'A'}), ({'cycle': 130, 'green': 28, 'volume': 848, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 1093, 'delay_tenths': 510, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 15, 'volume': 386, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1218, 'delay_tenths': 375, 'los': 'F'}), ({'cycle': 100, 'green': 37, 'volume': 509, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 271, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 670, 'sat_per_lane': 1700, 'lanes': 1}, {'vc_milli': 1970, 'delay_tenths': 320, 'los': 'F'})], [({'cycle': 140, 'green': 41, 'volume': 539, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 511, 'delay_tenths': 412, 'los': 'D'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 80, 'green': 24, 'volume': 865, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1601, 'delay_tenths': 280, 'los': 'F'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 130, 'green': 95, 'volume': 3055, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1100, 'delay_tenths': 175, 'los': 'F'}), ({'cycle': 80, 'green': 41, 'volume': 5005, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 1808, 'delay_tenths': 195, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 675, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 750, 'delay_tenths': 200, 'los': 'B'}), ({'cycle': 90, 'green': 47, 'volume': 1141, 'sat_per_lane': 1800, 'lanes': 3}, {'vc_milli': 404, 'delay_tenths': 130, 'los': 'B'})], [({'cycle': 120, 'green': 62, 'volume': 674, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 724, 'delay_tenths': 224, 'los': 'C'}), ({'cycle': 90, 'green': 30, 'volume': 700, 'sat_per_lane': 1800, 'lanes': 2}, {'vc_milli': 583, 'delay_tenths': 248, 'los': 'C'}), ({'cycle': 100, 'green': 34, 'volume': 2059, 'sat_per_lane': 1900, 'lanes': 2}, {'vc_milli': 1593, 'delay_tenths': 330, 'los': 'F'}), ({'cycle': 120, 'green': 51, 'volume': 1172, 'sat_per_lane': 1900, 'lanes': 1}, {'vc_milli': 1451, 'delay_tenths': 345, 'los': 'F'}), ({'cycle': 100, 'green': 50, 'volume': 900, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 1000, 'delay_tenths': 250, 'los': 'C'}), ({'cycle': 60, 'green': 40, 'volume': 800, 'sat_per_lane': 1800, 'lanes': 1}, {'vc_milli': 666, 'delay_tenths': 60, 'los': 'A'}), ({'cycle': 110, 'green': 46, 'volume': 726, 'sat_per_lane': 1700, 'lanes': 2}, {'vc_milli': 510, 'delay_tenths': 237, 'los': 'C'}), ({'cycle': 80, 'green': 16, 'volume': 1796, 'sat_per_lane': 1700, 'lanes': 3}, {'vc_milli': 1760, 'delay_tenths': 320, 'los': 'F'})]]
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	`{'delay_tenths': 245, 'los': 'F', 'vc_milli': 1024}`	`{'delay_tenths': 245, 'los': 'F', 'vc_milli': 1024}`	Passed
timing oracle 1	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	`{'delay_tenths': 248, 'los': 'C', 'vc_milli': 583}`	Passed
timing oracle 2	`{'delay_tenths': 320, 'los': 'F', 'vc_milli': 1007}`	`{'delay_tenths': 320, 'los': 'F', 'vc_milli': 1007}`	Passed
timing oracle 3	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	`{'delay_tenths': 79, 'los': 'A', 'vc_milli': 541}`	Passed
timing oracle 4	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	`{'delay_tenths': 250, 'los': 'C', 'vc_milli': 1000}`	Passed
timing oracle 5	`{'delay_tenths': 400, 'los': 'F', 'vc_milli': 1026}`	`{'delay_tenths': 400, 'los': 'F', 'vc_milli': 1026}`	Passed
timing oracle 6	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	`{'delay_tenths': 392, 'los': 'D', 'vc_milli': 495}`	Passed
timing oracle 7	`{'delay_tenths': 330, 'los': 'F', 'vc_milli': 1637}`	`{'delay_tenths': 330, 'los': 'F', 'vc_milli': 1637}`	Passed

SHA-256 / ccf05d6aaac4d4dcae5fc81b30fe81234f348e3c05fa8e97c40dd24eb7316479

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 2026-09-29T14:47:59.350214+00:00.

Case digest / facfb0c2eb1503ec1d5be99116e9acb6ad96b18b4f0c74d7030bfef45deed947