File size: 3,250 Bytes
c383c28 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 | #!/usr/bin/env python3
"""Does agreement between n0 and the fitted midpoint depend on fixed service times?
Additive reference condition with type-specific service times that share the
published MEANS but differ in variance: fixed (as published), exponential
(coefficient of variation 1), and lognormal with coefficient of variation 2.
The mean-based balance index n0 is identical across rows; a median-based index
is shown only to illustrate why the median is the wrong estimand for offered
load. Synthetic constructions only.
"""
from __future__ import annotations
import json, math
from pathlib import Path
import numpy as np
import capacity_simulation as S
SESSIONS = 500
DISTS = {"fixed": 0.0, "exponential": 1.0, "lognormal_cv2": 2.0}
def draw_cost(rng, mean, dist):
if dist == "fixed":
return mean
if dist == "exponential":
return float(rng.exponential(mean))
cv = DISTS[dist]; s2 = math.log(1 + cv * cv)
return float(rng.lognormal(math.log(mean) - s2 / 2, math.sqrt(s2)))
def session(rng, n, dist):
events = []
for minute in range(S.DURATION_MIN):
for agent in range(n):
for _ in range(rng.poisson(S.LAMBDA)):
k = int(rng.choice(3, p=S.TYPE_PROBS))
events.append((minute + rng.random(), agent, k, draw_cost(rng, S.TYPE_COSTS[k], dist)))
if not events:
return np.nan
events.sort(key=lambda e: e[0])
available, correct = 0.0, 0
for arrival, _, k, cost in events:
completion = max(arrival, available) + cost / S.BUDGET
ok = completion - arrival <= S.TYPE_DEADLINES[k]
correct += int(rng.random() < (0.95 if ok else 0.15))
available = completion
return correct / len(events)
def median_factor(dist):
if dist == "fixed": return 1.0
if dist == "exponential": return math.log(2)
return 1 / math.sqrt(1 + DISTS[dist] ** 2) # lognormal median / mean
def main():
n0 = S.BUDGET / (S.LAMBDA * float(S.TYPE_PROBS @ S.TYPE_COSTS))
out = {"n0_mean_based": n0}
for i, dist in enumerate(DISTS):
rng = np.random.default_rng(S.SEED + 100 + i)
values, means = {}, []
for n in S.TEAM_SIZES.astype(int):
sc = np.array([session(rng, n, dist) for _ in range(SESSIONS)]); sc = sc[np.isfinite(sc)]
values[n] = sc; means.append(float(sc.mean()))
theta = S.fit_curve(S.TEAM_SIZES, np.array(means))
lo, hi = S.bootstrap_midpoint(rng, values)
out[dist] = {"cv": DISTS[dist], "midpoint": float(theta[2]), "midpoint_ci": [float(lo), float(hi)],
"tau": float(theta[3]), "gap_to_n0": float(theta[2] - n0),
"n0_if_median_used": n0 / median_factor(dist)}
Path("service_variance.json").write_text(json.dumps(out, indent=2) + "\n")
print(f"mean-based n0 = {n0:.2f} in every row")
print(f"{'service times':15}{'CV':>5}{'fitted n_mid':>22}{'tau':>7}{'gap':>8}{'n0 from median':>16}")
for d in DISTS:
r = out[d]
print(f"{d:15}{r['cv']:>5.0f}{r['midpoint']:>9.2f} [{r['midpoint_ci'][0]:.2f},{r['midpoint_ci'][1]:.2f}]"
f"{r['tau']:>7.2f}{r['gap_to_n0']:>+8.2f}{r['n0_if_median_used']:>16.2f}")
if __name__ == "__main__":
main()
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