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Studien-Ergebnisse: Routing-Mechanismen × Adoption (MeshCore, Realdaten)

Erzeugt von study_sim.py. GEMESSEN (Realtopologie/Kalibrierung aus ../sim/data/) ist strikt getrennt von SIMULIERT (Flood-Routing-Modell + Mechanismen + Sweep, dieses Skript).

Topologie (GEMESSEN/abgeleitet, wie v3)

  • Aktiver Repeater-Subgraph: 814 Knoten (role=repeater, Geo, relay-aktiv/24h>0 ODER real als Pfad-Hop gesehen — reproduziert v3's ~831-Knoten-Subgraph).
  • Reichweiten-Linkgraph: 814 Knoten, 9275 Kanten; größte Komponente 776 Knoten / 9226 Kanten (hier wird simuliert).
  • Greedy-Relay-Menge (M4, CDS): 49 Knoten (6.3%).
  • Quervalidierung gegen beobachtete Kanten (topology_edges.json): 3459 beob. Kanten, 3306 zwischen aktiven Knoten, davon 1380 (41.7%) vom geometrischen Reichweitenmodell reproduziert.
  • Reale Detour-Median-Referenz (GEMESSEN): 2.11×.

Modellannahmen (SIMULIERT) — ehrlich getrennt von der Messung

  • Flood timing-getrieben (PQ nach Ankunftszeit), Stock-Knoten: first-packet-wins + Zufalls-Jitter. Airtime = Anzahl tatsächlich sendender Knoten je zugestellter Nachricht.
  • Link-Stochastik: eine Aussendung erreicht Nachbar v mit P=Reliability des Links (Monte-Carlo über Seed). Reliability des genutzten Pfads = Produkt der Link-Reliabilities.
  • Mechanismen sind lokale Regeln der Neu-Firmware-Knoten; Stock-Knoten fluten unverändert (eingebautes Sicherheitsnetz).

  • Baseline (M0, α=0): Lieferquote 0.930, Airtime 751.2 Sende-Ereignisse/Zustellung, Detour-Median 1.11.

  • Konfiguration: 5 Seeds, 120 Paare/Seed, MC=1; Laufzeit 763.5s.

Safety-Invariante

Für jeden (Mechanismus, α): Lieferquote ≥ Baseline UND Airtime ≤ Baseline. Verletzung ⇒ Mechanismus bei diesem α disqualifiziert.

Monte-Carlo-Rausch-Band: Mechanismen, die keine Sender unterdrücken (M1/M5/M7-hoch), haben dieselbe wahre Airtime/Lieferquote wie die Baseline; gemessene Mini-Abweichungen sind reines Sampling-Rauschen (je α/Seed andere RNG-Ziehungen). Als Verletzung gilt nur ein Unterschreiten außerhalb von ±2·Standardfehler der Baseline bzw. einer absoluten Mindesttoleranz (Lieferquote ±0.024, Airtime ±6.2 = 0.82%). Die Spalte Safety nutzt dieses Band; streng = ohne Band.

Ergebnis-Tabellen je Mechanismus (Rollout: Top-Traffic)

M0

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.01 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.05 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.1 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.25 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.5 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅

M1

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.935 +0.005 752.8 +0.2% 1.11 1.00 ✅
0.01 0.935 +0.005 752.1 +0.1% 1.12 1.00 ✅
0.05 0.938 +0.008 753.6 +0.3% 1.14 1.00 ✅
0.1 0.940 +0.010 753.9 +0.4% 1.12 1.00 ✅
0.25 0.933 +0.003 752.0 +0.1% 1.10 1.00 ✅
0.5 0.948 +0.018 753.9 +0.4% 1.00 1.00 ✅
1.0 0.940 +0.010 753.4 +0.3% 1.00 1.00 ✅

M2k2

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.947 +0.017 749.7 -0.2% 1.11 1.00 ✅
0.01 0.945 +0.015 746.4 -0.6% 1.12 1.00 ✅
0.05 0.933 +0.003 716.2 -4.7% 1.14 1.00 ✅
0.1 0.932 +0.002 676.3 -10.0% 1.14 1.00 ✅
0.25 0.898 -0.032 567.5 -24.5% 1.17 1.00 ❌ VERLETZT
0.5 0.867 -0.063 389.6 -48.1% 1.22 1.00 ❌ VERLETZT
1.0 0.795 -0.135 115.2 -84.7% 1.50 1.00 ❌ VERLETZT

M2k3

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.935 +0.005 749.3 -0.3% 1.12 1.00 ✅
0.01 0.940 +0.010 744.7 -0.9% 1.12 1.00 ✅
0.05 0.927 -0.003 714.9 -4.8% 1.12 1.00 ✅
0.1 0.927 -0.003 680.4 -9.4% 1.14 1.00 ✅
0.25 0.910 -0.020 577.7 -23.1% 1.14 1.00 ✅
0.5 0.895 -0.035 419.1 -44.2% 1.20 1.00 ❌ VERLETZT
1.0 0.867 -0.063 169.3 -77.5% 1.25 1.00 ❌ VERLETZT

M3

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.942 +0.012 750.2 -0.1% 1.12 1.00 ✅
0.01 0.932 +0.002 748.0 -0.4% 1.14 1.00 ✅
0.05 0.948 +0.018 723.4 -3.7% 1.13 1.00 ✅
0.1 0.943 +0.013 692.1 -7.9% 1.14 1.00 ✅
0.25 0.913 -0.017 609.0 -18.9% 1.14 1.00 ✅
0.5 0.897 -0.033 476.3 -36.6% 1.14 1.00 ❌ VERLETZT
1.0 0.738 -0.192 249.2 -66.8% 1.17 1.00 ❌ VERLETZT

M4

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.01 0.938 +0.008 743.6 -1.0% 1.12 1.00 ✅
0.05 0.932 +0.002 714.8 -4.8% 1.14 1.00 ✅
0.1 0.930 +0.000 677.1 -9.9% 1.12 1.00 ✅
0.25 0.850 -0.080 530.5 -29.4% 1.17 1.00 ❌ VERLETZT
0.5 0.738 -0.192 326.6 -56.5% 1.25 1.00 ❌ VERLETZT
1.0 0.068 -0.862 3.9 -99.5% 1.00 1.00 ❌ VERLETZT

M5

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.01 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.05 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.1 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.25 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.5 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅

M7_12

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.927 -0.003 752.0 +0.1% 1.12 1.00 ✅
0.01 0.950 +0.020 753.6 +0.3% 1.12 1.00 ✅
0.05 0.928 -0.002 746.1 -0.7% 1.12 1.00 ✅
0.1 0.938 +0.008 742.6 -1.1% 1.11 1.00 ✅
0.25 0.913 -0.017 719.2 -4.3% 1.12 1.00 ✅
0.5 0.910 -0.020 702.1 -6.5% 1.12 1.00 ✅
1.0 0.863 -0.067 669.5 -10.9% 1.12 1.00 ❌ VERLETZT

M7_15

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.952 +0.022 752.9 +0.2% 1.12 1.00 ✅
0.01 0.943 +0.013 752.4 +0.2% 1.12 1.00 ✅
0.05 0.940 +0.010 752.8 +0.2% 1.12 1.00 ✅
0.1 0.952 +0.022 749.8 -0.2% 1.12 1.00 ✅
0.25 0.943 +0.013 743.1 -1.1% 1.11 1.00 ✅
0.5 0.923 -0.007 736.3 -2.0% 1.12 1.00 ✅
1.0 0.910 -0.020 723.9 -3.6% 1.12 1.00 ✅

COMBI

α Lieferquote ΔDeliv Airtime ΔAirtime% Detour med Routen-Stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1node 0.927 -0.003 753.5 +0.3% 1.00 1.00 ✅
0.01 0.940 +0.010 747.0 -0.6% 1.00 1.00 ✅
0.05 0.932 +0.002 722.8 -3.8% 1.08 1.00 ✅
0.1 0.943 +0.013 687.9 -8.4% 1.00 1.00 ✅
0.25 0.888 -0.042 587.0 -21.9% 1.11 1.00 ❌ VERLETZT
0.5 0.887 -0.043 445.7 -40.7% 1.12 1.00 ❌ VERLETZT
1.0 0.683 -0.247 223.0 -70.3% 1.12 1.00 ❌ VERLETZT

Safety-Befund (alle Rollouts)

Folgende (Mechanismus, α, Rollout) verletzen die Invariante:

Mechanismus α Rollout Lieferquote (Base 0.930) Airtime (Base 751.2) Grund
M2k2 0.5 random 0.832 384.3 Lieferquote<Baseline
M2k2 1.0 random 0.795 115.2 Lieferquote<Baseline
M2k2 0.25 top_traffic 0.898 567.5 Lieferquote<Baseline
M2k2 0.5 top_traffic 0.867 389.6 Lieferquote<Baseline
M2k2 1.0 top_traffic 0.795 115.2 Lieferquote<Baseline
M2k3 0.5 random 0.872 417.4 Lieferquote<Baseline
M2k3 1.0 random 0.867 169.3 Lieferquote<Baseline
M2k3 0.5 top_traffic 0.895 419.1 Lieferquote<Baseline
M2k3 1.0 top_traffic 0.867 169.3 Lieferquote<Baseline
M3 0.5 random 0.880 465.5 Lieferquote<Baseline
M3 1.0 random 0.738 249.2 Lieferquote<Baseline
M3 0.5 top_traffic 0.897 476.3 Lieferquote<Baseline
M3 1.0 top_traffic 0.738 249.2 Lieferquote<Baseline
M4 0.05 random 0.898 710.5 Lieferquote<Baseline
M4 0.1 random 0.900 668.0 Lieferquote<Baseline
M4 0.25 random 0.880 558.0 Lieferquote<Baseline
M4 0.5 random 0.817 370.2 Lieferquote<Baseline
M4 1.0 random 0.068 3.9 Lieferquote<Baseline
M4 0.25 top_traffic 0.850 530.5 Lieferquote<Baseline
M4 0.5 top_traffic 0.738 326.6 Lieferquote<Baseline
M4 1.0 top_traffic 0.068 3.9 Lieferquote<Baseline
M7_12 1.0 random 0.863 669.5 Lieferquote<Baseline
M7_12 1.0 top_traffic 0.863 669.5 Lieferquote<Baseline
COMBI 0.1 random 0.898 681.0 Lieferquote<Baseline
COMBI 0.5 random 0.867 450.3 Lieferquote<Baseline
COMBI 1.0 random 0.683 223.0 Lieferquote<Baseline
COMBI 0.25 top_traffic 0.888 587.0 Lieferquote<Baseline
COMBI 0.5 top_traffic 0.887 445.7 Lieferquote<Baseline
COMBI 1.0 top_traffic 0.683 223.0 Lieferquote<Baseline

Ranking (Airtime-Gewinn bei gehaltener Lieferquote, α=1.0 Top-Traffic)

Rang Mechanismus ΔAirtime% @α=1.0 Lieferquote Safe@1.0 Detour med
1 M4 -99.5% 0.068 ❌ 1.00
2 M2k2 -84.7% 0.795 ❌ 1.50
3 M2k3 -77.5% 0.867 ❌ 1.25
4 COMBI -70.3% 0.683 ❌ 1.12
5 M3 -66.8% 0.738 ❌ 1.17
6 M7_12 -10.9% 0.863 ❌ 1.12
7 M7_15 -3.6% 0.910 ✅ 1.12
8 M5 +0.0% 0.930 ✅ 1.00
9 M1 +0.3% 0.940 ✅ 1.00

Adoptionsschwelle (erstes α mit ≥2% Airtime-Senkung & safe, Top-Traffic)

Mechanismus Schwelle α ΔAirtime% dort
M1 — (keine ≥2%-Senkung) —
M2k2 0.05 -4.7%
M2k3 0.05 -4.8%
M3 0.05 -3.7%
M4 0.05 -4.8%
M5 — (keine ≥2%-Senkung) —
M7_12 0.25 -4.3%
M7_15 1.0 -3.6%
COMBI 0.05 -3.8%

Kombi M3+M5+M7 (COMBI)

  • α=1node: Lieferquote 0.927 (-0.003), Airtime 753.5 (+0.3%), Detour-Median 1.00, Safety OK.
  • α=0.1: Lieferquote 0.943 (+0.013), Airtime 687.9 (-8.4%), Detour-Median 1.00, Safety OK.
  • α=0.25: Lieferquote 0.888 (-0.042), Airtime 587.0 (-21.9%), Detour-Median 1.11, Safety VERLETZT.
  • α=1.0: Lieferquote 0.683 (-0.247), Airtime 223.0 (-70.3%), Detour-Median 1.12, Safety VERLETZT.

Stress-Befund

Churn (20% instabile Knoten nach advert_count) & Linkausfall (α=1.0)

Mechanismus Szenario Lieferquote Airtime Routen-Stab.
M0 linkfail_10 0.907 742.4 1.00
M0 linkfail_20 0.908 740.6 1.00
M0 churn_20 0.874 574.0 1.00
M3 linkfail_10 0.775 255.3 1.00
M3 linkfail_20 0.787 259.4 1.00
M3 churn_20 0.719 210.9 1.00
M4 linkfail_10 0.057 3.7 1.00
M4 linkfail_20 0.048 3.0 1.00
M4 churn_20 0.060 3.3 1.00
M7_12 linkfail_10 0.850 666.6 1.00
M7_12 linkfail_20 0.838 658.2 1.00
M7_12 churn_20 0.843 530.0 1.00
COMBI linkfail_10 0.718 227.6 1.00
COMBI linkfail_20 0.723 235.1 1.00
COMBI churn_20 0.622 185.8 1.00

M6 (passives Topologie-Lernen + Feasible-Successor): eingesparte Re-Discovery-Airtime bei Linkausfall

Szenario gebrochene Paare Baseline-Reflood Ø eingespart % lokale Backup-Recovery
m6_linkfail_10 152 671.0 94% 0.88
m6_linkfail_20 224 687.9 96% 0.92

Limitierungen (ehrlich)

  • Linkmodell ist geometrisch (Log-Distance + PLE-Floor 2.0); reales Gelände/Antennenhöhe nicht abgebildet. Der reale SNR/Distanz-Zusammenhang ist schwach (|corr|≈0.42), darum ist Hop-Zahl der verlässlichere Hebel — das Modell respektiert das, ist aber eine bewusste Vereinfachung.
  • Quervalidierung gegen beobachtete Kanten ist nur teilweise deckend: das geometrische Modell und die beobachtete Flood-Stichprobe überlappen nur begrenzt (siehe Topologie-Abschnitt). Absolute Airtime-Zahlen sind daher modellabhängig; die relativen Mechanismus-Vergleiche sind robuster.
  • Timing-Jitter/Backoff-Fenster sind modelliert, nicht aus Hardware gemessen. M1/M3 hängen vom Timing-Modell ab.
  • M2 (counter-based) hört Kopien im selben diskreten Flood; ein reales kontinuierliches Backoff-Fenster ist gröber approximiert.
  • M5 ändert nur den gecachten Pfad (Detour), nicht die Flood-Airtime — so modelliert und so berichtet.
  • M6 ist als Airtime-Einsparungs-Modell (Backup statt Reflood) gerechnet, nicht als vollständige DV-Protokoll-Simulation.
  • Stichprobengröße: 5 Seeds × 120 Paare; Konfidenzintervalle nicht ausgewiesen.

🇬🇧 English Translation

Study Results: Routing Mechanisms × Adoption (MeshCore, Real-World Data)

Generated by study_sim.py. MEASURED (real topology/calibration from ../sim/data/) is strictly separated from SIMULATED (flood-routing model + mechanisms + sweep, this script).

Topology (MEASURED/derived, as in v3)

  • Active repeater subgraph: 814 nodes (role=repeater, Geo, relay-active/24h>0 OR actually seen as a path hop — reproduces v3's ~831-node subgraph).
  • Range link graph: 814 nodes, 9275 edges; largest component 776 nodes / 9226 edges (this is where simulation runs).
  • Greedy relay set (M4, CDS): 49 nodes (6.3%).
  • Cross-validation against observed edges (topology_edges.json): 3459 observed edges, 3306 between active nodes, of which 1380 (41.7%) reproduced by the geometric range model.
  • Real detour median reference (MEASURED): 2.11×.

Model Assumptions (SIMULATED) — honestly separated from measurement

  • Flood timing-driven (PQ by arrival time), stock nodes: first-packet-wins + random jitter. Airtime = number of actually transmitting nodes per delivered message.
  • Link stochastics: one transmission reaches neighbor v with P=link reliability (Monte-Carlo over seed). Reliability of the used path = product of link reliabilities.
  • Mechanisms are local rules of new-firmware nodes; stock nodes flood unchanged (built-in safety net).

  • Baseline (M0, α=0): Delivery rate 0.930, Airtime 751.2 transmission events/delivery, Detour median 1.11.

  • Configuration: 5 seeds, 120 pairs/seed, MC=1; runtime 763.5s.

Safety Invariant

For every (mechanism, α): Delivery rate ≥ Baseline AND Airtime ≤ Baseline. Violation ⇒ mechanism disqualified at this α.

Monte-Carlo noise band: Mechanisms that do not suppress any senders (M1/M5/M7-high) have the same true airtime/delivery rate as the baseline; measured micro-deviations are pure sampling noise (different RNG draws per α/seed). A violation is only counted when falling outside ±2·standard error of the baseline or an absolute minimum tolerance (delivery rate ±0.024, airtime ±6.2 = 0.82%). The Safety column uses this band; strict = without band.

Result Tables per Mechanism (Rollout: Top-Traffic)

M0

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.01 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.05 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.1 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.25 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.5 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅

M1

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.935 +0.005 752.8 +0.2% 1.11 1.00 ✅
0.01 0.935 +0.005 752.1 +0.1% 1.12 1.00 ✅
0.05 0.938 +0.008 753.6 +0.3% 1.14 1.00 ✅
0.1 0.940 +0.010 753.9 +0.4% 1.12 1.00 ✅
0.25 0.933 +0.003 752.0 +0.1% 1.10 1.00 ✅
0.5 0.948 +0.018 753.9 +0.4% 1.00 1.00 ✅
1.0 0.940 +0.010 753.4 +0.3% 1.00 1.00 ✅

M2k2

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.947 +0.017 749.7 -0.2% 1.11 1.00 ✅
0.01 0.945 +0.015 746.4 -0.6% 1.12 1.00 ✅
0.05 0.933 +0.003 716.2 -4.7% 1.14 1.00 ✅
0.1 0.932 +0.002 676.3 -10.0% 1.14 1.00 ✅
0.25 0.898 -0.032 567.5 -24.5% 1.17 1.00 ❌ VIOLATED
0.5 0.867 -0.063 389.6 -48.1% 1.22 1.00 ❌ VIOLATED
1.0 0.795 -0.135 115.2 -84.7% 1.50 1.00 ❌ VIOLATED

M2k3

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.935 +0.005 749.3 -0.3% 1.12 1.00 ✅
0.01 0.940 +0.010 744.7 -0.9% 1.12 1.00 ✅
0.05 0.927 -0.003 714.9 -4.8% 1.12 1.00 ✅
0.1 0.927 -0.003 680.4 -9.4% 1.14 1.00 ✅
0.25 0.910 -0.020 577.7 -23.1% 1.14 1.00 ✅
0.5 0.895 -0.035 419.1 -44.2% 1.20 1.00 ❌ VIOLATED
1.0 0.867 -0.063 169.3 -77.5% 1.25 1.00 ❌ VIOLATED

M3

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.942 +0.012 750.2 -0.1% 1.12 1.00 ✅
0.01 0.932 +0.002 748.0 -0.4% 1.14 1.00 ✅
0.05 0.948 +0.018 723.4 -3.7% 1.13 1.00 ✅
0.1 0.943 +0.013 692.1 -7.9% 1.14 1.00 ✅
0.25 0.913 -0.017 609.0 -18.9% 1.14 1.00 ✅
0.5 0.897 -0.033 476.3 -36.6% 1.14 1.00 ❌ VIOLATED
1.0 0.738 -0.192 249.2 -66.8% 1.17 1.00 ❌ VIOLATED

M4

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
0.01 0.938 +0.008 743.6 -1.0% 1.12 1.00 ✅
0.05 0.932 +0.002 714.8 -4.8% 1.14 1.00 ✅
0.1 0.930 +0.000 677.1 -9.9% 1.12 1.00 ✅
0.25 0.850 -0.080 530.5 -29.4% 1.17 1.00 ❌ VIOLATED
0.5 0.738 -0.192 326.6 -56.5% 1.25 1.00 ❌ VIOLATED
1.0 0.068 -0.862 3.9 -99.5% 1.00 1.00 ❌ VIOLATED

M5

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1node 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.01 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.05 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.1 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.25 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
0.5 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅

M7_12

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.927 -0.003 752.0 +0.1% 1.12 1.00 ✅
0.01 0.950 +0.020 753.6 +0.3% 1.12 1.00 ✅
0.05 0.928 -0.002 746.1 -0.7% 1.12 1.00 ✅
0.1 0.938 +0.008 742.6 -1.1% 1.11 1.00 ✅
0.25 0.913 -0.017 719.2 -4.3% 1.12 1.00 ✅
0.5 0.910 -0.020 702.1 -6.5% 1.12 1.00 ✅
1.0 0.863 -0.067 669.5 -10.9% 1.12 1.00 ❌ VIOLATED

M7_15

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.11 1.00 ✅
1node 0.952 +0.022 752.9 +0.2% 1.12 1.00 ✅
0.01 0.943 +0.013 752.4 +0.2% 1.12 1.00 ✅
0.05 0.940 +0.010 752.8 +0.2% 1.12 1.00 ✅
0.1 0.952 +0.022 749.8 -0.2% 1.12 1.00 ✅
0.25 0.943 +0.013 743.1 -1.1% 1.11 1.00 ✅
0.5 0.923 -0.007 736.3 -2.0% 1.12 1.00 ✅
1.0 0.910 -0.020 723.9 -3.6% 1.12 1.00 ✅

COMBI

α Delivery rate ΔDeliv Airtime ΔAirtime% Detour med Route stab. Safety
0.0 0.930 +0.000 751.2 +0.0% 1.00 1.00 ✅
1node 0.927 -0.003 753.5 +0.3% 1.00 1.00 ✅
0.01 0.940 +0.010 747.0 -0.6% 1.00 1.00 ✅
0.05 0.932 +0.002 722.8 -3.8% 1.08 1.00 ✅
0.1 0.943 +0.013 687.9 -8.4% 1.00 1.00 ✅
0.25 0.888 -0.042 587.0 -21.9% 1.11 1.00 ❌ VIOLATED
0.5 0.887 -0.043 445.7 -40.7% 1.12 1.00 ❌ VIOLATED
1.0 0.683 -0.247 223.0 -70.3% 1.12 1.00 ❌ VIOLATED

Safety Findings (all rollouts)

The following (mechanism, α, rollout) combinations violate the invariant:

Mechanism α Rollout Delivery rate (Base 0.930) Airtime (Base 751.2) Reason
M2k2 0.5 random 0.832 384.3 Delivery rate<Baseline
M2k2 1.0 random 0.795 115.2 Delivery rate<Baseline
M2k2 0.25 top_traffic 0.898 567.5 Delivery rate<Baseline
M2k2 0.5 top_traffic 0.867 389.6 Delivery rate<Baseline
M2k2 1.0 top_traffic 0.795 115.2 Delivery rate<Baseline
M2k3 0.5 random 0.872 417.4 Delivery rate<Baseline
M2k3 1.0 random 0.867 169.3 Delivery rate<Baseline
M2k3 0.5 top_traffic 0.895 419.1 Delivery rate<Baseline
M2k3 1.0 top_traffic 0.867 169.3 Delivery rate<Baseline
M3 0.5 random 0.880 465.5 Delivery rate<Baseline
M3 1.0 random 0.738 249.2 Delivery rate<Baseline
M3 0.5 top_traffic 0.897 476.3 Delivery rate<Baseline
M3 1.0 top_traffic 0.738 249.2 Delivery rate<Baseline
M4 0.05 random 0.898 710.5 Delivery rate<Baseline
M4 0.1 random 0.900 668.0 Delivery rate<Baseline
M4 0.25 random 0.880 558.0 Delivery rate<Baseline
M4 0.5 random 0.817 370.2 Delivery rate<Baseline
M4 1.0 random 0.068 3.9 Delivery rate<Baseline
M4 0.25 top_traffic 0.850 530.5 Delivery rate<Baseline
M4 0.5 top_traffic 0.738 326.6 Delivery rate<Baseline
M4 1.0 top_traffic 0.068 3.9 Delivery rate<Baseline
M7_12 1.0 random 0.863 669.5 Delivery rate<Baseline
M7_12 1.0 top_traffic 0.863 669.5 Delivery rate<Baseline
COMBI 0.1 random 0.898 681.0 Delivery rate<Baseline
COMBI 0.5 random 0.867 450.3 Delivery rate<Baseline
COMBI 1.0 random 0.683 223.0 Delivery rate<Baseline
COMBI 0.25 top_traffic 0.888 587.0 Delivery rate<Baseline
COMBI 0.5 top_traffic 0.887 445.7 Delivery rate<Baseline
COMBI 1.0 top_traffic 0.683 223.0 Delivery rate<Baseline

Ranking (Airtime gain while maintaining delivery rate, α=1.0 top-traffic)

Rank Mechanism ΔAirtime% @α=1.0 Delivery rate Safe@1.0 Detour med
1 M4 -99.5% 0.068 ❌ 1.00
2 M2k2 -84.7% 0.795 ❌ 1.50
3 M2k3 -77.5% 0.867 ❌ 1.25
4 COMBI -70.3% 0.683 ❌ 1.12
5 M3 -66.8% 0.738 ❌ 1.17
6 M7_12 -10.9% 0.863 ❌ 1.12
7 M7_15 -3.6% 0.910 ✅ 1.12
8 M5 +0.0% 0.930 ✅ 1.00
9 M1 +0.3% 0.940 ✅ 1.00

Adoption Threshold (first α with ≥2% airtime reduction & safe, top-traffic)

Mechanism Threshold α ΔAirtime% there
M1 — (no ≥2% reduction) —
M2k2 0.05 -4.7%
M2k3 0.05 -4.8%
M3 0.05 -3.7%
M4 0.05 -4.8%
M5 — (no ≥2% reduction) —
M7_12 0.25 -4.3%
M7_15 1.0 -3.6%
COMBI 0.05 -3.8%

Combo M3+M5+M7 (COMBI)

  • α=1node: Delivery rate 0.927 (-0.003), Airtime 753.5 (+0.3%), Detour median 1.00, Safety OK.
  • α=0.1: Delivery rate 0.943 (+0.013), Airtime 687.9 (-8.4%), Detour median 1.00, Safety OK.
  • α=0.25: Delivery rate 0.888 (-0.042), Airtime 587.0 (-21.9%), Detour median 1.11, Safety VIOLATED.
  • α=1.0: Delivery rate 0.683 (-0.247), Airtime 223.0 (-70.3%), Detour median 1.12, Safety VIOLATED.

Stress Findings

Mechanism Scenario Delivery rate Airtime Route stab.
M0 linkfail_10 0.907 742.4 1.00
M0 linkfail_20 0.908 740.6 1.00
M0 churn_20 0.874 574.0 1.00
M3 linkfail_10 0.775 255.3 1.00
M3 linkfail_20 0.787 259.4 1.00
M3 churn_20 0.719 210.9 1.00
M4 linkfail_10 0.057 3.7 1.00
M4 linkfail_20 0.048 3.0 1.00
M4 churn_20 0.060 3.3 1.00
M7_12 linkfail_10 0.850 666.6 1.00
M7_12 linkfail_20 0.838 658.2 1.00
M7_12 churn_20 0.843 530.0 1.00
COMBI linkfail_10 0.718 227.6 1.00
COMBI linkfail_20 0.723 235.1 1.00
COMBI churn_20 0.622 185.8 1.00
Scenario broken pairs Baseline reflood avg saved % local backup recovery
m6_linkfail_10 152 671.0 94% 0.88
m6_linkfail_20 224 687.9 96% 0.92

Limitations (honest)

  • Link model is geometric (log-distance + PLE floor 2.0); real terrain/antenna height not modeled. The real SNR/distance relationship is weak (|corr|≈0.42), so hop count is the more reliable lever — the model respects this, but it is a deliberate simplification.
  • Cross-validation against observed edges is only partially covering: the geometric model and the observed flood sample overlap only to a limited extent (see topology section). Absolute airtime numbers are therefore model-dependent; the relative mechanism comparisons are more robust.
  • Timing jitter/backoff windows are modeled, not measured from hardware. M1/M3 depend on the timing model.
  • M2 (counter-based) hears copies in the same discrete flood; a real continuous backoff window is more coarsely approximated.
  • M5 only changes the cached path (detour), not the flood airtime — modeled and reported as such.
  • M6 is computed as an airtime-savings model (backup instead of reflood), not as a full DV-protocol simulation.
  • Sample size: 5 seeds × 120 pairs; confidence intervals not reported.