27-EFT.WP.Packets.Light v1.0 | Appendix D — Metrics & Drift Measures (Packets.Light)

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Appendix D — Metrics & Drift Measures (Packets.Light)

One-sentence goal: Define a unified metric family and drift measures for the entire optical-packet chain—physics / framing / modulation / labeling / compensation / FSO / arrival time / switching & queueing / metrology / multipath / security / runtime—including conventions, dimensions, windowing, and thresholds, and close the loop with manifests and contracts.

I. Scope & Objects

• Objects: per-domain key metrics for manifest.packet.*:
  delta_form_*, OSNR / Q / EVM / BER, CD_res / PMD_res / NL_res, A_atm / L_point / σ_I^2 / Avail, T_arr*, lat_*, P_block / P_cont, MER / MP_res, E_balance / D_spec / Pol_anom / Timing_anom, runtime hit / stale / ρ / latency.
• Inputs: windowed data (time / frequency / set domains), a reference baseline ref@ts0 or golden path, RefCond, mask B and bandwidth RBW.
• Outputs: metrics.packet.* metric objects, drift.* decomposition & aggregation, C60-* contract annotations with evidence_uri.
• Constraints: all metrics declare unit(field) and dim(field) and pass check_dim( y − f(x) ); dual-form metrics must be replayable.

II. Terms & Variables

• Time & window: W = [ ts − Δt, ts ], monotone clock tau_mono, overlap O = 1 − H / W.
• Statistics & quantiles: p{q} denotes quantiles (e.g., p95); EWMA_α(z) is an exponential moving average.
• Reference baselines: x_ref, S_ref(f), T_arr_ref, OSNR_ref / EVM_ref, lat_ref, etc.
• Dimensional examples: unit(latency) = "s", unit(OSNR_dB) = "dB", unit(EVM) = 1, unit(T_arr) = "s".

III. Postulates P60D-*

• P60D-1 (Dual forms coexist): every core metric includes configured/analytic and measured/realized forms and records delta_form_*.
• P60D-2 (Explicit measures): frequency ( ∫_{f∈B} • df ), time ( ∫_{t∈W} • dt ), and set ( ∑_{pkt∈S} • ) domains and measures are explicit.
• P60D-3 (Dimensions & conversions): all log↔linear conversions are written as scale.note; every field passes check_dim.
• P60D-4 (Attributable drift): overall drift must be decomposable into physics / framing / modulation / labeling / compensation / FSO / arrival time / switching & queueing / metrology / multipath / security / runtime components.

IV. Minimal Equations S60D-*

1. Dual-form consistency
   • S60D-01: delta_form_phys = | T_arr^{form1} − T_arr^{form2} |;
     delta_form_mod = | EVM_pred − EVM_meas | or | BER_pred − BER_meas |.
   • S60D-02: delta_form_swrt = w_b | P_block^{cfg} − P_block^{meas} | + w_c | P_cont^{cfg} − P_cont^{meas} | + w_l | lat^{cfg} − lat^{meas} |.
   • S60D-03: delta_form_queue = | lat_total^{cfg} − lat_total^{meas} |.
   • S60D-04: delta_form_rt = | metric^{cfg}(W) − metric^{meas}(W) | (runtime).
2. Physics & compensation
   • S60D-11: OSNR_drift = OSNR_dB(W) − OSNR_dB(ref);
   • S60D-12: CD_res = | D_est − D_target |; PMD_res = τ̂_DGD; NL_res = EVM_after − EVM_linear;
   • S60D-13: tilt error ε_tilt = max_f | | H_link(f) | − \bar H | / \bar H |.
3. Framing & timebase
   • S60D-21: delta_form_frame = | t̂_cnt − t̂_cont |;
   • S60D-22: jitter σ_J = std( J(W) ); skew_ppm = 10^6 • skew;
   • S60D-23: alignment error e_align = τ* mod T_f.
4. Modulation & spectrum
   • S60D-31: EVM_rms = sqrt( ∑| e_k |^2 / ∑| s*_k |^2 );
   • S60D-32: ACLR = 10 log10( P_adj / P_main ), OBB = ∫_{f∉B} |X|^2 df / ∫_{f∈B} |X|^2 df;
   • S60D-33: PAPR = max( | x_n |^2 ) / E( | x_n |^2 ).
5. WDM / SDM / subcarriers
   • S60D-41: Iso_link = min_m Iso_m − Σ_margin (dB); XT_pwr (dB).
   • S60D-42: spectral efficiency SE = R_net / B_eff;
   • S60D-43: delta_form_label = w_1 | ACLR_cfg − ACLR_meas | + w_2 | OBB_cfg − OBB_meas | + w_3 | XT_cfg − XT_meas |.
6. FSO
   • S60D-51: P_rx_drift = P_rx(W) − P_rx(ref); Avail = 1 − P_outage;
   • S60D-52: δ_weather = | γ_atm(W) − γ_atm(ref) |, change in scintillation: σ_{I,eff}^2(W) − σ_{I,eff}^2(ref);
   • S60D-53: delta_form_fso = | P_rx^{cfg} − P_rx^{meas} | + w_σ | σ_{I,eff,cfg}^2 − σ_{I,eff,meas}^2 |.
7. Arrival time & harmonization
   • S60D-61: | T_arr* − t̂_cont | and | T_arr* − T_arr_ref |;
   • S60D-62: combined uncertainty u_c(T_arr*) (GUM/MC) and coverage U = k • u_c (see Appendix E).
8. Switching / queueing & throughput
   • S60D-71: ρ = λ_pkt • E[L] / C;
     lat_total = lat_prop + E[L]/C + lat_sw + lat_q + lat_proc;
   • S60D-72: P_block (Erlang-B/Erlang-C) and P_cont quantiles;
   • S60D-73: T_guard_violation_rate = rate( T_guard < T_guard_min ).
9. Metrology, multipath & security
   • S60D-81: ΔQ = | EVM_pred − EVM_meas | or | BER_pred − BER_meas |;
   • S60D-82: MER = ( ∑_{i>0} | a_i |^2 ) / | a_0 |^2, MP_res (frequency-domain residual ratio);
   • S60D-83: E_balance = | E_rx − ( E_tx − E_loss + E_gain ) | / E_tx; include D_spec, Pol_anom, Timing_anom (Ch. 13).
10. Runtime

• S60D-91: delta_form_rt (online dual-form), latency_p{q}, drop_rate, hit / stale_ratio, ρ_p95;
• S60D-92: panel_freshness = 1_{ update_interval ≤ Δt_panel_max }.

V. Metrology Pipeline M60-D* (Ready → Compute → Aggregate → Decide → Persist)

• Ready: lock RefCond, B / RBW, frame_spec, path/device inventories; select window Δt and quantiles { p50, p95, p99 }.
• Compute: generate per-domain metrics per S60D-*; compute dual-form delta_form_* synchronously; record log↔linear conversions in scale.note.
• Aggregate: compute EWMA_α and quantiles; form drifts drift_* = metric(W) − metric(ref); compute composite drift_score = Σ w_i • norm(drift_i) (weights persisted).
• Decide: apply thresholds from C60-*; attach evidence_uri and strategy cards for failures.
• Persist:
  manifest.packet.metrics.* = { metrics, drift_*, drift_score, windows, method, evidence_uri, contracts.*, signature }.

VI. Contract & Threshold Suggestions C60D-*

• C60D-01 (TwoForm): all delta_form_*_p95 ≤ tol_* (defaults per chapters).
• C60D-11 (Phys/Comp): OSNR_dB_p95 ≥ OSNR_min, CD_res ≤ D_max_res, PMD_res ≤ PMD_max_res, NL_res ≤ NL_max_res.
• C60D-21 (Framing): delta_form_frame_p95 ≤ 0.02 T_sym, σ_J_p95 ≤ J_max.
• C60D-31 (Mod/Spectrum): EVM_p95 ≤ EVM_max, ACLR ≥ ACLR_min, PAPR_p99 ≤ PAPR_max.
• C60D-41 (Label/Isolation): Iso_link ≥ Iso_min_dB, XT_pwr ≤ XT_max_dB, SE ≥ SE_min.
• C60D-51 (FSO): Avail ≥ Avail_min, delta_form_fso_p95 ≤ 1 dB.
• C60D-61 (Tarr): | T_arr* − t̂_cont |_p95 ≤ tol_align.
• C60D-71 (Swrt/Queue): lat_total_p95 ≤ SLA, ρ_p95 < 1, T_guard_violation_rate ≤ rate_max.
• C60D-81 (Meas/MPath/Sec): |ΔQ|_p95 ≤ τ_Q, MER_p95 ≤ MER_max, E_balance_p95 ≤ τ_E, D_spec_p95 ≤ τ_spec.
• C60D-91 (Runtime): hit ≥ 0.8, stale_ratio ≤ 0.02, delta_form_rt_p95 ≤ tol_rt.

VII. Implementation Bindings I60-* (Metrics APIs)

• compute_packet_metrics(manifests, refs, windows) -> metrics, drift_*
• estimate_spectral_response(path, devices) -> { H_link, ε_tilt }
• measure_fr_core(rx_stream, frame_spec) -> { delta_form_frame, σ_J, e_align }
• derive_osnr_evm(iq, osa, B, RBW) -> { OSNR_dB, EVM }
• label_isolation(trace, B_eff) -> { Iso_link, XT_pwr }
• fso_drift(weather_seq, meas_seq) -> { δ天气, P_rx_drift, Avail }
• latency_breakdown(ts_stream) -> { lat_* }
• security_metrics(x, y, plan, B) -> { E_balance, D_spec, Pol_anom, Timing_anom }
• aggregate_runtime_sli(stream) -> { delta_form_rt, latency_p{q}, hit, stale_ratio, ρ }
  Invariants: every return value carries unit / dim; dual-form fields present; RefCond and evidence hashes are traceable.

VIII. Cross-References

• Metric sources: Chapters 2–14; Interfaces: Appendix A; Contracts: Appendix B; Manifests: Appendix C; Uncertainty & guardbands: Appendix E.
• Companion volumes: PathCorrection / TimeBase / Instrument / Sync (two forms, timebase, calibration, replay).

IX. Quality & Risk Control

• Panel keys: OSNR_dB_p95, EVM_p95, lat_total_p95, Avail, Iso_link_min, ρ_p95, hit / stale_ratio, delta_form_*_p95, drift_score.
• Disposition ladder: adjust power/tilt → re-compensate → reshape/limit → re-route → expand guard → bypass/rollback.
• Audit: metric/drift curves, threshold tables & versions, evidence URIs & signature chains, replay scripts.

Summary

• This appendix unifies metrics and drift across all domains of Packets.Light into a computable, comparable, replayable system.
• With dual forms + dimensional compliance + manifestization at its core—and in concert with contracts and uncertainty—it enables an engineering loop of detect → act → verify → rollback end-to-end.